Quantum experiment preludes the endgame for local realism – photonic Bell violation closes the fair-sampling loophole

[Left to Right] Johannes Kofler, Sven Ramelow, Marissa Giustina, Rupert Ursin (© Brasch), Anton Zeilinger (© Godany)

Authors:
Johannes Kofler¹, Sven Ramelow^2,3, Marissa Giustina^2,3, Rupert Ursin^2,3, Anton Zeilinger^2,3

Affiliation:
¹Max Planck Institute of Quantum Optics (MPQ), Garching/Munich, Germany.
²Institute for Quantum Optics and Quantum Information – Vienna (IQOQI), Austrian Academy of Sciences, Vienna, Austria.
³Quantum Optics, Quantum Nanophysics, Quantum Information, University of Vienna, Faculty of Physics, Vienna, Austria.

Using photons, a recent experiment in Vienna closed a loophole in the arguments against local realism and now makes photons the first quantum system for which all major loopholes have been closed in separate experiments. This is good news for a final experiment closing all loopholes simultaneously.

“Local realism” is a world view in which the properties of physical objects exist independent of whether or not they are observed (realism), and in which no physical influence can propagate faster than the speed of light (locality). In 1964, in one of the most important works in the history of the foundations of quantum theory [1], the Irish physicist John Bell proved theoretically that local realism is in contradiction with the predictions of quantum mechanics. With his now famous “Bell inequality”, he showed that it is possible to determine experimentally which of the two radically different world views actually governs reality. The terms in the inequality are the correlations of measurement results. Bell’s inequality is satisfied by the predictions of any local realistic theory, whereas quantum mechanics predicts measurement outcomes that can violate it.

Past 2Physics articles by Johannes Kofler, Sven Ramelow, Rupert Ursin, Anton Zeilinger:

November 04, 2012: "Quantum Teleportation Over 143 Kilometers" by Xiao-song Ma, Johannes Kofler, Rupert Ursin and Anton Zeilinger,
November 13, 2011: "A New Scheme for Photonic Quantum Computing" by Nathan K. Langford, Sven Ramelow and Robert Prevedel,
May 30, 2009: "Transmission of Entangled Photons over a High-Loss Free-Space Channel" by Alessandro Fedrizzi, Rupert Ursin and Anton Zeilinger,
June 08, 2007: "Entanglement and One-Way Quantum Computing "
by Robert Prevedel and Anton Zeilinger

In a Bell test, pairs of systems, e.g. photons, are produced. From every pair, one photon is sent to a party usually called Alice, and the other photon is sent to another party known as Bob. They each choose which physical property they want to measure, for instance, a direction of their photon’s polarization. For pairs that are quantum entangled, the correlations of Alice’s and Bob’s measurement outcomes can exceed the correlations predicted by any local realistic theory and thus violate Bell’s inequality. Quantum entanglement – a term coined by the Austrian physicist Erwin Schrödinger – means that no photon taken by itself has a definite polarization, but that if one party measures the polarization of its photon, the other photon will always show a perfectly correlated polarization. Albert Einstein called this strange effect “spooky action at a distance”.

In addition to its preeminent importance in foundational physics, quantum entanglement and Bell’s inequality also play a quintessential role in the modern field of quantum information. There, individual quantum particles are the carriers of information, and the entanglement between them promises absolutely secure communication as well as enhanced computation power compared to any conceivable classical technology.

In the last decades, Bell’s inequality has been violated in numerous experiments and for several different physical systems such as photons and atoms. However, in experimental tests, “loopholes” arise that allow the observed correlations – although they violate Bell’s inequality – to still be explained by local realistic theories. The advocates of local realism can defend their worldview falling back on essentially three such loopholes. In the “locality loophole” the measurement result of one party is assumed to be influenced by a fast and hidden physical signal from the other party to produce the observed correlations. Similarly, in the “freedom-of-choice” loophole the measurement choices of Alice and Bob are considered to be influenced by some hidden local realistic properties of the particle pairs. These two loopholes have already been closed in photonic experiments [2-4] by separating Alice and Bob by large distances, and enforcing precise timing of the photon pair creation, Alice’s and Bob’s choice events, and their measurements. The local realist would then need superluminal signals to explain the measured correlations, but influences which are faster than light are not allowed in the local realistic world view.

