A Less Uncertain Uncertainty Principle

[From Left to Right] Mario Berta^1,2, Matthias Christandl^1,2, Roger Colbeck^1,3,4, Joseph M. Renes⁵, Renato Renner¹ ; Affiliation: ¹Institute for Theoretical Physics, Zurich, Switzerland; ²Faculty of Physics, Ludwig-Maximilians-Universität München, Munich, Germany; ³Perimeter Institute for Theoretical Physics, Waterloo, Canada; ⁴Institute of Theoretical Computer Science, Zurich, Switzerland; ⁵Institute for Applied Physics, Technische Universität Darmstadt, Germany.

A recent paper published in Nature Physics by researchers from Canada, Germany and Switzerland has made Heisenberg’s uncertainty principle — one of the central (and strangest) features in quantum physics — a lot less uncertain in some situations.

One question addressed by the uncertainty principle is whether it is possible to predict both the position and momentum (or other pairs of observables) of a subatomic particle. In its original formulation, the uncertainty principle implies that it is not. However, the paper shows that in the presence of quantum memory, a device capable of reliably storing quantum states, it is possible to predict both precisely. Intensive research efforts are currently focused on producing such a memory and there is hope that one will be available in the near future.

To illustrate the main ideas, the paper outlines an imaginary “uncertainty game” in which two people, Alice and Bob, begin by agreeing on two measurements, R and S, one of which will be performed. Bob then prepares a particle in a quantum state of his choosing. Without telling Alice what he has done, he sends the particle (over a channel) to Alice. Alice performs one of the two measurements (chosen at random) and tells Bob which observable she has measured, though not the measurement’s value. Bob wants to correctly guess the measurement value. If Bob had only a classical memory (e.g. a piece of paper), he would not be able to guess correctly all of the time — this is what Heisenberg’s uncertainty relation implies. However, if Bob is able to entangle the particle he sends with a quantum memory, for any measurement Alice makes on the particle, there is a measurement on Bob’s memory that always gives him the same outcome. His uncertainty has vanished.






The paper provides a new uncertainty relation valid in the presence of a quantum memory. More precisely, it proves a lower bound on the uncertainties of the measurement outcomes which depends on the amount of entanglement between the measured particle and the quantum memory. This had been conjectured by J.C. Boileau and J.M. Renes in 2008 [2] but was unproven until recent work by Berta et al [1].

There are a number of potential applications arising from this work, notably for the burgeoning field of quantum cryptography. Although it was realized in the 1970s that the uncertainty principle could be used as the basis for ultra-secure communications, most quantum cryptographic approaches to date have not made use of it directly. The results may also yield a new method of ‘witnessing’ entanglement. Creating entangled states between particles (such as photons) is notoriously difficult, and once created, the states are easily destroyed by noise in the environment. A more straightforward witnessing method would be of great value to experimentalists striving to generate this precious resource, a necessary step towards developing quantum computers.

References:
[1] Mario Berta, Matthias Christandl, Roger Colbeck, Joseph M. Renes, Renato Renner, "The uncertainty principle in the presence of quantum memory", Nature Physics, published online July 25th, 2010. Abstract.
[2] Joseph M. Renes and Jean-Christian Boileau, "Conjectured Strong Complementary Information Tradeoff", Phys. Rev. Lett. 103, 020402 (2009). Abstract. Arxiv-0806.3984.

[We thank the Perimeter Institute for Theoretical Physics, Waterloo, Canada for materials used in this posting]

Solving the Superconductor Puzzle

Thomas A. Maier [photo courtesy: Oak Ridge National Laboratory]

Superconducting materials, which transmit power resistance-free, are found to perform optimally when high- and low-charge density varies on the nanoscale level, according to research performed at the US Department of Energy's Oak Ridge National Laboratory (ORNL) and Institut für Theoretische Physik, Zürich, Switzerland.

In research toward better understanding the dynamics behind high-temperature superconductivity, the ORNL scientists rewrote computational code for the numerical Hubbard model that previously assumed copper-compound superconducting materials known as cuprates to be homogenous — the same electron density — from atom to atom. The paper is published in Physical Review Letters [1].

Lead author Thomas Maier and colleagues Gonzalo Alvarez, Michael Summers and Thomas Schulthess received the Association for Computing Machinery Gordon Bell Prize two years ago for their high-performance computing application. The application has now been used to examine the nanoscale inhomogeneities in superconductors that had long been noticed but left unexplained.













Researchers have found that atom clusters with inhomogenous stripes of lower density (shown in red) raise critical temperature needed to reach superconductor state [Courtsey: ORNL]

"Cuprates and other chemical compounds used as superconductors require very cold temperatures, nearing absolute zero, to transition from a phase of resistance to no resistance," said Jack Wells, director of the Office of Institutional Planning and a former Computational Materials Sciences group leader.

