A Light Transistor Based on Photons and Phonons

Tobias J. Kippenberg

Researchers at the Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland and the Max Planck Institute of Quantum Optics (MPQ), Germany discover a novel way to switch light all-optically on a chip.

The ability to control the propagation of light is at the technological heart of today’s telecommunication society. Researchers in the Laboratory of Photonics and Quantum Measurement led by Prof. Tobias J. Kippenberg (now EPFL) have discovered a novel principle to accomplish this, which is based on the interaction of light (photons) with mechanical vibrations (phonons). As they report in a recent publication [1], this scheme allows to control the transmission of a light beam past a chip-based optical micro-resonator directly by a second, stronger light beam. The new device could have numerous applications in telecommunication and quantum information technologies.

So far, this effect has only been observed in the interaction of laser light with atomic vapours, based on an effect referred to as “electromagnetically induced transparency” (EIT). EIT has been used to manipulate light propagation at an impressive level: slowing of light pulses and even full storage has been achieved. However, EIT is restricted to light of wavelengths matching the natural resonances of atoms. Also, these technologies are hardly compatible with chip-scale processing.

The novel principle, discovered by a team of scientists including Dr. Albert Schliesser and Dr. Samuel Deléglise and doctoral students Stefan Weis and Rémi Rivière, is based on optomechanical coupling of photons to mechanical oscillations inside an optical micro-resonator. These optomechanical devices are fabricated using standard nanofabrication methods – drawing on the techniques used in semiconductor integrated circuit processing available in the cleanroom of EPFL. They can both trap light in orbits and act, at the same time, as mechanical oscillators, possessing well-defined mechanical vibrational frequencies just like a tuning fork.

If light is coupled into the resonator, the photons exert a force: radiation pressure. While this force has been used for decades to trap and cool atoms, it is only in the last five years that researchers could harness it to control mechanical vibrations at the micro- and nanoscale. This has led to a new research field: cavity optomechanics, which unifies photonics and micro- and nanomechanics. The usually small radiation pressure force is greatly enhanced within an optical microresonator,and can therefore deform the cavity, coupling the light to the mechanical vibrations. For the optomechanical control of light propagation, a second, “control” laser can be coupled to the resonator in addition to the “signal” laser. In the presence of the control laser, the beating of the two lasers causes the mechanical oscillator to vibrate – which in turn prevents the signal light to enter the resonator by an optomechanical interference effect, leading eventually to a transparency window for the signal beam.

For a long time the effect remained elusive, “We have known for more than two years that the effect existed,” says Dr. Schliesser, who theoretically predicted the effect early on. “Once we knew where to look it was right there,” says Stefan Weis, one of the lead authors of the paper. In the subsequent measurements, “the agreement of theory and experiment is really striking”, comments Dr. Deléglise.

In contrast to atoms, this novel form of induced transparency does not rely on naturally occurring resonances and could therefore also be applied to previously inaccessible wavelength regions such as the technologically important telecommunication window (near-infrared). Optomechanical systems allow virtually unlimited design freedom using wafer-scale nano- and microfabrication techniques. Furthermore, already a single optomechanical element can achieve unity contrast, which in the atomic case normally not is possible.

The novel effect, which the researchers have termed “OMIT” (optomechanically induced transparency) to emphasize the close relation to EIT, may indeed provide entirely new functionality to photonics. Future developments based on OMIT could enable the conversion of a stream of photons into mechanical excitations (phonons). Such conversion of radio frequency signals into mechanical vibrations is used in cell-phone receivers today for narrow-band filtering, a principle that could potentially be applied to optical signals as well.

Figure 1: False-colour scanning electron micrograph of the microresonator used in the study of OMIT. The red top part is a silica toroid; it is supported by a silicon pillar (gray) on a semiconductor chip. The silica toroid serves both, as an excellent optical resonator for photons, and it supports mechanical vibrations (phonons). The mutual coupling of photons and phonons can be harnessed to control the propagation of light all-optically.

Furthermore, using OMIT, novel optical buffers could be realized that allow storing optical information for up to several seconds. Finally, with research groups all over the world reaching for control of optomechanical systems at the quantum level, the switchable coupling demonstrated in this work could serve as an important interface in hybrid quantum systems.

Figure 2: Principle of optomechanically induced transparency (OMIT). a) The signal laser (red beam), incident on the cavity, gets coupled into the resonator, and gets dissipated there. No light is returned from the system. b) In the additional presence of a control laser (green beam), the radiation pressure of the two beams drives the boundary of the cavity into resonant oscillations, preventing most of the signal beam to enter the cavity by an interference effect. In this case, the signal beam is returned by the optomechanical system.

Reference
[1] S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, T.J. Kippenberg, "Optomechanically induced transparency", Science, Vol.330, pp.1520-1523 (Dec 10, 2010). Abstract.

Quantum Walks of Correlated Photons in Integrated Waveguide Arrays

Alberto Peruzzo

[This is an invited article based on a recently published work by the authors -- 2Physics.com]

Authors: Alberto Peruzzo and Jeremy L. O’Brien

Affiliation: Centre for Quantum Photonics, H. H. Wills Physics Laboratory and Dept of Electrical & Electronic Engineering, University of Bristol, UK

Since their initial development for studying the random motion of microscopic particles (such as those suspended in a fluid), random walks have been a successful model for random processes applied in many fields, from computer science to economics. Such processes are random in the sense that at a particular time the choice for a particle to make a particular step is probabilistic and decided by flipping a coin.