The third way out for the local realist is called the “fair-sampling loophole” [5]. It works in the following manner: if only a small fraction of the produced photons is measured, a clever advocate of local realism can conceive a model in which the ensemble of all produced photons as a whole follows the rules of local realism, although the “unfair” sample of the actually measured photons was able to violate Bell’s inequality. (Think of randomly flipping many fair coins but looking at only some of them, where the coins showing heads tend to hide and thus have a smaller probability of being observed than those showing tails. When looking at only this incomplete and "unfair" subset of the coins, it wrongly appears as if the coins had a special distribution with more showing tails than heads.) This type of loophole has even been explicitly exploited in an experiment faking Bell violations without any entanglement [6]. The way to close the fair-sampling loophole is to achieve a high detection efficiency of the produced particle pairs by avoiding losses and using very good measurement devices. Until now, this has been accomplished for particles with mass such as ions and atoms [7,8], but never for photons. However, for such particles, the other two loopholes are very difficult to close and indeed have not yet been closed.

A recent experiment has, for the first time, closed the fair-sampling loophole for photons [9]. It employed a significantly optimized source of entangled pairs achieving excellent fiber coupling efficiencies and state-of-the-art high-efficiency superconducting detectors to reach the necessary total detection efficiency. The researchers were able to measure about 75% of all photons in each arm. This rules out all local realistic explanations that rely on unfair sampling using a form of Bell’s inequality developed about 20 years ago by the American physicist Philippe Eberhard, which requires an efficiency of only two thirds [10]. The recent experiment makes the photon the first physical system for which all three loopholes have been closed, albeit in different experiments.

Optical setup used in the quantum experiment. (Image: IQOQI Vienna, Jacqueline Godany 2012)

Although most scientists do not expect any surprises and believe that quantum physics will prevail over local realism, it is still conceivable that different loopholes are exploited in different experiments. It is this last piece in the history of Bell tests which is still missing – a final and conclusive experiment violating Bell’s inequality while closing all loopholes simultaneously [11]. It is not yet clear whether such an experiment will be achieved first for photons or atoms or some other quantum system, but if it can be successfully performed, one needs to accept at least one of the following radical views: there is a hidden faster-than-light communication in nature, or we indeed live in a world in which physical properties do not always exist independent of observation. Almost 50 years after the formulation of local realism, its endgame clearly has begun.

References:
[1] J. S. Bell, "On the Einstein Podolsky Rosen Paradox". Physics (NY) 1, 195 (1964). Full Text.
[2] Alain Aspect, Jean Dalibard, Gérard Roger, "Experimental test of Bell's inequalities using time varying analyzers". Physical Review Letters, 49, 1804 (1982). Abstract.
[3] Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, and Anton Zeilinger, "Violation of Bell's Inequality under Strict Einstein Locality Conditions". Physical Review Letters, 81, 5039 (1998). Abstract.
[4] Thomas Scheidl, Rupert Ursin, Johannes Kofler, Sven Ramelow, Xiao-Song Ma, Thomas Herbst, Lothar Ratschbacher, Alessandro Fedrizzi, Nathan K. Langford, Thomas Jennewein, and Anton Zeilinger, "Violation of local realism with freedom of choice". Proceedings of the National Academy of Sciences 107, 19708–19713 (2010). Abstract.
[5] Philip M. Pearle, "Hidden-Variable Example Based upon Data Rejection". Physical Review D 2, 1418 (1970). Abstract.
[6] Ilja Gerhardt, Qin Liu, Antía Lamas-Linares, Johannes Skaar, Valerio Scarani, Vadim Makarov, Christian Kurtsiefer, "Experimentally Faking the Violation of Bell’s Inequalities". Physical Review Letters, 107, 170404 (2011). Abstract.
[7] M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, "Experimental violation of a Bell's inequality with efficient detection". Nature 409, 791 (2001). Abstract.
[8] Julian Hofmann, Michael Krug, Norbert Ortegel, Lea Gérard, Markus Weber, Wenjamin Rosenfeld, Harald Weinfurter. "Heralded Entanglement Between Widely Separated Atoms". Science 337, 72 (2012). Abstract.
[9] Marissa Giustina, Alexandra Mech, Sven Ramelow, Bernhard Wittmann, Johannes Kofler, Jörn Beyer, Adriana Lita, Brice Calkins, Thomas Gerrits, Sae Woo Nam, Rupert Ursin, Anton Zeilinger, "Bell violation using entangled photons without the fair-sampling assumption". Nature 497, 227 (2013). Abstract.
[10] Philippe H. Eberhard, "Background Level and Counter Efficiencies Required for a Loophole-Free Einstein-Podolsky-Rosen Experiment". Physical Review A 47, 747 (1993). Abstract.
[11] Zeeya Merali, "Quantum Mechanics Braces for the Ultimate Test". Science 331, 1380 (2011). Abstract.

