Superposing Photons

Erwan Bimbard


[This is an invited article based on a recently published work by the authors and their collaborators from Canada, France and Germany -- 2Physics.com]






Authors: Erwan Bimbard, Alexander I. Lvovsky
Affiliation:
Institute for Quantum Information Science, University of Calgary, Canada,
Département de Physique, Ecole Normale Supérieure, Paris, France

The ability to generate and manipulate arbitrary quantum states of a particular system is necessary in order to use this system in quantum information technology. Scientists have developed this ability for a variety of physical settings, for example, ion traps [1] or superconducting cavities coupled to a Josephson qubit [2]. However, independently from the way future quantum computers may perform their own calculations, they will have to communicate among each other. There must be a communication medium able to carry quantum information over long distances without too much losses or decoherence. The only medium that satisfies this requirement is light.

The Quantum Information Technology Group at University of Calgary. Other authors of the 'Nature Photonics' paper [7] : Alexander Lvovsky (Leftmost) Andrew MacRae (4th from Left)and Nitin Jain (7th from Left).

Link to the Quantum Information Technology Group >>

The problem is that preparing arbitrary quantum states of photons is notoriously difficult because photons can not stand still while information is being encoded on them. Moreover, they are easily destroyed by any instrument they encounter. So far, for these reasons, only small islands have been explored in the vast ocean of quantum states of travelling light fields. Examples of quantum optical states prepared and analyzed to date include single- and two-photon states [3,4], superpositions of vacuum and single photon [5] and “Schrödinger kittens” [6].

To continue the naval allegory, exploring an ocean requires a map. In our case, the map is provided by photon number states, or Fock states. These states form a basis in the optical Hilbert space: any quantum state of light, however complex, can be written as a superposition of photon number states. If we could find a way of constructing arbitrary Fock state superpositions, we would have resolved our challenge. Unfortunately, such a vision is beyond practical reach, because there is an infinite number of Fock states and their energy is unlimited. It is possible, however, to approach this ideal with small steps.

What we accomplished, and reported in a recent paper in Nature Photonics[7], is extending the accessible part of the optical Hilbert space to the subspace spanned by the first three basis elements. In other words, we engineered and characterized arbitrary superpositions of 0-photon, 1-photon and 2-photon states.

In order to tailor the quantum state of a travelling light pulse without annihilating it, we made use of one of the most basic yet mysterious quantum phenomena: entanglement. We focused blue laser pulses into a nonlinear crystal that can convert a blue photon into an entangled pair of lower energy red photons going along two different paths or “channels”. Then we performed measurements on one of these channels (idler), which prepared the wanted state in the other channel (signal). Such remote state preparation is possible because of the entanglement between the channels: the two of them form a single system described by a global quantum state, so an interaction with one particle will affect the other, even though the two channels can be spatially separated.

To perform the measurement in the trigger channel, we mix, on beam splitters (half-silvered mirrors), the photons emerging from the crystal with those coming through two weak independent laser beams. Two of the beam splitter outputs are directed to ultra-sensitive single photon detectors, and we look for events where both these detectors “clicked” at the same time. We align our optics in such a way that it is impossible to determine whether the photons that trigger the detectors come from the crystal or the independent beams. Accordingly, a coincidence “click” indicates that the number of photons coming to detectors from the crystal could have been 0, 1 or 2. Because the photons in the crystal are always born in pairs, the signal channel will also contain 0, 1, or 2 photons.

A more thorough calculation involving the entangled nature of the optical state produced by the crystal shows that this alternative – 0, 1, or 2 photons in the signal channel – is not simply a probabilistic mixture, but a coherent superposition of these Fock states. By varying the amplitudes and phases of the two independent beams, we can change the probability amplitudes of the three components in the superposition. For example, if we set both amplitudes to zero, the “clicks” can occur only due to the photons from the crystal, and the state of the signal will be a pure two-photon state. If, on the other hand, we make the intensity of the independent beams high, they are likely to generate most of the “clicks”, so the signal will with high probability not contain any photons.

In order to verify that the signal state is what we expect it to be, we measured a large number of samples of this state and analyzed it using a technique known as optical homodyne tomography [8]. This technique allowed us to determine the signal states and compare them with theoretical predictions. By repeating the measurements for several different settings, we were able to show that arbitrary preparation of states within the set studied is indeed achievable for a travelling pulse of light, without destroying it or having to store it.

To summarize, this work enabled us to reach a whole new region of the optical Hilbert space and study the properties of new quantum states of light, at the same time unifying in a single experiment many previously investigated states. More practically, the kind of states produced during this experiment has immediate applications, for example, optimal estimation of the loss parameter in a gaussian bosonic channel [9].

References
[1] A. Ben-Kish, B. DeMarco, V. Meyer, M. Rowe, J. Britton, W. M. Itano, B. M. Jelenković, C. Langer, D. Leibfried, T. Rosenband, and D. J. Wineland, "Experimental Demonstration of a Technique to Generate Arbitrary Quantum Superposition States of a Harmonically Bound Spin-1/2 Particle", Phys. Rev. Lett, 90, 037902 (2003). Abstract.
[2] Max Hofheinz, H. Wang, M. Ansmann, Radoslaw C. Bialczak, Erik Lucero, M. Neeley, A. D. O'Connell, D. Sank, J. Wenner, John M. Martinis & A. N. Cleland, "Synthesizing arbitrary quantum states in a superconducting resonator", Nature, 459, 546 (2009). Abstract.
[3] A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State", Phys. Rev. Lett. 87, 050402 (2001). Abstract.
[4] A. Ourjoumtsev, R. Tualle-Brouri and P. Grangier, "Quantum Homodyne Tomography of a Two-Photon Fock State", Phys. Rev. Lett. 96, 213601 (2006). Abstract.
[5] A. I. Lvovsky and J. Mlynek, "Quantum-Optical Catalysis: Generating Nonclassical States of Light by Means of Linear Optics", Phys. Rev. Lett. 88, 250401 (2002). Abstract.
[6] Alexei Ourjoumtsev, Rosa Tualle-Brouri, Julien Laurat, Philippe Grangier, "Generating Optical Schrödinger Kittens for Quantum Information Processing", Science 312, 83-86 (2006). Abstract.
[7] Erwan Bimbard, Nitin Jain, Andrew MacRae, A. I. Lvovsky, "Quantum-optical state engineering up to the two-photon level", Nature Photonics, Published online: 14 February 2010 doi:10.1038/nphoton.2010.6. Abstract.
[8] A.I. Lvovsky and M.G. Raymer, "Continuous-variable optical quantum-state tomography", Rev. Mod. Phys. 81, 299 - 332 (2009). Abstract.
[9] G. Adesso, F. Dell'Anno, S. De Siena, F. Illuminati, and L. A. M. Souza, "Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states", Phys. Rev. A 79, 040305(R) (2009). Abstract.

World’s Most Precise Clock : NIST Developed Second ‘Quantum Logic Clock’ Based on Aluminum Ion

NIST postdoctoral researcher James Chin-wen Chou with the world’s most precise clock, based on the vibrations of a single aluminum ion. The ion is trapped inside the metal cylinder (center right) [Photo credit: J. Burrus/NIST]

In a paper published in the Feb 17th issue of Physical Review Letters [1], a team of physicists from National Institute of Standards and Technology (NIST) reported the successful development of the world’s most precise clock -- an enhanced version of an experimental atomic clock based on a single aluminum atom [2]. The new clock is more than twice as precise as the previous pacesetter based on a mercury atom [3].

The new aluminum clock would neither gain nor lose one second in about 3.7 billion years, according to measurements reported in Physical Review Letters. The new clock is the second version of NIST’s “quantum logic clock”, so called because it borrows the logical processing used for atoms storing data in experimental quantum computing, another major focus of the same NIST research group.

Background: The Origin of the Name ‘Quantum Logic Clock’

Logic is reasoning that determines an action or result based on which one of different possible options is received as input. In the NIST clock, the input options are two different quantum states, or internal energy levels, of an aluminum ion. Information about this state is transferred to a beryllium ion, which, depending on the input, produces different signals that are easily detected.