Past 2Physics articles based on works of this group:
Sep 20, 2009: "Shor's Quantum Factoring Algorithm Demonstrated on a Photonic Chip"
May 2, 2008: "Silicon Photonics for Optical Quantum Technologies"

In the quantum analogue – the quantum walk[1] – the walker is, at a given time, in a superposition of the possible states and different paths can interfere, exhibiting ballistic propagation with faster dynamics compared to the slow diffusion of classical random walks, prompting applications in quantum computer science and quantum communication. Indeed quantum walks have been shown to be universal for quantum computing, enable direct simulation of important physical, chemical and biological systems, and the possibility to study very large entangled states of several particles, with potential to investigate the existence of quantum- classical boundaries.

The first application of quantum walks was search algorithms on graphs (vertices connected by edges) and is more efficient than the classical search. Finding an element in a collection of N vertices using a quantum walk requires √N steps while the classical algorithm takes N steps to check all the vertices.

Quantum walks come in two types, the discrete time quantum walk (DTQW) and the continuous time quantum walk (CTQW). In a DTQW the step direction is specified by a coin and a shift operator, which are applied repeatedly, similarly to the classical random walk, but with the difference that now the coin flip is replaced by a quantum coin operation defining the superposition of the directions the step undertakes. The CTQW describes tunnelling of quantum particles through arrayed potential wells.

The theory of quantum walks have been extensively studied but only few experimental demonstration of several steps of single particle quantum walks with atoms, trapped ions, nuclear magnetic resonance and photons have been carried out so far.

Quantum walks are based on wave interference and require a stable environment to reduce the noise (decoherence) that would otherwise destroy the interference. Interferometric stability and miniaturization using phonics waveguide circuits have been shown to be a promising approach for quantum optics experiments, silica-on-silicon waveguides have been used to demonstrate high fidelity quantum information components [2, 3, 4] and a small scale quantum algorithm for prime number factorization [5].

We’ve implemented CTQW of photons designing periodic waveguide arrays in integrated photonic circuits that enable the injection of single photons and the coupling to single photon detectors at their output. The chips were fabricated in the high refractive index contrast material silicon oxynitride, enabling to quickly stop the coupling between neighbour waveguides so that high level of control over the propagation was possible.

Integrated quantum photonic circuit used to implement a continuous time quantum walk of two correlated photons.

In contrast to all previous demonstrations — which were restricted to single particle quantum walks that have exact classical counterparts — we have demonstrated the quantum walk of two identical photons spatially correlated within arrayed waveguide, observing uniquely quantum mechanical behaviour in the two-photon correlations at the outputs of this array [6]. Pairs of correlated photons were generated with a standard type I spontaneous parametric down-conversion process, a nonlinear process where a 402nm wavelength CW laser pumps a χ² nonlinear bismuth borate crystal generating pairs of photons at 804nm wavelength in conservation of energy and momentum. The correlated photons were coupled to the waveguide using fibre arrays and the correlations at the output were recorded by measuring two photon coincide events with a detection system of 12 avalanche single photons detectors and 3 programmable counting boards. The measured correlations fit with high similarity to our simulations.

Artist’s impression of the two-photon quantum walk.
Credit: Image by Proctor & Stevenson

We’ve shown that the results strongly depend on the input state and these correlations violate classical limits by 76 standard deviation, proving that such phenomena cannot be described using classical theory. This generalized form of quantum interference is similar to the Hong-Ou-Mandel dip effect in an optical beam splitter but in our case on a 21 mode system. Bunching of correlated photons reduces the probability of detecting two photons at the opposite sides of the array while enhancing the case of two particles at the same side.

Such two particle quantum walks have already been identified as a powerful computational tool for solving important problems such as graph isomorphism, and provide a direct route to powerful quantum simulations. Implementing new algorithms based on quantum walks will require integration of the single photon sources and detectors. These have already been showed to be compatible with integration, reducing coupling losses and considerably improving the overall performances. Reconfigurability and feedback will provide further necessary tools enabling to perform more challenging and interesting tasks.

Random walk is an extremely successful tool, employed in many scientific fields and their quantum analogues promise to be similarly powerful.

References:
[1] Y. Aharonov, L. Davidovich, N. Zagury, "Quantum Random Walks", Phys. Rev. A 48, 1687 (1993). doi:10.1103/PhysRevA.48.1687
[2] A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, J. L. O'Brien, "Silica-on-silicon waveguide quantum circuits", Science 320, pp. 646-649 (2008). doi:10.1126/science.1155441
[3] J. C. F. Matthews, A. Politi, A. Stefanov, J. L. O'Brien, "Manipulation of multiphoton entanglement in waveguide quantum circuits", Nature Photonics, 3, pp. 346-350 (2009). doi:10.1038/nphoton.2009.93
[4] A. Laing, A. Peruzzo, A. Politi, M. Rodas Verde, M. Halder, T. C. Ralph, M. G. Thompson, J. L. O'Brien, "High-fidelity operation of quantum photonic circuits", Quant. Phys., e-prints, arXiv:1004.0326v2.
[5] A. Politi, J. C. F. Matthews, J. L. O'Brien, "Shor's quantum factoring algorithm on a photonic chip", Science 325, no. 5945, pp. 1221, 2009. doi:10.1126/science.1173731.
[6] A. Peruzzo, M. Lobino, J.C.F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. O’Brien, "Quantum Walks of Correlated Photons", Science 329, pp. 1500-1503 (2010). doi:10.1126/science.1193515 .

Four-Fold Quantum Memory

Jeff Kimble (photo courtesy: Caltech Particle Theory Group)

Researchers at the California Institute of Technology (Caltech) have demonstrated quantum entanglement for a quantum state stored in four spatially distinct atomic memories.