Storage and Control of Optical Photons

Authors of the paper in Physical Review Letters (reference [1] ).
Left to Right: 
(top row) D. Maxwell, D. J. Szwer, D. Paredes-Barato, 
(middle row) H. Busche, J. D. Pritchard, A. Gauguet, 
(bottom row) K. J. Weatherill, M. P. A. Jones, C. S. Adams.



Authors: 
David Szwer and Hannes Busche

Affiliation:
Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, UK.





Quantum communication and information processing rely on robust carriers of quantum information (qubits), and optical photons are prime candidates. Light can easily be transmitted using optical technologies such as fibre cables, and barely interact with other photons or the environment. To process the information they carry however, controllable interactions between the single photons are needed. Physicists at Durham University in the UK have combined two advanced techniques of quantum optics with a microwave synthesiser, to control the interactions between individual photons [1,2]. The photons were stored in a cloud of rubidium atoms as so-called Rydberg polaritons. Due to long-ranged interactions between them, only a single photon may be stored in a volume of a few micrometres, limiting the number of stored photons to about three. The microwaves manipulated the photons while they were stored, forcing them to interact in ways whose details are still not fully understood. The ability to not only induce interactions on the level of single optical photons, but also to control them using microwave fields, could be an important new angle for future quantum technologies.

A beam of light is one of the least substantial things you'll ever encounter. It is the very essence of something fast and untrappable - so much so that Einstein invented relativity specifically because he couldn't imagine what light would be like if it was stationary. And although light reflects off mirrors and scatters off other objects, we never consider that two light beams could bounce off each other.

However, in specially tuned systems physicists can not only stop light, but make light interact with light. Our work achieves both these effects, making the interaction work at the single-photon level and even controlling it with microwaves.

The loophole that allows us to do these things is that light isn't always the pure electromagnetic wave that it is in vacuum. When light travels through matter, like glass or water, the electric field of the light slightly distorts the atoms in the matter, and they tug back on the light. This slows the light down (to half-speed or slower), and is ultimately responsible for lenses, optical fibres, rainbows and other phenomena.

Almost always, matter responds linearly to light so that the distortion from one beam does not affect another. At very high intensities, nonlinear effects can appear that do allow light to affect light. However, the dependence is so weak that it only manifests at very high powers. We care about the quantum nature of light, which only becomes apparent at the level of single photons. Photons carry a tiny amount of energy: a normal red laser pointer (emitting 1mW of power) produces over 3 million billion photons every second. Hence photons almost never interact.