NIST scientists use lasers to cool the two ions which are held 4 thousandths of a millimeter apart in an electromagnetic trap. Aluminum is the larger of the two ions, while the beryllium emits light under the conditions of this experiment. Scientists hit the ions with pulses from a “clock laser” within a narrow frequency range. If the laser frequency is at the center of the frequency range, the precise “resonance frequency” of aluminum, this ion jumps to a higher energy level, or 1 in the binary language of computers. Otherwise, the ion remains in the lower energy state, or 0.

If there is no change in the aluminum ion, then another laser pulse causes both ions to begin rocking side to side in unison because of their physical proximity and the interaction of their electrical charges. An additional laser pulse converts this motion into a change in the internal energy level of the beryllium ion. This pulse reverses the direction of the ion’s magnetic “spin,” and the beryllium goes dark, a signal that the aluminum remained in the 0 state.

On the other hand, if the aluminum ion jumps to the higher energy level, then the additional laser pulses fail to stimulate a shared rocking motion and have no effect on the beryllium ion, which keeps emitting light. Scientists detect this light as a signal that the aluminum ion jumped from 0 to 1.

The goal is to tune the clock laser to the exact frequency that prompts the aluminum to jump from 0 to 1. The actual measurement of the ticking of the clock is provided not by the ions but rather by the clock laser’s precisely tuned center frequency, which is measured with a “frequency comb,” a tool for measuring very high optical frequencies, or colors of light.

“This paper is a milestone for atomic clocks” for a number of reasons, says NIST postdoctoral researcher James Chou, who developed most of the improvements.

In addition to demonstrating that aluminum is now a better timekeeper than mercury, the latest results confirm that optical clocks are widening their lead—in some respects—over the NIST-F1 cesium fountain clock, the U.S. civilian time standard, which currently keeps time to within 1 second in about 100 million years.

Because the international definition of the second (in the International System of Units, or SI) is based on the cesium atom, cesium remains the “ruler” for official timekeeping, and no clock can be more accurate than cesium-based standards such as NIST-F1.

The logic clock is based on a single aluminum ion (electrically charged atom) trapped by electric fields and vibrating at ultraviolet light frequencies, which are 100,000 times higher than microwave frequencies used in NIST-F1 and other similar time standards around the world. Optical clocks thus divide time into smaller units, and could someday lead to time standards more than 100 times as accurate as today’s microwave standards. Higher frequency is one of a variety of factors that enables improved precision and accuracy.

The ion trap where the main action takes place in the NIST aluminum ion clock. The aluminum ion and partner magnesium ion sit in the slit running down the center of the device between the electrodes [Photo credit: J. Koelemeij/NIST]

Aluminum is one contender for a future time standard to be selected by the international community. NIST scientists are working on five different types of experimental optical clocks, each based on different atoms and offering its own advantages. NIST’s construction of a second, independent version of the logic clock proves it can be replicated, making it one of the first optical clocks to achieve that distinction. Any future time standard will need to be reproduced in many laboratories.

NIST scientists evaluated the new logic clock by probing the aluminum ion with a laser to measure the exact "resonant" frequency at which the ion jumps to a higher-energy state, carefully accounting for all possible deviations such as those caused by ion motions. No measurement is perfect, so the clock’s precision is determined based on how closely repeated measurements can approach the atom’s exact resonant frequency. The smaller the deviations from the true value of the resonant frequency, the higher the precision of the clock.

Physicists also evaluate the performance of new optical clocks by comparing them to older optical clocks. In this case, NIST scientists compared their two logic clocks by using the resonant laser frequency from one clock to probe the ion in the other clock. Fifty-six separate comparisons were made, each lasting between 15 minutes and 3 hours.

The two logic clocks exhibit virtually identical “tick” rates—differences don’t show up until measurements are extended to 17 decimal places. The agreement between the two aluminum clocks is more than 10 times closer than any previous two-clock comparison, with the lowest measurement uncertainty ever achieved in such an evaluation, according to the paper.

The enhanced logic clock differs from the original version in several ways. Most importantly, it uses a different type of “partner” ion to enable more efficient operations. Aluminum is an exceptionally stable source of clock ticks but its properties are not easily manipulated or detected with lasers. In the new clock, a magnesium ion is used to cool the aluminum and to signal its ticks. The original version of the clock used beryllium, a smaller and lighter ion that is a less efficient match for aluminum.

Clocks have myriad applications. The extreme precision offered by optical clocks is already providing record measurements of possible changes in the fundamental “constants” of nature, a line of inquiry that has important implications for cosmology and tests of the laws of physics, such as Einstein’s theories of special and general relativity. Next-generation clocks might lead to new types of gravity sensors for exploring underground natural resources and fundamental studies of the Earth. Other possible applications may include ultra-precise autonomous navigation, such as landing planes by GPS.

Reference
[1] C.-W. Chou, D.B. Hume, J.C.J. Koelemeij, D.J. Wineland, and T. Rosenband, "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks", Physical Review Letters, 104, 070802 (2010). Abstract.
[2] T. Rosenband, D.B. Hume, P.O. Schmidt, C.W. Chou, A. Brusch, L. Lorini, W.H. Oskay, R.E. Drullinger, T.M. Fortier, J.E. Stalnaker, S.A. Diddams, W.C. Swann, N.R. Newbury, W.M. Itano, D.J. Wineland, and J.C. Bergquist, "Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place", Science, 319, 1808 (2008). Abstract. 2Physics Report.
[3] W.H. Oskay, S.A. Diddams, E.A. Donley, T.M. Fortier, T.P. Heavner, L. Hollberg, W.M. Itano, S.R. Jefferts, M.J. Jensen, K. Kim, F. Levi, T.E. Parker and J.C. Bergquist, "A single-atom optical clock with high accuracy. Physical Review Letters. July 14 (2006) Abstract. 2Physics Report.

[We thank National Institute of Standards and Technology for materials used in this posting]

Single Photons Observed at Seemingly Faster-than-Light Speeds

Paul Lett [Photo courtesy: Joint Quantum Institute, U. Maryland]

Researchers at the Joint Quantum Institute (JQI), a collaboration of the National Institute of Standards and Technology (NIST) and the University of Maryland at College Park, can speed up photons (particles of light) to seemingly faster-than-light speeds through a stack of materials by adding a single, strategically placed layer. This experimental demonstration confirms intriguing quantum-physics predictions that light’s transit time through complex multilayered materials need not depend on thickness, as it does for simple materials such as glass, but rather on the order in which the layers are stacked. This is the first published study [1] of this dependence with single photons.

Strictly speaking, light always achieves its maximum speed in a vacuum, or empty space, and slows down appreciably when it travels through a material substance, such as glass or water. The same is true for light traveling through a stack of dielectric materials, which are electrically insulating and can be used to create highly reflective structures that are often used as optical coatings on mirrors or fiber optics.

In a follow up to earlier experimental measurements [2], the JQI researchers created stacks of approximately 30 dielectric layers, each about 80 nanometers thick, equivalent to about a quarter of a wavelength of the light traveling through it. The layers alternated between high (H) and low (L) refractive index material, which cause light waves to bend or reflect by varying amounts. After a single photon hits the boundary between the H and L layers, it has a chance of being reflected or passing through.

When encountering a stack of 30 layers alternating between L and H, the rare photons that completely penetrate the stack pass through in about 12.84 femtoseconds (fs, quadrillionths of a second). Adding a single low-index layer to the end of this stack disproportionately increased the photon transit time by 3.52 fs to about 16.36 fs. (The transit time through this added layer would be only about 0.58 fs, if it depended only upon the layer’s thickness and refractive index.) On the contrary, adding an extra H layer to a stack of 30 layers alternating between H and L would reduce the transit time to about 5.34 fs, so that individual photons seem to emerge through the 2.6-micron-thick stack at superluminal (faster-than-light) speeds.