Their work, described in the November 18 issue of the journal Nature [1], also demonstrated a quantum interface between the atomic memories—which represent something akin to a computer "hard drive" for entanglement—and four beams of light, thereby enabling the four-fold entanglement to be distributed by photons across quantum networks. The research represents an important achievement in quantum information science by extending the coherent control of entanglement from two to multiple (four) spatially separated physical systems of matter and light.

The proof-of-principle experiment, led by the William L. Valentine Professor and professor of physics H. Jeff Kimble, helps to pave the way toward quantum networks [2]. Similar to the Internet in our daily life, a quantum network is a quantum "web" composed of many interconnected quantum nodes, each of which is capable of rudimentary quantum logic operations (similar to the "AND" and "OR" gates in computers) utilizing "quantum transistors" and of storing the resulting quantum states in quantum memories. The quantum nodes are "wired" together by quantum channels that carry, for example, beams of photons to deliver quantum information from node to node. Such an interconnected quantum system could function as a quantum computer, or, as proposed by the late Caltech physicist Richard Feynman in the 1980s, as a "quantum simulator" for studying complex problems in physics.

Link to Professor Jeff Kimble's Quantum Optics group at Caltech >>

Quantum entanglement is a quintessential feature of the quantum realm and involves correlations among components of the overall physical system that cannot be described by classical physics. Strangely, for an entangled quantum system, there exists no objective physical reality for the system's properties. Instead, an entangled system contains simultaneously multiple possibilities for its properties. Such an entangled system has been created and stored by the Caltech researchers.

Previously, Kimble's group entangled a pair of atomic quantum memories and coherently transferred the entangled photons into and out of the quantum memories [3]. For such two-component—or bipartite—entanglement, the subsystems are either entangled or not. But for multi-component entanglement with more than two subsystems—or multipartite entanglement—there are many possible ways to entangle the subsystems. For example, with four subsystems, all of the possible pair combinations could be bipartite entangled but not be entangled over all four components; alternatively, they could share a "global" quadripartite (four-part) entanglement.

Hence, multipartite entanglement is accompanied by increased complexity in the system. While this makes the creation and characterization of these quantum states substantially more difficult, it also makes the entangled states more valuable for tasks in quantum information science.

[Image Credit: Nature/Caltech/Akihisa Goban] The fluorescence from the four atomic ensembles. These ensembles are the four quantum memories that store an entangled quantum state.

To achieve multipartite entanglement, the Caltech team used lasers to cool four collections (or ensembles) of about one million Cesium atoms, separated by 1 millimeter and trapped in a magnetic field, to within a few hundred millionths of a degree above absolute zero. Each ensemble can have atoms with internal spins that are "up" or "down" (analogous to spinning tops) and that are collectively described by a "spin wave" for the respective ensemble. It is these spin waves that the Caltech researchers succeeded in entangling among the four atomic ensembles.

The technique employed by the Caltech team for creating quadripartite entanglement is an extension of the theoretical work of Luming Duan, Mikhail Lukin, Ignacio Cirac, and Peter Zoller in 2001 for the generation of bipartite entanglement by the act of quantum measurement. This kind of "measurement-induced" entanglement for two atomic ensembles was first achieved by the Caltech group in 2005 [4].

In the current experiment, entanglement was "stored" in the four atomic ensembles for a variable time, and then "read out"—essentially, transferred—to four beams of light. To do this, the researchers shot four "read" lasers into the four, now-entangled, ensembles. The coherent arrangement of excitation amplitudes for the atoms in the ensembles, described by spin waves, enhances the matter–light interaction through a phenomenon known as superradiant emission.

"The emitted light from each atom in an ensemble constructively interferes with the light from other atoms in the forward direction, allowing us to transfer the spin wave excitations of the ensembles to single photons," says Akihisa Goban, a Caltech graduate student and coauthor of the paper. The researchers were therefore able to coherently move the quantum information from the individual sets of multipartite entangled atoms to four entangled beams of light, forming the bridge between matter and light that is necessary for quantum networks.

The Caltech team investigated the dynamics by which the multipartite entanglement decayed while stored in the atomic memories. "In the zoology of entangled states, our experiment illustrates how multipartite entangled spin waves can evolve into various subsets of the entangled systems over time, and sheds light on the intricacy and fragility of quantum entanglement in open quantum systems," says Caltech graduate student Kyung Soo Choi, the lead author of the Nature paper. The researchers suggest that the theoretical tools developed for their studies of the dynamics of entanglement decay could be applied for studying the entangled spin waves in quantum magnets.

Further possibilities of their experiment include the expansion of multipartite entanglement across quantum networks and quantum metrology. "Our work introduces new sets of experimental capabilities to generate, store, and transfer multipartite entanglement from matter to light in quantum networks," Choi explains. "It signifies the ever-increasing degree of exquisite quantum control to study and manipulate entangled states of matter and light."

In addition to Kimble, Choi, and Goban, the other authors of the paper, "Entanglement of spin waves among four quantum memories," are Scott Papp, a former postdoctoral scholar in the Caltech Center for the Physics of Information now at the National Institute of Standards and Technology in Boulder, Colorado, and Steven van Enk, a theoretical collaborator and professor of physics at the University of Oregon, and an associate of the Institute for Quantum Information at Caltech.