To slow photons to a crawl, bring them to a full stop and make them interact, we therefore need to deliberately engineer our own medium. We start from an extremely thin and cold gas of the element rubidium (it’s normally a solid metal) created by laser cooling and trapping techniques [3]. The gas is about a million times more dilute than normal air (number of atoms per unit volume), so the experiment is done in a vacuum chamber. The gas needs to be extremely cold, just 100 μK (a ten-thousandth of a degree above absolute zero), because if the gas atoms move too fast they’ll mix up the light they’re storing.

Figure 1: Relevant energy levels of rubidium, showing the 780 nm (red, signal) and 480 nm (blue, control) spectral lines, and the Rydberg-Rydberg microwaves. 

 Gases like rubidium are useful because they have strong resonance lines – specific frequencies of light they interact with strongly and correspond to transitions between the discrete energy levels of the atom. We use two lines in rubidium, of wavelength 780 nm (less than a thousandth of a millimetre, a dim red colour) and 480 nm (bright blue). The red light is the signal we store – it excites normal, ground-state atoms to a particular excited energy level. The blue light takes atoms from that excited state to an even higher level called a Rydberg state. It affects how the rubidium atoms respond to the red light, not only preventing them from scattering the signal, but also slowing it down greatly because it is mixed so strongly with atomic distortion. If we turn the blue light off while signal is travelling through the cloud, the red photons are stopped and transformed completely into atomic distortion: a specific pattern of Rydberg excitations called a polariton.

Unlike photons, Rydberg states do interact with each other extremely strongly, causing shifts in the resonance frequencies needed to excite nearby atoms to Rydberg states. As a single Rydberg excitation shifts the remaining atoms out of resonance with our blue light, a blockade effect occurs preventing multiple Rydberg excitations within a volume of a few micrometres. If photons are mixed with Rydberg states, like in our cloud, the photons gain this ability to interact strongly and the blockade applies to them, imposing a minimum separation between photons. Photons that are too close together are scattered out of the cloud. If the cloud is dense enough, this leads to a continuous laser beam being filtered into a series of individual photons, as demonstrated recently by a group at MIT [4]. Alternatively we can stop light in the cloud, and allow the blockade to work while the photons are stored – this was done not only in our experiment, but also by a group at Georgia Tech where a single photon source was implemented [5]. Reliable single-photon sources like this are important for many other quantum experiments, as well as for quantum cryptography [6].

Our cloud is large enough for about three polaritons to sit in a line, each containing a single photon shared among many atoms. Due to the blockade, they are separated by a distance called the blockade radius, which measures the strength of interaction between two Rydberg atoms. This interaction is called the Van der Waals interaction, and it’s the same force that sticks molecules to each other in most solids around you.

Once we have some photons stored, our next step is to beam microwaves at the cloud, tuned to a transition between two different Rydberg states. One of these is the state we stored a photon in (called “S”), and the other state was previously empty (called “P”). Our blue light is only tuned to interact with the S state, not the P, so it will only release a stored photon if the polariton is in S. In an isolated Rydberg polariton, this would drive regular sine-wave “Rabi” oscillations between the two states. So if we apply microwaves for just long enough to transfer to P, and then turn the blue beam on, we don’t retrieve the photon.

Figure 2: Diagram of the experiment, showing the cloud of atoms with three stored polaritons. The two single-photon detectors shown are used to prove that the number of stored photons is limited, via a Hanbury Brown & Twiss experiment [7.8].

Instead of a single polariton, we’re most interested in what happens when the polaritons aren’t isolated, but have neighbours to interact with. The microwaves make them oscillate at the same rate. For a start, photons are only retrieved from the cloud when all polaritons are in S. This leads to the Rabi oscillations (shown in Figure 3) having flattened bottoms and sharper peaks when we scan the microwaves, and the exact shape helps us estimate the number of polaritons we have. Also, while the polaritons are half-way between S and P, they have large electric dipole moments – (the static electricity equivalent of a tiny bar magnet). The original van der Waals interaction is replaced with resonant dipole-dipole interactions – this makes them interact much more strongly than before, and at longer distances. Blockade was caused by the atoms within a polariton interacting – but now the polaritons interact with each other. We see that at low microwave powers, these interactions completely prevent the stored photons being retrieved, scattering them out of the cloud in other directions. But stronger microwaves can overwhelm the dipole-dipole interactions, and we see oscillations again.