What the JQI researchers are seeing can be explained by the wave properties of light. In this experiment, the light begins and ends its existence acting as a particle—a photon. But when one of these photons hits a boundary between the layers of material, it creates waves at each surface, and the traveling light waves interfere with each other just as opposing ocean waves cause a riptide at the beach. With the H and L layers arranged just right, the interfering light waves combine to give rise to transmitted photons that emerge early. No faster than light speed information transfer occurs because, in actuality, it is something of an illusion: only a small proportion of photons make it through the stack, and if all the initial photons were detected, the detectors would record photons over a normal distribution of times.

References
[1] N. Borjemscaia, S.V. Polyakov, P.D. Lett and A. Migdall, "Single-photon propagation through dielectric bandgaps", Optics Express, v 18, p 2279 (2010). Abstract.
[2] N. Rutter, S.V. Polyakov, P. Lett amd A. Migdall, "Photon tunneling through dielectric bandgaps and evanescent gaps", Presented at the American Physical Society March Meeting, New Orleans, La. Session: W14.00010. Abstract. News.

[We thank Joint Quantum Institute at University of Maryland and National Institute of Standards and Technology for materials used in this report]

Simulating the Physics of a Free Dirac Particle

Christian Roos

[This is an invited article based on a recently published work by the author and his collaborators from Austria and Spain -- 2Physics.com]

Author: Christian Roos

Affiliation: Institut für Experimentalphysik, Universität Innsbruck, Austria
and
Institute for Quantum Optics and Quantum Information
Austrian Academy of Sciences

By the mid 1920s physicists had established the dynamics of quantum particles in the non-relativistic limit. The celebrated Schrödinger equation established a framework that allowed tackling a vast range of problems in atomic, molecular and solid state physics. However, the equation is limited to the regime of particles with velocities that are small compared to the speed of light. In 1928, Dirac put forward an equation to describe electrons in a way that successfully reconciles quantum physics with special theory of relativity. The Dirac equation provides a natural explanation of spin as an intrinsic property of the electron. It has not only positive energy solutions but also solutions with negative energies which led to the prediction of anti-matter.

In 1930, at a time when the interpretation of solutions to Dirac equation was still debated, Schrödinger noticed another peculiar feature: the equation admits solutions where the centre-of-mass of a quantum particle exhibits a trembling motion, called Zitterbewegung, in the absence of external forces [1]. This effect is surprising because according to Newton’s first law, a particle that experiences no forces should move in a straight line. In real quantum particles, such as electrons, this trembling motion would have a very small amplitude (10^-13m) and an extremely high frequency (10²¹ Hz). Moreover, it arises only as an interference effect in solutions comprised of positive and negative energy components. Such solutions, which might seem irrelevant, arise, however, in the presence of external fields. For free electrons, this phenomenon does to seem to be experimentally accessible.

It is, however, possible to engineer other quantum systems such that they mimic the physics of the Dirac equation. One such system is an ion held in an ion trap and cooled and manipulated by laser light [2]. How can such a trapped non-relativistic quantum particle simulate the physics of a free Dirac particle? To answer this question, it is helpful to look first at the case of a classical particle held in a harmonic potential. The motion of this particle is described by a circle in phase space. For a particle that is resonantly excited by an external driving force, its phase space trajectory will turn into a helix. In a frame where the phase space coordinates rotate at the resonance frequency of the particle, the helix turns into a straight line which the particle follows with constant velocity, i.e. the particle looks like a free particle in the absence of forces.

The same approach can be followed in the case of a relativistic quantum particle. Using a trapped ion, internal energy levels of the ion can be used for encoding the four spinor components representing the particle’s wave function. The term that couples the particle’s momentum operator and the spinor components in the Dirac equation can be simulated in the trapped-ion case by laser beams coupling the ion’s internal states with its motion. The term representing the ion’s rest energy is simulated by another laser-ion interaction that modifies the internal-state energies. In this way, a perfect match is achieved between the form of the Dirac equation and the Schrödinger equation describing the quantum physics of the trapped ion.

In an experiment reported in the Nature issue of the 7th January [3], this proposal is realized using a single trapped ⁴⁰Ca⁺ held in a linear ion trap (see Fig.1).

Fig.1: Experimental setup. An ion trap set up in a ultra-high vacuum system is used to store a ⁴⁰Ca⁺ ion. The ion is illuminated by laser light that serves to laser-cool, manipulate and detect the particle. (Image Credit: C. Lackner, IQOQI)

The goal of the experiment consists in observing the trembling motion predicted by Schrödinger. For this, the ion’s motion is first laser-cooled to the lowest energy state in which the ion is localized to a space of about 10 nm, the uncertainty in the position being due to the Heisenberg uncertainty relation. Then, for a certain amount of time, a suitable combination of laser beams is switched on to simulate the physics of the Dirac equation. The final step consists in a measurement that detects the change in the ion’s position. These three basic steps take no longer than 20 ms to carry out. They are repeated over and over again in order to measure the ion motion as a function of time. In perfect agreement with Schrödinger’s prediction, we indeed observe a trembling motion which is shown in Fig. 2.

Fig.2: Measured ‘Zitterbewegung’. (a) Average position of the ion as a function of time. The ion motion is composed of a uniform motion on top of which the trembling motion appears. (b) Time evolution of the ion’s wave function. Its two spinor components are shown in red and blue. The trembling motion disappears as soon as the two spinor components are no longer spatially overlapped.

Why can this experiment be called a quantum simulation? In the 1980's Richard Feynman and others proposed a new method for approaching quantum mechanical problems that are too hard to solve on ordinary computers. Their idea was to use a more accessible quantum system to simulate quantum effects of interest. To date, only a few quantum systems can be controlled well enough to act as a quantum simulator. In our experiment, we have performed a quantum simulation of a free Dirac particle using a single trapped ion manipulated with laser light. In this case, the quantum-mechanical state space has no more than 100 dimensions, a size that can be handled perfectly well by any current desktop computer. So the experiment is far from outperforming computers. But the small size of the quantum system is also an advantage because it allows us to compare experiment and theoretical prediction and in this way test the concept of a quantum simulator. The hope is that in the future systems of trapped ions or neutral atoms held in optical lattices might be used to simulate and study quantum phenomena that can no longer be analyzed by computer simulations.

References
[1] “Über die kräftefreie Bewegung in der relativistischen Quantenmechanik”, Sitz. Preuss. Akad. Wiss. Phys.-Math. Kl. 24, 418–428 (1930).
[2] “Robust Dirac equation and quantum relativistic effects in a single trapped ion”, L. Lamata, J. León, T. Schätz, E. Solano. Phys. Rev. Lett. 98, 253005 (2007). Abstract.
[3] “Quantum simulation of the Dirac equation”, R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos, Nature 463, 68 (2010). Abstract.

Creation of ‘Synthetic Magnetic Fields’ for Neutral Atoms

Ian Spielman [photo courtesy: Joint Quantum Institute, University of Maryland]

The current (December 3) issue of the journal 'Nature' carries an article describing the creation of the so-called “synthetic” magnetic fields for ultracold gas atoms, in effect “tricking” neutral atoms into acting as if they are electrically charged particles subjected to a real magnetic field.

This important new capability in ultracold atomic gases is achieved by a team of researchers at the Joint Quantum Institute (JQI), a collaboration of the University of Maryland and the National Institute of Standards and Technology (NIST). The demonstration of this capability not only paves the way for exploring the complex natural phenomena involving charged particles in magnetic fields, but may also contribute to an exotic new form of quantum computing.

As researchers have become increasingly proficient at creating and manipulating gaseous collections of atoms near absolute zero, these ultracold gases have become ideal laboratories for studying the complex behavior of material systems. Unlike usual crystalline materials, they are free of obfuscating properties, such as impurity atoms, that exist in normal solids and liquids.

However, studying the effects of magnetic fields is problematic because the gases are made of neutral atoms and so do not respond to magnetic fields in the same way as charged particles do. So how would you simulate, for example, such important exotic phenomena as the quantum Hall effect, in which electrons can “divide” into quasiparticles carrying only a fraction of the electron’s electric charge?