References
[1] K.S. Choi, A. Goban, S.B. Papp, S.J. van Enk, H. J. Kimble, "Entanglement of spin waves among four quantum memories", Nature 468, 412-416 (18 November 2010). Abstract.
[2] H.J. Kimble, "The quantum internet", Nature 453, 1023-1030 (19 June 2008). Abstract.
[3] K. S. Choi, H. Deng, J. Laurat, H. J. Kimble, "Mapping photonic entanglement into and out of a quantum memory", Nature 452, 67-71 (6 March 2008). Abstract.
[4] C.W. Chou, H. de Riedmatten, D. Felinto, S.V. Polyakov, S.J. van Enk, H.J. Kimble, "Measurement-induced entanglement for excitation stored in remote atomic ensembles", Nature 438, 828-832 (8 December, 2005). Abstract.

Random Numbers Game with Quantum Dice

A simple device measures the quantum noise of vacuum fluctuations and generates true random numbers.

Image caption: A true game of chance: Max Planck researchers produce true random numbers by making the randomly varying intensity of the quantum noise visible. To do this, they use a strong laser (coming from the left), a beam splitter, two identical detectors and several electronic components. The statistical spread of the measured values follows a Gaussian bell-shaped curve (bottom). Individual values are assigned to sections of the bell-shaped curve that correspond to a number.


Behind every coincidence lies a plan - in the world of classical physics, at least. In principle, every event, including the fall of dice or the outcome of a game of roulette, can be explained in mathematical terms. Researchers at the Max Planck Institute for the Science of Light in Erlangen have constructed a device that works on the principle of true randomness [1]. With the help of quantum physics, their machine generates random numbers that cannot be predicted in advance. The researchers exploit the fact that measurements based on quantum physics can only produce a special result with a certain degree of probability, that is, randomly. True random numbers are needed for the secure encryption of data and to enable the reliable simulation of economic processes and changes in the climate.

The phenomenon we commonly refer to as chance is merely a question of a lack of knowledge. If we knew the location, speed and other classical characteristics of all of the particles in the universe with absolute certainty, we would be able to predict almost all processes in the world of everyday experience. It would even be possible to predict the outcome of a puzzle or lottery numbers. Even if they are designed for this purpose, the results provided by computer programs are far from random: "They merely simulate randomness but with the help of suitable tests and a sufficient volume of data, a pattern can usually be identified," says Christoph Marquardt. In response to this problem, a group of researchers working with Gerd Leuchs and Christoph Marquardt at the Max Planck Institute for the Science of Light and the University of Erlangen- Nuremberg and Ulrik Andersen from the Technical University of Denmark have developed a generator for true random numbers.

True randomness only exists in the world of quantum mechanics. A quantum particle will remain in one place or another and move at one speed or another with a certain degree of probability. "We exploit this randomness of quantum-mechanical processes to generate random numbers," says Christoph Marquardt.

The scientists use vacuum fluctuations as quantum dice. Such fluctuations are another characteristic of the quantum world: there is nothing that does not exist there. Even in absolute darkness, the energy of a half photon is available and, although it remains invisible, it leaves tracks that are detectable in sophisticated measurements: these tracks take the form of quantum noise. This completely random noise only arises when the physicists look for it, that is, when they carry out a measurement.

To make the quantum noise visible, the scientists resorted once again to the quantum physics box of tricks: they split a strong laser beam into equal parts using a beam splitter. A beam splitter has two input and output ports. The researchers covered the second input port to block light from entering. The vacuum fluctuations were still there, however, and they influenced the two partial output beams. The physicists then send them to the detectors and measure the intensity of the photon stream. Each photon produces an electron and the resulting electrical current is registered by the detector.

When the scientists subtract the measurement curves produced by the two detectors from each other, they are not left with nothing. What remains is the quantum noise. "During measurement the quantum-mechanical wave function is converted into a measured value," says Christian Gabriel, who carried out the experiment with the random generator with his colleagues at the Max Planck Institute in Erlangen: "The statistics are predefined but the intensity measured remains a matter of pure chance." When plotted in a Gaussian bellshaped curve, the weakest values arise frequently while the strongest occur rarely. The researchers divided the bell-shaped curve of the intensity spread into sections with areas of equal size and assigned a number to each section.

Needless to say, the researchers did not decipher this quantum mechanics puzzle to pass the time during their coffee breaks. "True random numbers are difficult to generate but they are needed for a lot of applications," says Gerd Leuchs, Director of the Max Planck Institute for the Science of Light in Erlangen. Security technology, in particular, needs random combinations of numbers to encode bank data for transfer. Random numbers can also be used to simulate complex processes whose outcome depends on probabilities. For example, economists use such Monte Carlo simulations to predict market developments and meteorologists use them to model changes in the weather and climate.

There is a good reason why the Erlangen-based physicists chose to produce the random numbers using highly complex vacuum fluctuations rather than other random quantum processes. When physicists observe the velocity distribution of electrons or the quantum noise of a laser, for example, the random quantum noise is usually superimposed by classical noise, which is not random. "When we want to measure the quantum noise of a laser beam, we also observe classical noise that originates, for example, from a shaking mirror," says Christoffer Wittmann who also worked on the experiment. In principle, the vibration of the mirror can be calculated as a classical physical process and therefore destroys the random game of chance.

"Admittedly, we also get a certain amount of classical noise from the measurement electronics," says Wolfgang Mauerer who studied this aspect of the experiment. "But we know our system very well and can calculate this noise very accurately and remove it." Not only can the quantum fluctuations enable the physicists to eavesdrop on the pure quantum noise, no one else can listen in. "The vacuum fluctuations provide unique random numbers," says Christoph Marquardt. With other quantum processes, this proof is more difficult to provide and the danger arises that a data spy will obtain a copy of the numbers. "This is precisely what we want to avoid in the case of random numbers for data keys," says Marquardt.