Figure 3: The microwave-induced Rabi oscillations between two Rydberg states. Microwave power increases from left to right. The dashed line shows the transition from low power (dominated by Rydberg-Rydberg interactions) to high power (dominated by the microwaves).

This is a subtle system, and not yet fully understood. There is plenty more experimental and theoretical work to do. But we can already imagine applications. By controlling strong interactions between individual photons, it may be possible to build quantum logic gates that could be used in super-fast quantum computers, or super-secure quantum cryptography. There are also similarities between the way that specific Rydberg states can “hop” between polaritons, and the hopping of excitations along light harvesting complexes in plants. Experiments like these may help model photosynthesis, perhaps even helping scientists design more efficient solar cells.

Bibliography
[1] D. Maxwell, D. J. Szwer, D. Paredes-Barato, H. Busche, J. D. Pritchard, A. Gauguet, K. J. Weatherill, M. P. A. Jones, C. S. Adams, "Storage and Control of Optical Photons Using Rydberg Polaritons". Physical Review Letters , 110, 103001 (2013). Abstract.
[2] Antoine Browaeys, "Viewpoint: Catch and Release of Photons". Physics , 6, 25 (2013). Article.
[3] Nobel Prize in Physics 1997: Link.
[4] Thibault Peyronel, Ofer Firstenberg, Qi-Yu Liang, Sebastian Hofferberth, Alexey V. Gorshkov, Thomas Pohl, Mikhail D. Lukin, Vladan Vuletić, "Quantum nonlinear optics with single photons enabled by strongly interacting atoms". Nature, 488, 57-60 (2012). Abstract.
[5] Y.O. Dudin,  A. Kuzmich, "Strongly Interacting Rydberg Excitations of a Cold Atomic Gas. Science". 336, 887-889 (2012). Abstract.
[6] Alexios Beveratos, Rosa Brouri, Thierry Gacoin, André Villing, Jean-Philippe Poizat, and Philippe Grangier, "Single Photon Quantum Cryptography". Physical Review Letters, 89, 187901 (2002). Abstract.
[7] Michel Orrit, "Photon Statistics in Single Molecule Experiments". Single Molecules, 3, 255-265 (2002). Abstract.
[8] R. Hanbury Brown, R.Q.  Twiss, "Correlation between Photons in two Coherent Beams of Light". Nature, 177, 27-29 (1956). Abstract.

Macroscopic, Sub-Kelvin Refrigeration from Electron Tunneling

From left to right: Jason Underwood, Peter Lowell, Galen O’Neil, Joel Ullom

Authors: Peter Lowell, Galen O’Neil, Jason Underwood, Joel Ullom

Affiliation: 
National Institute of Standards and Technology, Boulder, Colorado, USA

Modern science often requires sub-Kelvin temperatures in order to observe quantum mechanical effects. Examples include quantum information studies, quantum computing and quantum sensors that can be used for measurements of radiation from microwave to gamma-ray wavelengths with unprecedented sensitivity. Cryogenic temperatures of 4K are easily reached using commercial mechanical refrigerators. The simplest method of reaching lower temperatures is by vacuum pumping on cryogenic liquids such as liquid ³He, which can reach as low as about 300mK. Achieving yet lower temperature is challenging and requires large, complex and expensive refrigerators. Our goal is to improve the availability of sub-300mK temperatures by creating simpler refrigeration techniques.