The answer Ian Spielman and his colleagues came up with is a clever physical trick to make the neutral atoms behave in a way that is mathematically identical to how charged particles move in a magnetic field. A pair of laser beams illuminates an ultracold gas of rubidium atoms already in a collective state known as a Bose-Einstein condensate. The laser light ties the atoms' internal energy to their external (kinetic) energy, modifying the relationship between their energy and momentum. Simultaneously, the researchers expose the atoms to a real magnetic field that varies along a single direction, so that the alteration also varies along that direction.

A pair of laser beams (red arrows) impinges upon an ultracold gas cloud of rubidum atoms (green oval) to create synthetic magnetic fields (labeled Beff). (Inset) The beams, combined with an external magnetic field (not shown) cause the atoms to "feel" a rotational force; the swirling atoms create vortices in the gas [Image courtesy: JQI]

In a strange inversion, the laser-illuminated neutral atoms react to the varying magnetic field in a way that is mathematically equivalent to the way a charged particle responds to a uniform magnetic field. The neutral atoms experience a force in a direction perpendicular to both their direction of motion and the direction of the magnetic field gradient in the trap. By fooling the atoms in this fashion, the researchers created vortices in which the atoms swirl in whirlpool-like motions in the gas clouds. The vortices are the “smoking gun,” Spielman says, for the presence of synthetic magnetic fields.

A harbinger of the synthetic magnetic fields is the formation of vortices (spots). These spots, the number of which increases with increasing synthetic field, mark the points about which atoms swirled with a whirlpool-like motion. The measurement units in each panel indicate the size of the external magnetic field gradient applied to the gas of atoms, with larger external fields producing more vortices. [Image courtesy: JQI]

Previously, other researchers had physically spun gases of ultracold atoms to simulate the effects of magnetic fields, but rotating gases are unstable and tend to lose atoms at the highest rotation rates.

In their next step, the JQI researchers plan to partition a nearly spherical system of 20,000 rubidium atoms into a stack of about 100 two-dimensional “pancakes” and increase their currently observed 12 vortices to about 200 per-pancake. At a one-vortex-per-atom ratio, they could observe the quantum Hall effect and control it in unprecedented ways. In turn, they hope to coax atoms to behave like a class of quasiparticles known as “non-abelian anyons,” a required component of “topological quantum computing,” in which anyons dancing in the gas would perform logical operations based on the laws of quantum mechanics.

Reference
"Synthetic magnetic fields for ultracold neutral atoms"
Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto & I. B. Spielman.
Nature, 462, 628-632 (3 December, 2009). Abstract.

[We thank National Institute of Standards and Technology for materials used in this report]

Quantum Fingerprints of Chaos

Poul Jessen [photo courtesy: College of Optical Sciences, University of Arizona]

In a recent article in the journal Nature, Prof. Poul Jessen and his group in the College of Optical Sciences at the University of Arizona have reported some interesting outcomes of a series of experiments showing clear fingerprints of classical-world chaos in a quantum system designed to mimic a textbook example of chaos known as the "kicked top."

Chaotic behavior is the rule, not the exception, in the world we experience through our senses, the world governed by the laws of classical physics. Even tiny, easily overlooked events can completely change the behavior of a complex system, to the point where there is no apparent order to most natural systems we deal with in everyday life.

The weather is one familiar case, but other well-studied examples can be found in chemical reactions, population dynamics, neural networks and even the stock market. Scientists who study "chaos" - which they define as extreme sensitivity to infinitesimally small tweaks in the initial conditions - have observed this kind of behavior only in the deterministic world described by classical physics.

The University of Arizona team (front row, L to R) Worawarong Rakreungdet, Souma Chaudhury, Brian Anderson and (back, L to R) Aaron Smith, Enrique Montano, Jae Hoon Lee, and Poul Jessen [photo courtesy: College of Optical Sciences, University of Arizona]

Until now, no one has produced experimental evidence that chaos occurs in the quantum world, the world of photons, atoms, molecules and their building blocks. This is a world ruled by uncertainty: An atom is both a particle and a wave, and it's impossible to determine its position and velocity simultaneously.

And that presents a major problem. If the starting point for a quantum particle cannot be precisely known, then there is no way to construct a theory that is sensitive to initial conditions in the way of classical chaos.

Yet quantum mechanics is the most complete theory of the physical world, and therefore should be able to account for all naturally occurring phenomena.

"The problem is that people don't see [classical] chaos in quantum systems," said Poul Jessen. "And we believe quantum mechanics is the fundamental theory, the theory that describes everything, and that we should be able to understand how classical physics follows as a limiting case of quantum physics."

Now, however, Jessen and his group in UA's College of Optical Sciences have performed a series of experiments that show just how classical chaos spills over into the quantum world. They studied the quantum version of a spinning top with this laboratory apparatus.

The quantum version of the top is the "spin" of individual laser-cooled cesium atoms that Jessen's team manipulate with magnetic fields and laser light, using tools and techniques developed over a decade of painstaking laboratory work.

"Think of an atom as a microscopic top that spins on its axis at a constant rate of speed," Jessen said. He and his students repeatedly changed the direction of the axis of spin, in a series of cycles that each consisted of a "kick" and a "twist". Because spinning atoms are tiny magnets, the "kicks" were delivered by a pulsed magnetic field. The "twists" were more challenging, and were achieved by subjecting the atom to an optical-frequency electric field in a precisely tuned laser beam.

They imaged the quantum mechanical state of the atomic spin at the end of each kick-and-twist cycle with a tomographic technique that is conceptually similar to the methods used in medical ultrasound and CAT scans. The end results were pictures and stop-motion movies of the evolving quantum state, showing that it behaves like the equivalent classical system in some significant ways.

One of the most dramatic quantum signatures the team saw in their experiments was directly visible in their images: They saw that the quantum spinning top observes the same boundaries between stability and chaos that characterize the motion of the classical spinning top. That is, both quantum and classical systems were dynamically stable in the same areas, and dynamically erratic outside those areas.

Jessen's experiment revealed a new signature of chaos for the first time. It is related to the uniquely quantum mechanical property known as "entanglement" which is best known from a famous thought experiment proposed by Albert Einstein, in which two light particles, or photons, are emitted with polarizations that are fundamentally undefined but nevertheless perfectly correlated. Later, when the photons have traveled far apart in space, their polarizations are both measured at the same instant in time and found to be completely random but always at right angles to each other.

"It's as though one photon instantly knows the result for the other and adjusts its own polarization accordingly," Jessen said. By itself, Einstein's thought experiment is not directly related to quantum chaos, but the idea of entanglement has proven useful, Jessen added.

Theorists have speculated that the onset of chaos will greatly increase the degree to which different parts of a quantum system become entangled. Jessen took advantage of atomic physics to test this hypothesis in his laboratory experiments. The total spin of a cesium atom is the sum of the spin of its valence electron and the spin of its nucleus, and those spins can become quantum correlated exactly as the photon polarizations in Einstein's example. In Jessen's experiment, the electron and nuclear spins remained unentangled as a result of stable quantum dynamics, but rapidly became entangled if the dynamics were chaotic.

Entanglement is a buzzword in the science community because it is the foundation for quantum cryptography and quantum computing. However, Jessen clarified,"Our work is not directly related to quantum computing and communications. It just shows that this concept of entanglement has tendrils in all sorts of areas of quantum physics because entanglement is actually common as soon as the system gets complicated enough."

Reference
"Quantum signatures of chaos in a kicked top"
S. Chaudhury, A. Smith, B. E. Anderson, S. Ghose & P. S. Jessen,
Nature 461, 768-771 (2009). Abstract.

Colorful Quantum Entanglement

Paulo Nussenzveig (left) and Marcelo Martinelli in their lab, in Brazil.



[This is an invited article based on recently published works of the authors and their collaborators -- 2Physics.com]




Authors: Paulo Nussenzveig and Marcelo Martinelli

Affiliation: Experimental Physics Department, Instituto de Fisica -- USP,
Sao Paulo, Brazil
Link to the Laboratory of Coherent Manipulation of Atoms and Light (LMCAL) >>

Quantum entanglement has just become more colorful. In a recent experiment, three bright beams of light, all of different wavelengths, were entangled [1]. Physicists have been playing around with this mind-boggling concept since 1935, but recently they have acquired enormous control over quantum systems. Entanglement is now viewed as a valuable resource to enable sophisticated information tasks. Indeed, the field of quantum information science relies heavily on entanglement in order to perform quantum computing, teleportation, and communication. A quantum internet is envisaged as a dream to be pursued, with information being conveyed among its nodes via quantum teleportation [2].