Although the quantum dice are based on mysterious phenomena from the quantum world that are entirely counterintuitive to everyday experience, the physicists do not require particularly sophisticated equipment to observe them. The technical components of their random generator can be found among the basic equipment used in many laser laboratories. "We do not need either a particularly good laser or particularly expensive detectors for the set-up," explains Christian Gabriel. This is, no doubt, one of the reasons why companies have already expressed interest in acquiring this technology for commercial use.

References:
[1] Christian Gabriel, Christoffer Wittmann, Denis Sych, Ruifang Dong, Wolfgang Mauerer, Ulrik L. Andersen, Christoph Marquardt, Gerd Leuchs, "A generator for unique quantum random numbers based on vacuum states", Nature Photonics, 4, 711-715 (October, 2010). Abstract.
[2] More information about the quantum random number generator >>

'Quantum Cats' Made of Photons

NIST research associate Thomas Gerrits at the laser table used to create "quantum cats" made of photons [Photo courtesy: NIST, Boulder, CO, USA]

Researchers at the National Institute of Standards and Technology (NIST) have created "quantum cats" made of photons (particles of light), boosting prospects for manipulating light in new ways to enhance precision measurements as well as computing and communications based on quantum physics.

The NIST experiments, described in a forthcoming paper in Physical Review A, repeatedly produced light pulses that each possessed two exactly opposite properties—specifically, opposite phases, as if the peaks of the light waves were superimposed on the troughs. Physicists call this an optical Schrödinger's cat. NIST's quantum cat is the first to be made by detecting three photons at once and is one of the largest and most well-defined cat states ever made from light. (Larger cat states have been created in different systems by other research groups, including one at NIST.)

A "cat state" is a curiosity of the quantum world, where particles can exist in "superpositions" of two opposite properties simultaneously. Cat state is a reference to German physicist Erwin Schrödinger's famed 1935 theoretical notion of a cat that is both alive and dead simultaneously.

"This is a new state of light, predicted in quantum optics for a long time," says NIST research associate Thomas Gerrits, lead author of the paper. "The technologies that enable us to get these really good results are ultrafast lasers, knowledge of the type of light needed to create the cat state, and photon detectors that can actually count individual photons."

These colorized plots of electric field values indicate how closely the NIST "quantum cats" (left) compare with theoretical predictions for a cat state (right). The purple spots and alternating blue contrast regions in the center of the images indicate the light is in the appropriate quantum state [Image credit: Thomas Gerrits/NIST]

The NIST team created their optical cat state by using an ultrafast laser pulse to excite special crystals to create a form of light known as a squeezed vacuum, which contains only even numbers of photons. A specific number of photons were subtracted from the squeezed vacuum using a beam splitter. The photons were identified with a NIST sensor that efficiently detects and counts individual photons [2]. Depending on the number of subtracted photons, the remaining light is in a state that is a good approximation of a quantum cat says Gerrits—the best that can be achieved because nobody has been able to create a "real" one, by, for instance, the quantum equivalent to superimposing two weak laser beams with opposite phases.

NIST conducts research on novel states of light because they may enhance measurement techniques such as interferometry, used to measure distance based on the interference of two light beams. The research also may contribute to quantum computing—which may someday solve some problems that are intractable today—and quantum communications, the most secure method known for protecting the privacy of a communications channel. Larger quantum cats of light are needed for accurate information processing.

References
[1] T. Gerrits, S. Glancy, T. Clement , B. Calkins, A. Lita, A. Miller, A. Migdall, S.W. Nam, R. Mirin and E. Knill, "Generation of optical coherent state superpositions by number-resolved photon subtraction from squeezed vacuum", Physical Review A. Accepted for publication.
Abstract: We have created heralded coherent state superpositions (CSS), by subtracting up to three photons from a pulse of squeezed vacuum light. To produce such CSSs at a sufficient rate, we used our high-efficiency photon-number-resolving transition edge sensor to detect the subtracted photons. This is the first experiment enabled by and utilizing the full photon-number-resolving capabilities of this detector. The CSS produced by three-photon subtraction had a mean photon number of 2.75 (errorbar: -0.24+0.06) and a fidelity of 0.59 (errorbar: -0.14+0.04) with an ideal CSS. This confirms that subtracting more photons results in higher-amplitude CSSs.
[2] A. E. Lita, B. Calkins, L. A. Pellouchoud, A. J. Miller, S. Nam, "Superconducting transition-edge sensors optimized for high-efficiency photon-number resolving detectors", Proc. SPIE, Vol. 7681, 76810D (2010); doi:10.1117/12.852221. Abstract.

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

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]

Quantum Gravity and Entanglement

Mark Van Raamsdonk

[Every year (since 1949) the Gravity Research Foundation honors best submitted essays in the field of Gravity. This year's prize goes to Mark Van Raamsdonk for his essay "Building Up Spacetime with Quantum Entanglement". The five award-winning essays will be published in the Journal of General Relativity and Gravitation (GRG) and subsequently, in a special issue of the International Journal of Modern Physics D (IJMPD). Today we present here an invited article from Prof. Raamsdonk on his current work.
-- 2Physics.com ]

Author: Mark Van Raamsdonk
Affiliation: Department of Physics and Astronomy,
University of British Columbia, Vancouver, Canada.