Normal metal–insulator–superconductor (NIS) tunnel junctions can be utilized for a new type of refrigeration for cooling below 300mK using quantum mechanical effects. When a voltage bias is applied to a NIS junction, it cools the electrons in a normal metal because only the hottest electrons from the normal metal can tunnel into the superconductor, which causes the electron gas remaining in the normal metal to cool down. The selective tunneling is made possible by the energy gap in the superconductor. The effect is analogous to blowing on a cup of coffee; the stream of air removes the hottest particles, which causes the coffee to cool down. The cooling power of a NIS junction is controlled by the voltage bias, so any temperature between the launch and base temperature is accessible by changing the voltage bias. Also, since individual NIS devices provide the cooling power, simply adding more junctions can increase the cooling power.

As a result of electron-phonon decoupling at sub-Kelvin temperatures, NIS refrigerators ordinarily cool the electrons, while the atomic lattice remains at roughly the same temperature. To cool the atomic lattice, we extended the normal metal containing the cold electrons onto a thin, thermally isolating membrane. Such a structure allows the NIS refrigerator to cool down the atomic lattice along with the electrons. The NIS junctions will then cool anything connected to the membrane. The downside to this technique is that the membrane is small and fragile, which makes it difficult to connect to other objects.

The ability of NIS junctions to behave as refrigerator is well known [1] but they have never been able to be used as a general refrigerator since scientists could not attach arbitrary payloads. The novel process, as described in Applied Physics Letters [2], was to make NIS refrigerators behave more like a general-purpose refrigerator, where the user can cool any arbitrary object, much like one can cool an arbitrary object inside a kitchen refrigerator. This was difficult because of the fragility of the membranes and the low cooling power of a single NIS device. To build a general-purpose refrigerator, we suspended a copper block with thin Kevlar cords to minimize stray power loads. This copper block was connected to the cooled membrane of the NIS refrigerator by tiny gold wires, which required extremely delicate microassembly to avoid breaking the fragile membrane.

Figure 1: Photograph of NIST's prototype solid-state refrigerator uses quantum physics in the square chip mounted on the green circuit board to cool the much larger copper platform (in the middle of the photo) below standard cryogenic temperatures. Other objects can also be attached to the platform for cooling.

Measurements of our refrigerator (see Figure 1) showed that over the course of about 18 hours, the copper block was cooled from 290mK to 256mK with about 700pW of cooling power at 290mK. This is the same fractional temperature reduction that is achieved by a kitchen refrigerator. One of the current refrigeration technologies used to reach sub-300mK temperatures, the dilution refrigerator, resembles a kitchen refrigerator in that it relies on compressors and pumps, which makes it complicated to use and prone to mechanical failure. In comparison, our NIS refrigerator is powered by quantum mechanics and has no moving parts. It only requires a small voltage bias to operate and can be powered off of a small battery. The simplicity of operation and relatively small size, several inches on a side, provide advantages over dilution and adiabatic demagnetization refrigerators.

Although we have demonstrated cooling a block of copper about one million times larger than the refrigerators themselves, these refrigerators aren’t quite ready for commercialization. We will improve the NIS refrigerators so they can cool from 300mK to 100mK by using more devices, and making more aggressive design choices. We can further expand the temperature range of our refrigerator using similar devices made of different materials. For example, electron coolers have demonstrated cooling from 1K to 400mK [3] and below 100mK [4] based on the same quantum mechanical principles. We can apply the same techniques to build general-purpose refrigerators based on these electron coolers. Eventually, our goal is to develop a composite, multi-stage cooler that can cool from 1K to below 100mK.

This work is supported by NASA.

References:
[1] Juha T Muhonen, Matthias Meschke and Jukka P Pekola, "Micrometre-scale refrigerators". Reports on Progress in Physics, 75, 046501 (2012). Abstract.
[2] Peter J. Lowell, Galen C. O'Neil, Jason M. Underwood, and Joel N. Ullom, "Macroscale refrigeration by nanoscale electron transport". Applied Physics Letters, 102, 082601 (2013). Abstract.
[3] O. Quaranta, P. Spathis, F. Beltram, and F. Giazotto, "Cooling electrons from 1 to 0.4 K with V-based nanorefrigerators", Applied Physics Letters, 98, 032501 (2011). Abstract.
[4] Galen C. O'Neil, Peter J. Lowell, Jason M. Underwood, and Joel N. Ullom, "Measurement and modeling of a large-area normal-metal/insulator/superconductor refrigerator with improved cooling", Physical Review B, 85, 134504 (2012). Abstract.