Since quantum hardware is still composed of different physical systems, which do not always share common resonances for interaction with light, one faces challenges to exchange quantum information among them. By entangling light beams of different wavelengths, this is no longer a problem. This is what was achieved, with one beam in the visible portion of the spectrum (532.251 nm) and two in the near infrared (1062.102 nm and 1066.915 nm). Research was performed by a group at the University of São Paulo, in Brazil, with participation of two researchers (former students in Brazil) from the new Max Planck Institute for the Science of Light, in Germany.

Entanglement in continuous variable (CV) systems, such as bright beams of light, is generated by means of nonlinear optical processes [3]. The lowest nonlinear order is two, corresponding to processes in which three fields are coupled. Examples are second harmonic generation, sum- and difference-frequency generation, and parametric down-conversion. This latter process is used for the generation of twin photons, a well-known way of producing entangled qubits (e.g. polarization-entangled photons). A nonlinear crystal is pumped by a laser, generating spontaneously emitted pairs of photons. In each fundamental process, a pump photon is annihilated and a pair of lower-frequency photons is created. If the crystal is placed inside a cavity, resonant for all three fields involved, photons are emitted in occupied modes (stimulated emission). The resulting gain can overcome losses and the system oscillates, similarly to a laser. This optical parametric oscillator (OPO), as sketched in Fig. 1, was used by the researchers to generate the three-color entanglement.

Fig. 1 : Sketch of an OPO. A nonlinear optical crystal is placed within two mirrors, forming a cavity. Green incident light is down-converted into twin beams of infrared light.

In order to measure entanglement, researchers had to cool the crystal, to reduce thermal vibrations (phonons), which were responsible for generating unwelcome phase noise in the optical fields. In a tripartite Gaussian state, there is a necessary and sufficient criterion to check for entanglement, due to Simon [4] and extended by Werner and Wolf [5]. By measuring the full covariance matrix of the three-field system, researchers could check that the lowest symplectic eigenvalue under partial transposition with respect to each beam was smaller than one, demonstrating full inseparability (Fig. 2).

Fig. 2: Full tripartite inseparability. Symplectic eigenvalues corresponding to transposition by the pump (green), signal (red) and idler (blue) are lower than one for a broad range of values of the pump power relative to the threshold power (from ref. [1]).

Three-color entangled beams can be useful for communications. Since quantum resources are in general very fragile, the robustness of the entanglement against losses was studied. The researchers observed a subtle quantum property hitherto only witnessed in few-particle systems, called entanglement sudden death [6]. Entanglement was lost for partial attenuation, in certain situations. However, in others the researchers showed that entanglement can be kept alive. The states that were generated have different sensitivity to losses, warranting further investigations.

Entanglement implies a certain “familiarity” among the constituents of a system composed of different parts. The Brazilian experiment generates entanglement among the pump and the twins to which it gives birth: one can think of it as “quantum genealogy”, since it is shown that the twins are entangled to their “mother”.

References
[1] "Three-Color Entanglement", A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, Science Express, DOI: 10.1126/science.1178683 (September 17, 2009). Abstract.
[2] "The Quantum Internet", H. J. Kimble, Nature 453, 1023 (2008). Abstract.
[3] "Quantum information with continuous variables", S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005). Abstract.
[4] "Peres-Horodecki Separability Criterion for Continuous Variable Systems", R. Simon, Phys. Rev. Lett. 84, 2726 (2000). Abstract.
[5] "Bound Entangled Gaussian States", R. F. Werner and M. M. Wolf, Phys. Rev. Lett. 86, 3658 (2001). Abstract.
[6] "Environment-Induced Sudden Death of Entanglement", M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, Science 316, 579 (2007). Abstract.

Shor's Quantum Factoring Algorithm Demonstrated on a Photonic Chip

From L to R: Jeremy L. O'Brien, Alberto Politi, Jonathan C. F. Matthews (photo by: Carmel King)

A primitive quantum computer that uses single particles of light — photons — whizzing through a silicon chip to perform a mathematical calculation has been reported by a team of physicists and engineers in 'Science'. This is a major step forward in the quest to realise a super-powerful quantum computer and the first time such a calculation has been performed on a photonic chip.

The chip takes four photons that carry the input for the calculation, it then implements a quantum programme (Shor’s algorithm) to find the prime factors of 15, and outputs the answer – 3 and 5.

“This task could be done much faster by any school kid,” said PhD student, Alberto Politi, from the University of Bristol who, together with fellow PhD student Jonathan Matthews performed the experiment, “but this is a really important proof-of-principle demonstration.”

Image: The waveguide chip used to perform the algorithm

Finding prime factors may seem like a mathematical abstraction, but it lies at the heart of modern encryption schemes, including those used for secure internet communication. The ability of quantum computers to simulate quantum systems may also prove to be a powerful tool in the development of new materials or pharmaceuticals.

The team from the University of Bristol’s newly established Centre for Nanoscience and Quantum Information have spent several years developing devices where photons propagate in silica waveguides — much like in optical fibres — micro-fabricated on a silicon chip.

“This approach results in miniature, high-performance, and scalable devices,” said Professor Jeremy O’Brien, Director of the Centre for Quantum Photonics, who led the research. “The realisation of a quantum algorithm on a chip is an extremely important step towards an all-optical quantum computer”

“Despite recent advances, the ability to perform even small-scale quantum algorithms has largely been missing,” said Matthews. “For the last few years, researchers at the Centre for Quantum Photonics have been working towards building fully functional quantum circuits on a chip to solve this issue,” added O’Brien.

Past 2Physics article by Jeremy O’Brien and Alberto Politi:
"Silicon Photonics for Optical Quantum Technologies"

The team coupled four photons into and out of the chip using optical fibres. On the chip the photons traveled through silica waveguides that were brought together to form a sequence of quantum logic gates. The output was determined by which waveguides the photons exited the chip in. By detecting the photons at the output of the device they confirmed high-performance operation of the quantum algorithm.

“As well as quantum computing and quantum metrology, ‘on-chip’ photonic quantum circuits could have important applications in quantum communication, since they can be easily integrated with optical fibres to send photons between remote locations,” said Politi.

O’Brien concurred and added: “The really exciting thing about this result is that it will enable the development of large scale quantum circuits for photons. This opens up all kinds of possibilities”.

Reference
"Shor’s Quantum Factoring Algorithm on a Photonic Chip",
Alberto Politi, Jonathan C. F. Matthews, Jeremy L. O'Brien,
Science, Vol. 325. no. 5945, p. 1221 (2009). Abstract.

Operation of an Electrical Amplifier Close to the Quantum Limit

Dartmouth researchers (L to R) Joel Stettenheim, Alex Rimberg, and Weiwei Xue

[This is an invited article based on recent works of the author and his team members -- 2Physics.com]

Author: Alex Rimberg

Affiliation: Dept of Physics and Astronomy, Dartmouth College, USA

Link to Rimberg Group >>

Classically, it is possible to imagine purely passive measurements in which an instrument collects information from some measured system without disturbing it in any way. Measurements of quantum mechanical systems, in contrast, must always be active. A measuring device, no matter how sophisticated, must influence what it is being used to measure; such influence is commonly referred to as backaction. Since the backaction associated with the measurement randomly changes the behavior of the system, the act of measurement must always introduce additional noise. The result is a strict lower bound on the minimal noise an amplifier can introduce for a given sensitivity [1]. This bound on amplifier performance is essentially a manifestation of the uncertainty principle, and implies that there is a well-defined limit on how "good' an amplifier can be.

In a paper recently published in Nature Physics, researchers at Dartmouth College have operated an electrical amplifier that very nearly approaches this quantum limit [2]. The amplifier in question is a superconducting single electron transistor (S-SET), which is well-known to be one of the world's most sensitive detectors of electrical charge. It has been suggested for sometime that the SET can be closely approach the quantum limit [1,3]. However, technical limitations have prevented researchers from approaching the limit by closer than a factor of roughly 20.