Quantum Mechanics and Entanglement :

The development of quantum mechanics in the early 20th century is surely one of the most remarkable achievements of mankind. Quantum mechanics is fundamentally different than the physical theories developed earlier to describe physics on macroscopic scales, yet is absolutely essential in understanding atomic scale physics. At the heart of quantum mechanics is the idea of quantum superposition: in quantum mechanics, objects can in some sense be in two places at once (or more generally two physical configurations at once). Mathematically speaking, every state of a physical system can be associated with a kind of vector, and if A and B are vectors representing two allowed physical configurations, then A + B is also an allowed physical state. In a simple example, A could be a state where an object is in one place, and B could be a state where the same object is in a different place; A + B then represents a state where a single object has no definite location. If a measurement of the object’s location is performed, no definite prediction for the result is possible; we will find it either in one location or the other, and quantum mechanics can at best predict the probability for each possible outcome.

2Physics articles by past winners of the Gravity Research Foundation award:
Alexander Burinskii (2009): "Beam Pulses Perforate Black Hole Horizon"
T. Padmanabhan (2008): "Gravity : An Emergent Perspective"
Steve Carlip (2007): "Symmetries, Horizons, and Black Hole Entropy"

Intimately related to the idea of quantum superposition is the notion of quantum entanglement. If we have a physical system with two parts (e.g. a ball and a box) then in a general quantum state, we cannot say with certainty what is the state of the ball (e.g. whether or not it is in the box) or what is the state of the box (e.g. whether the box is open or closed). But for certain quantum states, this uncertainty can be correlated for the two objects. For example, suppose A represents a quantum state where the ball is in the box and the box is closed, and B represents a quantum state where the ball is not in the box and the box is open. Then in the state A + B, neither the location of the ball nor the state of the box is definite, but a measurement which determines the state of the box effectively also determines the location of the ball: if we measure the state A+B and find the box closed, we can be sure that the ball is in the box; if we find it open, we can be sure the ball is not in the box. In this situation, we say that the ball and the box are entangled, since a measurement of one part of the system influences the quantum state of the other part of the system. In practice, it would be exceedingly difficult to prepare a macroscopic system such as a ball and box in such an entangled state, but such situations are commonplace at the atomic scale. The phenomenon of entanglement is an intrinsically quantum phenomenon; indeed, it can be shown that a computer making use of quantum entanglement can perform certain calculations far faster than any ordinary computer; entanglement is the basic property of quantum systems that allows quantum computation.

Strange as they may seem, the rules of quantum mechanics have now been tested beyond any reasonable doubt and allow us to understand physical processes in nature with incredible precision. For certain properties of elementary particles, predications based on quantum mechanics have been shown to be correct to one part in 100,000,000 or better. We now have a fully quantum mechanical description (known as quantum field theory) for the strong, weak, and electromagnetic forces, that allows us to understand how these interactions operate even at distance scales 100,000,000,000,000 times smaller than we can resolve with our eyes.

Quantum Gravity :

The approach that allowed physicists to develop a quantum mechanical theory for the strong, weak, and electromagnetic forces turns out not to work when applied to the remaining force, the force of gravity. In fact, it fails miserably. As a result, finding the correct quantum mechanical theory of gravity has been a prominent open question for decades; indeed it is one of the greatest challenges in theoretical physics. While Einstein’s Theory of General Relativity is almost entirely adequate for the purposes of describing the observed gravitational dynamics of planets, stars, galaxies, and even the expansion of the universe as a whole, it cannot be the whole story, since it does not incorporate the quantum mechanics principles that are believed to underlie all physics in our universe. Usually, a quantum mechanical description of nature is only necessary at very short distance scales; at macroscopic distance scales, the pre-20th century ``classical’’ physics provides an excellent approximation. But there are certain situations, such as in the interior of a black hole, in the early universe just after the big bang, or in a hypothetical scattering of particles with energies many orders of magnitude larger than we can currently produce in an accelerator, where gravitational effects would be important at distance scales small enough that a quantum mechanical description of the physics is essential. Finding the right theory of quantum gravity is essential if we want to fully understand the workings of nature.

String theory and the AdS/CFT correspondence :

One example of a theory that is fully quantum-mechanical but also includes gravitational physics is provided by string theory. Until the mid 1990s, the mathematical description of string theory was such that it allowed only relatively simple calculations; for example, one could predict the results for scattering of a fixed number of particles (including gravitons) on some fixed spacetime background (e.g. flat spacetime). This was not an entirely satisfactory situation. We recall that in Einstein’s theory of gravity, space itself is a dynamical entity that can be curved or warped by matter and energy; it is the effect of this warping on other objects that gives rise to gravitational ``forces.’’ In a complete theory of quantum gravity, different quantum states should correspond to spacetimes with different geometries (i.e. different warpings); the original formulation of string theory could most readily describe only different types of particles on a fixed geometry.

The situation for string theory changed dramatically between 1995 and 1997 in what is now known as “the Second Superstring Revolution.” (The first revolution was the period in the mid 1980s when it became clear that the original formulation of string theory was mathematically consistent.) This period culminated in a stunning proposal by Juan Maldacena known as the AdS/CFT correspondence, or gauge theory / gravity duality. (This followed an earlier proposal of the same nature by Tom Banks, Willy Fischler, Steve Shenker, and Lenny Susskind). The proposal states that there is an exact equivalence between certain examples of string theory (full-fledged theories of quantum gravity) and certain ordinary quantum mechanical systems without gravity (often quantum field theories). These much simpler ordinary quantum mechanical systems suffer none of the restrictions found in the original formulation of string theory, and thus, via the equivalence, may be used to provide a complete formulation of the corresponding string theory, able to quantum mechanically describe gravity and other forces on a spacetime which can fluctuate dynamically. Remarkably, this much better formulation of string theory turns out to be no more complicated than the quantum mechanical description of the other forces, completely understood almost half a century ago.