Liquid nitrogen is used to cool superconductors into phase transition. The colder the conductive material has to get to reach the resistance-free superconductor phase, the less efficient and more costly are superconductor power infrastructures. Such infrastructures include those used on magnetic levitation trains, hospital Magnetic Resonance Imaging, particle accelerators and some city power utilities.

In angle-resolved photoemission experiments and transport studies on a cuprate material that exhibits striped electronic inhomogeneity, scientists for years observed that superconductivity is heavily affected by the nanoscale features and in some respect even optimized.

"The goal following the Gordon Bell Prize was to take that supercomputing application and learn whether these inhomogenous stripes increased or decreased the temperature required to reach transition," Wells said. "By discovering that striping leads to a strong increase in critical temperature, we can now ask the question: is there an optimal inhomogeneity?"

In an ideal world, a material could become superconductive at an easily achieved and maintained low temperature, eliminating much of the accompanying cost of the cooling infrastructure.

"The next step in our progress is a hard problem," Wells said. "But from our lab's point of view, all of the major tools suited for studying this phenomenon — the computational codes we've written, the neutron scattering experiments that allow us to examine nanoscale properties — are available to us here."

Reference
[1] T. A. Maier, G. Alvarez, M. Summers, T. C. Schulthess, "Dynamic Cluster Quantum Monte Carlo Simulations of a Two-Dimensional Hubbard Model with Stripelike Charge-Density-Wave Modulations: Interplay between Inhomogeneities and the Superconducting State", Phys. Rev. Lett. 104, 247001 (2010). Abstract.

[We thank Oak Ridge National Laboratory for materials used in this posting]

Watching An Atom's Electrons Move in Real Time

Stephen Leone [photo courtesy: University of California, Berkeley]

An international team of scientists led by groups from the Max Planck Institute of Quantum Optics (MPQ) in Garching, Germany, and from the U.S. Department of Energy’s Lawrence Berkeley National Laboratory and the University of California at Berkeley has used ultrashort flashes of laser light to directly observe the movement of an atom’s outer electrons for the first time.

Through a process called attosecond absorption spectroscopy, researchers were able to time the oscillations between simultaneously produced quantum states of valence electrons with great precision. These oscillations drive electron motion.

“With a simple system of krypton atoms, we demonstrated, for the first time, that we can measure transient absorption dynamics with attosecond pulses,” says Stephen Leone of Berkeley Lab’s Chemical Sciences Division, who is also a professor of chemistry and physics at UC Berkeley. “This revealed details of a type of electronic motion – coherent superposition – that can control properties in many systems.”

Image 1: A classical diagram of a krypton atom (background) shows its 36 electrons arranged in shells. Researchers have measured oscillations of quantum states (foreground) in the outer orbitals of an ionized krypton atom, oscillations that drive electron motion.

Leone cites recent work by the Graham Fleming group at Berkeley on the crucial role of coherent dynamics in photosynthesis as an example of its importance, noting that “the method developed by our team for exploring coherent dynamics has never before been available to researchers. It’s truly general and can be applied to attosecond electronic dynamics problems in the physics and chemistry of liquids, solids, biological systems, everything.”

The team’s demonstration of attosecond absorption spectroscopy began by first ionizing krypton atoms, removing one or more outer valence electrons with pulses of near-infrared laser light that were typically measured on timescales of a few femtoseconds (a femtosecond is 10^-15 second, a quadrillionth of a second). Then, with far shorter pulses of extreme ultraviolet light on the 100-attosecond timescale (an attosecond is 10^-18 second, a quintillionth of a second), they were able to precisely measure the effects on the valence electron orbitals.

The results of the pioneering measurements performed at MPQ by the Leone and Krausz groups and their colleagues are reported in the August 5 issue of the journal Nature.

Parsing the fine points of valence electron motion

Valence electrons control how atoms bond with other atoms to form molecules or crystal structures, and how these bonds break and reform during chemical reactions. Changes in molecular structures occur on the scale of many femtoseconds and have often been observed with femtosecond spectroscopy, in which both Leone and Krausz are pioneers.

Zhi-Heng Loh of Leone’s group at Berkeley Lab and UC Berkeley worked with Eleftherios Goulielmakis of Krausz’s group to perform the experiments at MPQ. By firing a femtosecond pulse of infrared laser light through a chamber filled with krypton gas, atoms in the path of the beam were ionized by the loss of one to three valence electrons from their outermost shells.

Image 2: Femtosecond-scale pulses were fired to ionize krypton atoms (wide beam). Separately created attosecond-scale pulses (narrow beam) were absorbed by the krypton atoms. Spectroscopy mapped the precise timing of the oscillation between quantum states thus created.