To understand the difficulties researchers have faced, it is necessary to have some understanding of how the SET is usually operated as a charge detector. The most sensitive approaches are currently based on the radio-frequency SET technique (RF-SET) [4], in which a radio-frequency wave is reflected off the SET,and the reflected wave is amplified by a secondary classical amplifier. When a charge moves near the SET, its conductance changes -- causing changes in the amplitude of the reflected wave.

The SET is a high-impedance device (about 25 kOhm) while coaxial cable is relatively low impedance (usually 50 Ohm). To make energy transfer from the SET to later classical amplifiers more efficient, an LC matching network is used to impedance match the SET to the coaxial line. In principle, it is possible to make the impedance matching and power transfer nearly perfect. In practice, however, unless great care is taken, the matching network will be imperfect, and some power coming from the SET will be lost. The loss occurs either by having the outgoing power reflected back toward the SET, or lost in the matching network, or both.

Why is this a problem? A quantum-limited amplifier disturbs the system it is measuring, collects all possible information based on the disturbance, and transmits the information, via a chain of classical amplifiers, to the laboratory (the macroscopic world). If any information is lost, either by dissipation or through being buried in the inevitable classical noise of the amplifier chain, the result is to move the measurement away from the quantum limit: the same disturbance occurs but the measurement uncertainty is higher. In the case of the RF-SET, if the matching network is lossy, or impedance matching is imperfect, the result will necessarily be less than quantum limited performance. Worse, in most cases the impedance matching is imperfect enough that noise from the classical amplifier chain dominates the measurement. Note however, that even if the classical amplifiers introduced no noise of their own, imperfect matching necessarily implies a departure from the quantum limit.

In order to optimize the matching network, the Dartmouth researchers developed fully superconducting on-chip matching networks consisting of a superconducting spiral and a parasitic capacitance [5]. The resulting networks are nearly lossless, and due to their very small parasitic capacitance, provide excellent impedance matching at their resonant frequency of 1 GHz. As a result, the power transfer from the S-SET to the subsequent amplifiers is vastly improved, allowing the Dartmouth team to measure the quantum noise of the S-SET near a particularly useful operating point for the first time.

The particular operating point chosen was a feature known as the Double-Josephson-quasiparticle (DJQP) resonance that occurs at bias voltages too small to break Cooper pairs at both junctions. Instead, charge is transferred through the S-SET by means of a complex cycle of Cooper pair and quasiparticle tunneling. A special characteristic of the DJQP cycle is that when operated here, the S-SET has been predicted to have a combination of charge sensitivity and backaction that will allow it to closely approach the quantum limit [3].

By measuring the quantum noise of the S-SET near this feature, it was possible to demonstrate that the S-SET can either emit or absorb energy from the resonator, depending on its precise bias conditions. Classical amplifiers are characterized by a singlenoise parameter because they are equally likely to emit or absorb energy. Quantum mechanically, however, an amplifier may be much more likely to emit than absorb, or vice versa, depending on its precise operating conditions. As a result, two parameters are required to describe the noise. Here, the noise was described by a damping rate that described the S-SET's net tendency to emit or absorb energy from the LC tank circuit, and an effective temperature that describes the degree of asymmetry between emission and absorption. The resulting values of the effective temperature and damping, shown in Fig. 1, constitute the first complete and quantitative characterization of the quantum noise of the S-SET near the DJQP resonance.

Fig. 1: (a) S-SET damping rate and (b) S-SET effective temperature. Together, these give a complete and quantitative description of the S-SET quantum noise.

In addition, the charge sensitivity of the S-SET near the DJQP resonance was shown to be excellent, approaching the world record for RF-SET operation. By estimating the charge fluctuations on the S-SET island, it was possible to determine the backaction the S-SET would likely have on a system such as a quantum dot. Ignoring the noise of the classical amplifiers, the S-SET operated within a factor of 3.6 of the quantum limit, a factor of five improvement over the nearest previous results.

Near quantum limited amplifiers such as this one could have a host of applications in the fields of quantum computation and quantum measurement. They would allow fast, efficient measurement of qubits, might lead the way to direct observation of quantum charge oscillations, and could potentially be used in the preparation of exotic squeezed quantum states.

References
[1] "Amplifying Quantum Signals with the Single-Electron Transistor,"
M. H. Devoret and R. J. Schoelkopf, Nature 406, 1039(2000). Abstract.
[2] "Measurement of Quantum Noise in a Single-Electron Transistor near the Quantum Limit," W. W. Xue, Z. Ji, Feng Pan, Joel Stettenheim, M. P. Blencowe, A. J. Rimberg, Nature Phys. 5, 660(2009). Abstract.
[3] "Resonant Cooper Pair Tunneling: Quantum Noise and Measurement Characteristics,"
A. A. Clerk, S. M. Girvin, A. K. Nguyen and A. D. Stone, Phys. Rev. Lett. 89, 176804 (2002). Abstract.
[4] "The Radio-Frequency Single-Electron Transistor (RF-SET): A Fast and Ultrasensitive Electrometer," R. J. Schoelkopf, P. Wahlgren, A. A. Kozhevnikov, P. Delsing and D. E. Prober, Science, 280, 1238 (1998). Abstract.
[5] "On-Chip Matching Networks for Radio-Frequency Single-Electron Transistors," W. W. Xue, B. Davis, F. Pan, J. Stettenheim, T. J. Gilheart, A. J. Rimberg and Z. Ji, Appl. Phys.Lett. 91, 093511 (2007). Abstract.

NIST Physicists Demonstrate Sustained Quantum Processing in Step Toward Building Quantum Computers

Jonathan Home

In a paper published online in Science Express, physicists at the Time and Frequency Division of the National Institute of Standards and Technology (NIST, Boulder, CO) have demonstrated sustained, reliable information processing operations on electrically charged atoms (ions). Their new device is able to perform a complete set of quantum logic operations without significant loss of information in transit. This path-breaking work overcomes significant hurdles in scaling up ion-trapping technology from small demonstrations to larger quantum processors.

“The significant advance is that we can keep on computing, despite the fact we’re doing a lot of qubit transport,” says first author Jonathan Home.

In the new demonstration, the team of researchers repeatedly performed a combined sequence of five quantum logic operations and 10 transport operations while reliably maintaining the 0s and 1s of the binary data stored in the ions, which serve as quantum bits (qubits) for a hypothetical quantum computer, and retaining the ability to subsequently manipulate this information. Previously, scientists at NIST and elsewhere have been unable to coax any qubit technology into performing a complete set of quantum logic operations while transporting information without disturbances degrading the later processes.

[Image Credit: J. Jost, NIST] NIST team demonstrated sustained, reliable quantum information processing in the ion trap at the left center of this photograph, improving prospects for building a practical quantum computer. The ions are trapped inside the dark slit (3.5 mm long and 200 micron wide) between the gold-covered alumina wafers. By changing the voltages applied to each of the gold electrodes, scientists can move the ions between the six zones of the trap.

The NIST group performed some of the earliest experiments on quantum information processing and has previously demonstrated many basic components needed for computing with trapped ions. The new research combines previous advances with two crucial solutions to previously chronic vulnerabilities: cooling of ions after transport so their fragile quantum properties can be used for subsequent logic operations and storing data values in special states of ions that are resistant to unwanted alterations by stray magnetic fields.

As a result, the NIST researchers have now demonstrated on a small scale all the generally recognized requirements for a large-scale ion-based quantum processor. Previously they could perform all of the following processes a few at a time, but now they can perform all of them together and repeatedly: (1) “initialize” qubits to the desired starting state (0 or 1), (2) store qubit data in ions, (3) perform logic operations on one or two qubits, (4) transfer information between different locations in the processor, and (5) read out qubit results individually (0 or 1).