Geometry from Entanglement :

According to the AdS/CFT correspondence, there must be a dictionary that allows us to associate to every state of some conventional quantum mechanical system a state of the corresponding equivalent quantum gravity theory. Different states in the quantum mechanics correspond to different spacetime geometries (i.e. different distributions of matter and a different warping of space). For example, the quantum state A might correspond to completely empty space, while the state B corresponds to space with some gravitational waves, and state C corresponds to a space with orbiting black holes. While the dictionary between quantum state and corresponding spacetime is known for very simple states, more generally the correspondence is far from obvious. Ideally, one would like to know the gravity interpretation for an arbitrary quantum state of the conventional system; understanding the general dictionary is a crucial open question for the field.

The central suggestion in my essay [1] is that crucial information about what the spacetime associated to a given quantum state looks like is contained in how the various parts of the ordinary quantum are entangled with each other in the given state. While the arguments rely on some specific results in string theory, it is not difficult to give some sense of where the idea comes from.

To start, suppose that a specific quantum system has a corresponding gravity theory such that each state of the system corresponds to some spacetime. Now consider a second quantum system, which we obtain by taking two copies of the first system (with no physical interactions between the two systems). For the larger system, the simplest states are those with no entanglement between the two parts. That is, we can consider a state A = (A1,A2) in which the first system is in state A1 and the second system is in state A2. Now A1 and A2 each correspond to some particular spacetime according to the AdS/CFT correspondence. Thus, we can interpret the state A of the larger system as corresponding to two completely disconnected spacetimes (imagine our universe and some parallel universe with which there is no possible communication).

More generally, we can consider states which are quantum superpositions such as (A1,A2) + (B1,B2) . For such states, there is entanglement between the two parts. In [1], based on various earlier works, I pointed out that for states with enough entanglement (certain states which are quantum superpositions (A1,A2) + (B1,B2) + (C1,C2) + … with many states in the superposition) the resulting complicated state can be interpreted as a single connected spacetime, in which two distinct parts are connected by something like a wormhole (or a black hole/white hole). Since all the individual states in the superposition had interpretations as disconnected spacetimes, we can say that a quantum superposition of disconnected spacetimes has produced a connected spacetime. Alternately, we can say that by entangling the two parts of our original quantum system, we have managed to connect up two parts of the corresponding spacetime.

Starting from this hint of a connection between entanglement and spacetime geometry, one can argue that more quantitative measures of entanglement in states of a quantum system give direct information about quantitative geometrical quantities in the corresponding spacetimes, such as areas and geodesic distances. The complete picture for how to deduce the spacetime associated with a particular state in the AdS/CFT correspondence is certainly still beyond our reach, but I believe these connections between entanglement and geometry may be an important part of the story. If correct, they suggest a deep connection between quantum gravity and quantum information theory (the natural setting for studies of entanglement in quantum systems) that may be of fundamental importance.

References
[1] Mark Van Raamsdonk, “Building up spacetime with quantum entanglement,” arXiv:1005.3035. Link.
[2] Nielsen, M.A., Chuang, I.L., “Quantum Computation and Quantum Information” (Cambridge University Press, Cambridge, 2000).
[3] Juan Maldacena, “The Illusion of Gravity” -, Scientific American, November 2005. Link.
[4] Brian Greene, "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory" (Vintage Series, Random House Inc, February 2000).

Entanglement with Frequency Combs

David Hayes

For the first time, physicists have employed a powerful technique of laser physics – the “optical frequency comb” – to entangle two trapped atoms [1]. This form of control is a promising candidate for use as a means of quantum control for quantum computing and information-processing, and offers substantial operational advantages over other methods.

The team, led by the Joint Quantum Institute (JQI) Fellow Christopher Monroe, began by preparing two ytterbium ions, spaced about five micrometers apart in an electrical trap, in identical minimal-energy ground states. [See Figure 1] The goal of the experiment was to entangle these two ions – that is, to place them in a condition in which the quantum state of one is inextricably correlated with the state of the other – using light from a single high-speed pulsed laser.

>>Link to `Trapped Ion Quantum Information Group' led by Christopher Monroe, University of Maryland

Past 2Physics articles on the work of this group:
"Long-Distance Teleportation between Two Atoms"
"Quantum Entanglement between Single Atoms One Meter Apart!"

[Click on the figures 1-3 below to view higher resolution versions]

Entanglement is the resource that will likely be used for transferring quantum information from place to place in any future quantum computer or information-processing system. As a result, there is intense global interest in finding dependable, high-speed entanglement schemes.

The researchers entangled the ions in a two-part process in which both parts occur simultaneously, generated by the laser pulses. In part one, the ions are placed in a superposition of two hyperfine states – tiny energy differences within a single excitation level of an atom that result from electrons’ interaction with the nucleus. The hyperfine states serve as a two-level system that permits each ion to function as a quantum information bit, or “qubit,” as it exists in some combination of both states at the same time.

In part two, the laser pulses give each ion a momentum “kick” that depends on which qubit state it is in. These kicks are slight physical displacements that cause each positively charged ion to affect the other through interaction of their electrical fields. There are multiple pathways by which a sequence of photons can place each ion in a given quantum vibrational state. Owing to a peculiarity of quantum mechanics, when it is impossible to know which photon sequence put the ions in their target vibrational states, the ions are entangled. [See Figure 2]

“These sorts of procedures have been done before with continuous-wave lasers,” says Dave Hayes, first author on the paper, “but never with a frequency comb.”