The experimenters separately generated extreme-ultraviolet attosecond pulses (using the technique called “high harmonic generation”) and sent the beam of attosecond probe pulses through the krypton gas on the same path as the near-infrared pump pulses.

By varying the time delay between the pump pulse and the probe pulse, the researchers found that subsequent states of increasing ionization were being produced at regular intervals, which turned out to be approximately equal to the time for a half cycle of the pump pulse. (The pulse is only a few cycles long; the time from crest to crest is a full cycle, and from crest to trough is a half cycle.)

“The femtosecond pulse produces a strong electromagnetic field, and ionization takes place with every half cycle of the pulse,” Leone says. “Therefore little bursts of ions are coming out every half cycle.”

Although expected from theory, these isolated bursts were not resolved in the experiment. The attosecond pulses, however, could precisely measure the production of the ionization, because ionization – the removal of one or more electrons – leaves gaps or “holes,” unfilled orbitals that the ultrashort pulses can probe.

The attosecond pulses do so by exciting electrons from lower energy orbitals to fill the gap in krypton’s outermost orbital – a direct result of the absorption of the transient attosecond pulses by the atoms. After the “long” femtosecond pump pulse liberates an electron from the outermost orbital (designated 4p), the short probe pulse boosts an electron from an inner orbital (designated 3d), leaving behind a hole in that orbital while sensing the dynamics of the outermost orbital.

In singly charged krypton ions, two electronic states are formed. A wave-packet of electronic motion is observed between these two states, indicating that the ionization process forms the two states in what’s known as quantum coherence.

Says Leone, “There is a continual ‘orbital flopping’ between the two states, which interfere with each other. A high degree of interference is called coherence.” Thus when the attosecond probe pulse clocks the outer valence orbitals, it is really clocking the high degree of coherence in the orbital motion caused by ionization.

Image 3: In krypton’s single ionization state, quantum oscillations in the valence shell cycled in a little over six femtoseconds. Attosecond pulses probed the details (black dots), filling the gap in the outer orbital with an electron from an inner orbital, and sensing the changing degrees of coherence between the two quantum states thus formed (below).


Indispensable attosecond pulses

“When the bursts of ions are made quickly enough, with just a few cycles of the ionization pulse, we observe a high degree of coherence,” Leone says. “Theoretically, however, with longer ionization pulses the production of the ions gets out of phase with the period of the electron wave-packet motion, as our work showed.”

So after just a few cycles of the pump pulse, the coherence is washed out. Thus, says Leone, “Without very short, attosecond-scale probe pulses, we could not have measured the degree of coherence that resulted from ionization.”

The physical demonstration of attosecond transient absorption by the combined efforts of the Leone and Krausz groups and their colleagues will, in Leone’s words, “allow us to unravel processes within and among atoms, molecules, and crystals on the electronic timescale” – processes that previously could only be hinted at with studies on the comparatively languorous femtosecond timescale.

Reference
Eleftherios Goulielmakis, Zhi-Heng Loh, Adrian Wirth, Robin Santra, Nina Rohringer, Vladislav Yakovlev, Sergey Zherebtsov, Thomas Pfeifer, Abdallah Azzeer, Matthias Kling, Stephen Leone, and Ferenc Krausz, “Real-time observation of valence electron motion,” Nature, 466, 739-743 (5 August 2010). Abstract.

[This report is written by Paul Preuss of Lawrence Berkeley National Laboratory]

Transition from Superfluid to Mott Insulator

Karina Jiménez-García [photo courtesy: Joint Quantum Institute, Maryland]

Researchers studying a gas of trapped ultracold atoms have identified a set of conditions, never before observed but in excellent agreement with new theoretical predictions, that determine the onset of a critical “phase transition” in atomic arrays used to model the behavior of condensed-matter systems.

The findings provide a novel insight into the way collections of atoms suddenly cease to be a superfluid, which flows without resistance, and switch to a very different state called a “Mott insulator.” That transition and similar phenomena are of central interest to the science of solid-state materials, including superconductors.

“This work shows that the transition can be precisely controlled and confirms that it can be described by only two independent variables,” says lead researcher Karina Jiménez-García, a member of Ian Spielman’s group at the National Institute of Standards and Technology (NIST) and the Joint Quantum Institute (JQI). The group reports its findings in a forthcoming issue of Physical Review Letters [1].

In order to understand the behavior of materials on the atomic and molecular scale, researchers often cannot experiment directly with samples. In many cases, they need model systems – analogous, at microscopic dimensions, to the physical models built by engineers to test the dynamics of a planned structure – that allow them to change one or two experimental parameters at a time while holding the rest constant. That can be prohibitively difficult, if not impossible, in bulk samples of real material.