Through its use of ions, the experiment showcases one promising architecture for a quantum computer, a potentially powerful machine that theoretically could solve some problems that are currently intractable, such as breaking today’s most widely used encryption codes. Relying on the unusual rules of the submicroscopic quantum world, qubits can act as 0s and 1s simultaneously, unlike ordinary digital bits, which hold only one value at any given time. Quantum computers also derive their power from the fact that qubits can be “entangled,” so their properties are linked, even at a distance. Ions are one of a number of different types of quantum systems under investigation around the world for use as qubits in a quantum computer. There is no general agreement on which system will turn out to be the best.

These experiments stored the qubits in two beryllium ions held in a trap with six distinct zones. Electric fields are used to move the ions from one zone to another in the trap, and ultraviolet laser pulses of specific frequencies and duration are used to manipulate the ions’ energy states. The scientists demonstrated repeated rounds of a sequence of logic operations (four single-qubit operations and a two-qubit operation) on the ions and found that operational error rates did not increase as they progressed through the series, despite transporting qubits across macroscopic distances (960 micrometers, or almost a millimeter) while carrying out the operations.

The researchers applied two key innovations to quantum-information processing. First, they used two partner magnesium ions as “refrigerants” for cooling the beryllium ions after transporting them, thereby allowing logic operations to continue without any additional errors due to heating incurred during transport. The strong electric forces between the ions enabled the laser-cooled magnesium to cool down the beryllium ions, and thereby remove heat associated with their motion, without disturbing the stored quantum information. The new experiment is the first to apply this “sympathetic cooling” in preparation for successful two-qubit logic operations.

The other significant innovation was the use of three different pairs of energy states within the beryllium ions to hold information during different processing steps. This allowed information to be held in ion states that were not altered by magnetic field fluctuations during ion storage and transport, eliminating another source of processing errors. Information was transferred to different energy levels in the beryllium ions for performing logic operations or reading out their data values.

The experiment began with two qubits held in separate zones of the ion trap, so they could be manipulated individually to initialize their states, perform single-qubit logic operations, and read out results. The ions were then combined in a single trap zone for a two-qubit logic operation and again separated and transported to different trap regions for subsequent single-qubit logic operations. To evaluate the effectiveness of the processes, the scientists performed the experiment 3,150 times for each of 16 different starting states. The experimental results for one and two applications of the sequence of operations were then compared to each other, as well as to a theoretical model of perfect results.

The NIST quantum processor worked with an accuracy of 94%, averaged over all iterations of the experiment. In addition, the error rate was the same for each of two consecutive repeats of the logical sequence, demonstrating that the operations are insulated from errors that might have been introduced by ion transport. The error rate of 6 percent is not yet close to the 0.01% threshold identified by experts for fault-tolerant quantum computing, Home notes. Reducing the error rate is a focus of current NIST research. Another issue in scaling up the technology to build a practical computer will be controlling ions in large, complex arrays of traps—work also being pursued by the group.

There are also more mundane challenges: The researchers successfully performed five rounds of the logic and transport sequence (a total of 25 logic operations plus 4 preparation and analysis steps), but an attempt to continue to a sixth round crashed the conventional computer used to control the lasers and ions of the quantum processor. Nonetheless, the new demonstration moves ion-trap technology significantly forward on the path to a large quantum processor.

Reference
J.P. Home, D. Hanneke, J.D. Jost, J.M. Amini, D. Leibfried and D.J. Wineland. "Complete methods set for scalable ion trap quantum information processing". Science Express (Published Online August 6, 2009). Abstract.

[We thank NIST for materials used in this posting]

Walking in the Quantum World

Michal Karski, Artur Widera, and Dieter Meschede (Left to Right)

[This is an invited article based on recent works of the authors -- 2Physics.com]

Authors: Artur Widera, Michal Karski and Dieter Meschede

Affiliation: Institut für Angewandte Physik der Universität Bonn, Germany

While the random motion of classical particles is well understood and such random walks have found their way into most fields of modern science, quantum particles are expected to behave differently. The intriguing new properties of these quantum walks may lead to novel applications in quantum information science as quantum search algorithms, for example, or yield insight into the transition from the classical to the quantum regime. A quantum walk in position space has recently been observed with single Caesium (Cs) atoms by fluorescence microscopy [1].

Imagine a walker, e.g. a particle, which can move stepwise on a line. In each time step, let the walker now move randomly to the right or to the left, just as the diffusive Brownian motion of a particle. The probability of finding the particle at a certain position is given by a binomial distribution, with high probability at the initial position and a width that scales with the square-root of the number of steps taken. This well known scaling serves as the basis for numerous models in modern science, for example to estimate the speed of searching algorithms.

In the quantum world, two effects change the particle’s motion drastically: First, quantum particles can be in so-called coherent superpositions, for example, of moving to the left and to the right. This sounds weird, but atoms in coherent superpositions are routinely used, for instance, in atomic clocks where the atoms are in a superposition of two spin states. As a consequence of these coherent superpositions, the quantum particle is delocalized over two lattice sites as it moves simultaneously to the left and to the right. If this delocalization is successively repeated for more and more steps, the particle delocalizes over more and more sites of the line. At certain positions, two parts of the delocalized atom can be re-combined at a common site. Here, the second quantum effect becomes important:
Quantum mechanical objects are described by wave functions and as such they can interfere. Depending on their respective path, they can amplify or extinguish each other. This leads to a drastically changed probability distribution of finding a particle at a certain position. In particular, for a quantum walk it is unlikely to find the particle at the initial position. Its distribution rather shows pronounced peaks with large probability at the outermost edges. The width of the resulting distribution scales linearly with the number of steps. This ballistic scaling is envisioned to speed up search algorithms in quantum search devices or quantum computers.

Figure 1: (a) A single atom is trapped at an initial site of an optical lattice and prepared in a coherent superposition of two states, red and blue. (b) The two states are selectively shifted into opposite directions along the lattice, delocalizing the atom (c) over two sites. (d) After another step of coherent superposition and state-dependent shifting, two parts of the atomic wave function are re-combined, giving rise to matter wave interference.

Experimentally, we realized a quantum walk using single Cs atoms. In an ultra-high vacuum, the atoms were cooled by laser light to approximately 10 µK and then trapped in a so-called optical lattice. This is generated by two counter propagating laser beams forming a standing wave which provides a periodic intensity pattern in space. The Cs atoms are trapped in the intensity maxima of this standing wave. To create coherent superpositions, we used microwave radiation which allows us manipulating the internal states of the atom, similar to those used in atomic clocks. The superposition created is then transferred to position space by using the fact that the optical lattice can be state-selectively moved [2].

This means one of the two internal states is moved to the left, the other to the right. Experimentally this is realized by controlling the polarization of the counter propagating laser beams. After a shifting step, each part of the wave function is again brought into a coherent superposition before a next shifting step and so forth. Finally, after a certain number of steps the system is illuminated and imaged onto a CCD camera [3]. Due to the measurement, the delocalized wave function collapses to one position where the Cs atom is detected. To reconstruct the distribution, hundreds of identical measurements were performed.

Figure 2: Reconstructed wave function of a single atom in the optical lattice. (a) The atom is localized at a lattice site. (b) The atom has performed a 24 step random walk. (c) The atom has performed a 24 step quantum walk.

From the measurements we find that a particle performing a quantum walk shows the expected linear spreading. If the coherence of the process is intentionally destroyed, the classical random walk behaviour is recovered. Our system shows the quantum regime for approximately ten steps of the walk, where the particle is delocalized over more than twenty lattice sites. Then, imperfections, noise and uncontrolled interaction with the environment turns the quantum walk gradually into a random walk.

The quantum walk not only illustrates the mind-boggling laws of quantum mechanics; it might serve as a first step towards the development of novel search algorithms exploiting the properties of quantum mechanics and as a precursor for quantum information processing devices, such as quantum cellular automata [4-6]. Moreover, it can yield deeper insight into the transition from the microscopic quantum world to our every-day classical world.