An optical frequency comb is a peculiar property of pulsed, “mode-locked” lasers. In the cavity of a laser, photons with a narrow range of frequencies reflect back and forth between the two mirrors on either end. [See Figure 3] Many of those frequencies will be suppressed by destructive interference; they cancel themselves out because the round-trip distance from mirror to mirror in the cavity is not an integer multiple of their wavelengths. But many frequencies will have exactly the right wavelengths to resonate in the cavity, forming standing waves like a jump rope. Each of those standing waves is a mode of the cavity.

When all the modes have the same phase relationship to each other, they are said to be “mode-locked,” and something remarkable happens: At periodic intervals, the standing waves interfere constructively – that is, reinforce each other – forming a very brief, intense pulse with a duration in the picosecond range or even shorter. (A picosecond is one millionth of one millionth of a second.) The JQI team used a train of 1-picosecond pulses separated by 12.5 nanoseconds.

Each pulse consists of multiple frequencies, which over time build up into a pattern of sharply defined frequency spikes that are uniformly spaced like the teeth in a comb. If the energy difference between any two comb frequencies corresponds exactly with an atomic quantum transition, it will produce it. But many desired effects – including those sought by the JQI team – do not precisely match any spacing in the teeth of a single comb. So the scientists split the main pulsed laser beam into separate beams and applied slight frequency offsets to them with devices called acousto-optic modulators (AOMs).

By tuning the system with the AOMs, the team can create any frequency difference they want to produce both the target effects: generating qubit states in the ions, and entangling the ions by momentum kicks. For the latter, Hayes says, “when we can use two teeth from offset combs to match the energy of transition between motion quanta, we’re in business to entangle neighboring ions.”

“There are inherent advantages of the frequency comb method,” Hayes notes. “One consideration is cost. Mode-locked lasers are just cheaper, especially for ions because the transitions are usually in the ultraviolet. Continuous-wave lasers in that frequency range are really expensive, while it’s simple to generate uv light with these high power pulses.” The main criterion governing the type of pulsed laser to be used is the bandwidth – the range of frequencies that can be carried in the pulses.

The JQI researchers used a titanium-doped sapphire laser for this experiment. “What’s special about the beam,” Hayes says, “is that the bandwidth of a single pulse is larger than the energy difference between the two qubit states.”

The comb method is also attractive because of the potential for much higher laser powers, delivered in a much shorter time span, which could allow quantum logic gates to operate very fast. While this aspect was not part of this demonstration, it will be addressed in future experiments. But more generally, as Hayes explains, “the optical frequency comb has so many frequency markers that this system should also be useful for the quantum control of almost any optical quantum system, from other atomic species to molecules or even quantum dots.”

We thank Curt Suplee for writing this article.

Reference
[1] “Entanglement of Atomic Qubits Using an Optical Frequency Comb,” D. Hayes, D.N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko and C. Monroe, Physical Review Letters, 104, 140501 (2010). Abstract.

Theory of Quantum Mechanics Applies to the Motion of Large Objects

(L to R) Andrew Cleland, Aaron O'Connell and John Martinis [photo credit: George Foulsham / Univ of California, Santa Barbara]

A team of physicists from University of California, Santa Barbara has provided the first clear demonstration that the theory of quantum mechanics applies to the mechanical motion of an object large enough to be seen by the naked eye. Their work satisfies a longstanding goal among physicists.

In a paper published in the March 17 issue of the advance online journal Nature [1], Aaron O'Connell, a doctoral student in physics, and John Martinis and Andrew Cleland, professors of physics, describe the first demonstration of a mechanical resonator that has been cooled to the quantum ground state, the lowest level of vibration allowed by quantum mechanics. With the mechanical resonator as close as possible to being perfectly still, they added a single quantum of energy to the resonator using a quantum bit (qubit) to produce the excitation. The resonator responded precisely as predicted by the theory of quantum mechanics.

"This is an important validation of quantum theory, as well as a significant step forward for nanomechanics research," said Cleland.

The researchers reached the ground state by designing and constructing a microwave-frequency mechanical resonator that operates similarly to –– but at a higher frequency than –– the mechanical resonators found in many cellular telephones. They wired the resonator to an electronic device developed for quantum computation, a superconducting qubit, and cooled the integrated device to temperatures near absolute zero. Using the qubit as a quantum thermometer, the researchers demonstrated that the mechanical resonator contained no extra vibrations. In other words, it had been cooled to its quantum ground state.

Micrograph of the resonator

The researchers demonstrated that, once cooled, the mechanical resonator followed the laws of quantum mechanics. They were able to create a single phonon, the quantum of mechanical vibration, which is the smallest unit of vibrational energy, and watch as this quantum of energy exchanged between the mechanical resonator and the qubit. While exchanging this energy, the qubit and resonator become "quantum entangled," such that measuring the qubit forces the mechanical resonator to "choose" the vibrational state in which it should remain.

In a related experiment, they placed the mechanical resonator in a quantum superposition, a state in which it simultaneously had zero and one quantum of excitation. This is the energetic equivalent of an object being in two places at the same time. The researchers showed that the resonator again behaved as expected by quantum theory.

Reference
[1] A. D. O’Connell, M. Hofheinz, M. Ansmann, Radoslaw C. Bialczak, M. Lenander, Erik Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, John M. Martinis & A. N. Cleland, "Quantum ground state and single-phonon control of a mechanical resonator", Nature advance online publication 17 March 2010 [doi:10.1038/nature08967]. Abstract.

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