But in recent years, quantum science has made it possible to create accurate and highly illuminating models of condensed-matter systems by using ensembles of individual atoms which are confined by electrical and magnetic forces into patterns that mimic the fundamental physics of the repeating structural pattern, or “lattice,” of a solid material.

Improving these quantum-mechanical models is an important research area at JQI, and Spielman’s group has been investigating a model for the superfluid-to-Mott insulator (SF-MI) phase transition – the point at which the atoms cease to share the same quantum properties, as if each atom were spread over the entire lattice, and change into a set of individual atoms trapped at specific locations, that do not communicate with one another.

Figure 1

The group’s experimental setup at NIST’s Gaithersburg, MD facility uses a cloud of about 200,000 atoms of rubidium that have been cooled to near absolute zero and confined in a combination of magnetic and optical potentials. In those conditions, a majority of the atoms forms a Bose-Einstein condensate (BEC), an exotic condition in which all the atoms coalesce into exactly the same quantum state.

Then the team loads the BEC – which is about 10 micrometers in diameter, or about one-tenth the width of a human hair – into an “optical lattice” that forms at the intersection of three laser beams placed at right angles to one another [See Figure 1], two horizontal and one vertical. Interference patterns in the beams’ waves cause regularly spaced areas of higher and lower energy; atoms naturally tend to settle into the lowest-energy locations like eggs in an egg carton.

The depth of the lattice wells (the cavities in the egg carton) is adjusted by varying the intensity of the laser beams. [See Figure 2] In a relatively shallow lattice, atoms can easily “tunnel” from one site to another in the condensate superfluid state, whereas deep lattice wells tend to hold each atom in place, producing the non-condensate insulator state. “We can tune the depth of all the wells in the carton by adjusting the intensity of the laser beams which create it,” Jiménez-García explains. “We can go from a flat carton to a carton with very deep wells.”

Figure 2 (click to view hi resolution image)

That general lab arrangement – ultracold trapped atoms suspended in an optical lattice – is the current standard worldwide for experiments on condensed-matter models. But it has a serious problem: The mathematical theory behind the model is predicated on a completely homogenous system, whereas arrays such as the JQI group uses are only homogenous on small spatial scales. Globally, they are inhomogenous because the magnetic trapping potential is not uniform across the width of the trap. As a result, the equations used to calculate expected outcomes do not accurately predict the SF-MI transition, compromising their utility.

Last year, however, an international collaboration of theorists determined [2] that in such configurations, where there were spatially separated SF and MI phases, the quantum state of the system could be fully specified by the relationship between only two variables: the characteristic density of the system (a composite of trapping potential, total number of trapped atoms, tunneling energy, lattice spacing and dimensionality); and the strength of the interactions between neighboring atoms.

Jiménez-García and colleagues in the JQI group set out to see if they could make an experimental system that performed according to the theorists’ specifications.

They set the depth of the vertical lattice beam such that it partitioned the roughly spherical BEC into about 60 two-dimensional, pancake-shaped segments, and then used a method similar to medical MRI scanning to select and analyze just a couple of individual 2D segments at the same time. The inhomogeneity of the originally 3D atomic sample results in the selection of 2D systems with different total number of atoms, ranging from 0 (at the edges of the system) to 4000 atoms (in the center of the system), allowing the researchers to examine a broad range of total atom numbers and lattice depths.

Because the trapping potential was not homogenous across the BEC, the group’s lattices were not completely orthogonal. “What we get instead,” Jiménez-García says, “is an array of egg cartons which have a parabolic curvature. Imagine each egg carton with the overall shape of a bowl, and the whole system as a stack of egg carton bowls.”

To determine the state of the atoms in the 2D slice, the scientists abruptly turn off the trap and let the atoms begin to fly apart. After a few thousandths of a second, they take a picture of the expanding population. If the atoms were deep into the SF state, the images will show a tightly focused bunch. If they were in the MI state, the bunch will have dispersed farther and appear more diffuse. “We detect a sharp peak in the momentum distribution which we associate with the condensate fraction,” Jiménez-García says. “Wider dispersion – that is, less condensate fraction -- would mean more MI.”

After measuring about 1300 different samples, the group was able to determine that the two-variable theory completely described the state of each slice.

References
[1] K. Jimenez-Garcia, R.L. Compton, Y.-J. Lin, W.D. Phillips, J.V. Porto and I.B. Spielman, "Phases of a 2D Bose Gas in an Optical Lattice", accepted for publication in Physical Review Letters. arXiv:1003.1541.
[2] Marcos Rigol, George G. Batrouni, Valery G. Rousseau, Richard T. Scalettar, "State diagrams for harmonically trapped bosons in optical lattices", Phys. Rev. A 79, 053605 (2009). Abstract.