References
[1] M. Karski, L. Förster, J. Choi, A. Steffen, W. Alt, D. Meschede, and A. Widera, "Quantum Walk in Position Space with Single Optically Trapped Atoms", Science 325, 174 (2009). Abstract.
[2] O. Mandel, M. Greiner, A. Widera, T. Rom, T.W. Hänsch, and I. Bloch, "Coherent transport of neutral atoms in spin-dependent optical lattice potentials", Phys. Rev. Lett. 91, 010407 (2003). Abstract.
[3] M. Karski, L. Förster, J. Choi, W. Alt, A. Widera, and D. Meschede, "Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging", Phys. Rev. Lett. 102, 053001 (2009). Abstract.
[4] R. Raussendorf, "Quantum cellular automaton for universal quantum computation", Phys. Rev. A 72, 022301 (2005). Abstract.
[5] D. J. Shepherd, T. Franz, and R. F. Werner, "Universally Programmable Quantum Cellular Automaton", Phys. Rev. Lett. 97, 020502 (2006). Abstract.
[6] K. G. H. Vollbrecht and J. I. Cirac, "Reversible universal quantum computation within translation-invariant systems", Phys. Rev. A 73, 012324 (2006). Abstract.

Topological Insulators : A New State of Quantum Matter

M. Zahid Hasan

[This is an invited article based on a series of recent works by the author and his collaborators -- 2Physics.com]

Author: M. Zahid Hasan

Affiliation: Joseph Henry Laboratories of Physics, Department of Physics,
Princeton University, USA

Most quantum states of condensed-matter systems or the fundamental forces are categorized by spontaneously broken symmetries. The remarkable discovery of quantum Hall effects (1980s) revealed that there exists an organizational principle of matter based not on the broken symmetry but only on the topological distinctions in the presence of time-reversal symmetry breaking [1,2]. In the past few years, theoretical developments suggest that new classes of topological states of quantum matter might exist in nature [3,4,5]. Such states are purely topological in nature in the sense that they do not break time-reversal symmetry, and hence can be realized without any applied magnetic field : "Quantum Hall-like effects without magnetic field".

Research Team at Princeton University: [L to R] David Hsieh, Dong Qian, L. Andrew Wray, YuQi Xia

This exotic phase of matter is a subject of intense research because it is predicted to give rise to dissipationless (energy saving) spin currents, quantum entanglements and novel macroscopic behavior that obeys axionic electrodynamics rather than Maxwell's equations [6]. Unlike ordinary quantum phases of matter such as superconductors, magnets or superfluids, topological insulators are not described by a local order parameter associated with a spontaneously broken symmetry but rather by a quantum entanglement of its wave function, dubbed topological order. In a topological insulator this quantum entanglement survives over the macroscopic dimensions of the crystal and leads to surface states that have unusual spin textures.

Topologically ordered phases of matter are extremely rare and are experimentally challenging to identify. The only known example was the quantum Hall effect discovered in the 1980s by von Klitzing (Nobel Prize 1985). It was identified by measuring a quantized magneto-transport in a two-dimensional electron system under a large external magnetic field at very low temperatures, which is characterized by robust conducting states localized along the one-dimensional edges of the sample. Two-dimensional topological insulators, on the other hand, are predicted to exhibit similar edge states even in the absence of a magnetic field because spin-orbit coupling can simulate its effect (Fig.1A) due to the relativistic terms added in a band insulator's Hamiltonian.

Remarkably, three-dimensional topological insulators, an entirely new state of matter with no charge quantum Hall analogue, are also postulated to exist. And its topological order or exotic quantum entanglement is predicted to give rise to unusual conducting two-dimensional surface states (Fig.1B) that have novel spin-selective energy-momentum dispersion relations. Utilizing state-of-the-art angle-resolved photoemission spectroscopy, an international collaboration led by scientists from Princeton University have studied the electronic structure of several bismuth based spin-orbit materials [7,8,9]. By systematic tuning of the incident photon energy, it was possible to isolate surface quantum states from the bulk states, which confirmed that these materials realized a three-dimensional topological insulator phase.

Figure 1. (A) Schematic of the 1D edge states in a 2D topological insulator. The red and blue curves represent the edge current with opposite spin character. (B) Schematic of the 2D surface states in a 3D topological insulator. (C) Most elemental topological Insulators exhibit odd number of Dirac cones on their surface unlike the even numbers observed in graphene. Topological insulator Dirac cones are spin polarized where as Dirac cones in graphene are not.

The remarkable property of the surface states of a 3D topological insulator is that its Fermi surface supports a geometrical quantum entanglement phase, which occurs when the spin-polarized Fermi surface encloses the Kramers' points and on the surface Brillouin zone an odd number of times in total (Fig.2B). ARPES intensity map of the (111) surface states of bulk insulating Bi1-xSbx (Fig.2A) shows that a single Fermi surface encloses . However, determination of the degeneracy of the additional Fermi surface around requires a detailed study of its energy-momentum dispersion. ARPES spectra along the - direction (Fig.2C) reveal that the Fermi surface enclosing is actually composed of two bands, therefore two Fermi surfaces enclose , leading to a total of seven and Fermi surface enclosures.

Figure 2. (A) ARPES surface state (SS) Fermi surface of insulating Bi1-xSbx showing spin polarization directions as indicated by red and blue arrows. (B) Schematic of the SS Fermi surface of a 3D topological insulator. (C) ARPES energy-momentum dispersion of the surface states. The shaded areas denote the bulk bands while the dashed white lines are guides to the eye for surface state dispersions. (D) A single Dirac cone is observed in Bi2Te3.

These results constitute the first direct experimental evidence of a topological insulator in nature which is fully quantum entangled. The observed spin-texture in BiSb is consistent with a magnetic monopole image field beneath the surface. It shows that spin-orbit materials are a new family in which exotic topological order quantum phenomena, such as dissipationless spin currents and axion-like electrodynamics, may be found without the need for an external magnetic field. The results presented in this study also demonstrate a general measurement algorithm of identifying and characterizing topological insulator materials for future research which can be utilized to discover, observe and study other forms of topological order and quantum entanglements in nature. A detailed study of topological order and quantum entanglement can potentially pave the way for fault-tolerant (topological) quantum computing [10].

Figure 3: A new type of quantum matter called a topological insulator contains only half an electron pair (represented by just one Dirac cone in schematic crystal structure at top left), which is observed in the form of a single ring (red) in the center of the electron-map (top right) with electron spin in only one direction. This highly unusual observation shows that if an electron is tagged "red" and then undergoes a full 360-degree revolution about the ring, it does not recover its initial face as an ordinary everyday object would, but instead acquires a different color "blue" (represented by the changing color of the arrows around the ring). This new quantum effect can be the basis for the realization of a rare quantum phase that had been a long-sought key ingredient for developing quantum computers that can be highly fault-tolerant.

References:
[1] K. von Klitzing, G. Dorda, M. Pepper, "New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance", Phys. Rev. Lett. 45, 494-497 (1980). Abstract.
[2] D.C. Tsui, H. Stormer, A.C. Gossard, "Two-dimensional magnetotransport in the extreme quantum limit", Phys. Rev. Lett. 48, 1559-1562 (1982). Abstract.
[3] L. Fu, C. L. Kane and E. J. Mele, "Topological insulators in three dimensions", Physical Review Letters 98, 106803 (2007). Abstract.
[4] J. E. Moore and L. Balents, "Topological invariants of time-reversal-invariant band structures", Physical Review B 75, 121306(R) (2007). Abstract.
[5] S.-C. Zhang, "Topological states of quantum matter", Physics 1, 6 (2008). Abstract.
[6] M. Franz, "High energy physics in a new guise", Physics 1, 36 (2008). Abstract.
[7] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava and M. Z. Hasan, "A topological Dirac insulator in a quantum spin Hall phase", Nature 452, 970 (2008). Abstract.
[8] Y. Xia, D. Qian, L. Wray, D. Hsieh, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava and M. Z. Hasan, "Observation of a large-gap topological insulator class with single surface Dirac cone”, Nature Physics 5, 398 (2009). Abstract.
[9] D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava and M. Z. Hasan, "Observation of Unconventional Quantum Spin Textures in Topological Insulators", Science 323, 919 (2009). Abstract.
[10] A. Akhmerov, J. Nilsson, C. Beenakker, “Electrically detected interferometry of Majorana fermions in a topological insulator”, Phys. Rev. Lett. 102, 216404 (2009). Abstract.