Experimental Boson Sampling

[From left to right] Part of the Oxford integrated quantum optics team: Steve Kolthammer,
Ben Metcalf, Merritt Moore, Peter Humphreys, Justin Spring, and Ian Walmsley

Authors: Steve Kolthammer, Justin Spring, Ian Walmsley

Affiliation: Department of Physics, University of Oxford, UK

A long-term ambition of many quantum physicists these days is to construct and understand large and complex quantum systems. This goal is driven in part by the notion that such systems have the potential to reveal interesting phenomena that cannot be studied by classical simulation. Such phenomena occur widely across the natural sciences, from biochemistry to condensed matter physics. The notion of complexity itself, however, is perhaps on firmest ground within the framework of computation. Here complexity refers to how the physical resources needed to achieve a particular task depend on the size of the task. Dramatic cases in which a quantum algorithm provides an exponential advantage over the best known classical algorithm make clear the potential for a quantum system to process information in ways that would eclipse even the most fantastically advanced classical machines.

Past 2Physics articles by this Group:
December 25, 2011: "Entang-bling" by Ian Walmsley and Joshua Nunn
August 07, 2011: "Building a Quantum Internet" by Joshua Nunn

Despite steady progress in manipulating and measuring simple quantum systems, a gulf remains between the theoretical promise of quantum computation and what has been shown in the laboratory. Bridging this divide requires not only further experimental advances but also the development of models of computation which are easier to test. In 2010, Scott Aaronson and Alex Arkhipov reported important progress toward the latter in a study of the computational power inherent in the quantum interference of indistinguishable, non-interacting bosons [1]. The specific problem they posed, termed boson sampling, is appealing due to its relatively straight-forward implementation with linear optical elements, such as beam splitters and phase shifters, sources of indistinguishable single photons, and single-photon detectors.

Importantly, this scheme does not require on-demand entanglement and feed-forward control, which are required for other approaches to linear-optical quantum computing and difficult to achieve in the laboratory. From a computational perspective, the key advance by Aaronson and Arkhipov was to show strong evidence that boson sampling is in fact interesting – that is, it cannot be solved efficiently by classical computation.

The essence of the boson sampling problem can be readily understood by examining the quantum machine which solves it. Our machine begins by injecting indistinguishable single photons into a linear optical network of single-mode waveguides. Due to quantum interference as the photons traverse the network, the photons emerge in a complicated entangled state. The positions of the photons are then measured by single-photon detectors. The machine bears some resemblance to the classical Galton board, illustrated below, in which balls randomly fall through an array of pegs. However, while these distinguishable classical balls take familiar, distinct paths down the board, rolling either left or right off of each peg they encounter, the photons in some sense collectively take all possible paths through their network.

Surprisingly, the interference of these paths makes it hard for a classical computer to predict where the photons tend to emerge! In the quantum case, the probability for a particular measurement outcome after N photons are injected into a network described by a unitary matrix U, is related to the permanent of a specific N x N submatrix of U. The permanent, a function of a matrix similar to the determinant, is noteworthy since its computation is hard. Aaronson and Arkhipov showed that an efficient classical algorithm that samples from a distribution of matrix permanents, precisely the task accomplished by the quantum machine, is very unlikely to exist.

Classical Galton board (left) and quantum boson sampling machine (right).

Last month, our group was one of two teams to report initial boson sampling experiments in Science [2, 3]. In fact, a remarkable interest in boson sampling became apparent last December when four groups - with experiments undertaken in Oxford, Brisbane, Vienna, and Rome - presented results on arXiv.org within the same week [2-5]. In our measurements, the principles of boson sampling were verified with three and four photons in a photonic chip. The photons were generated by degenerate parametric down-conversion, a nonlinear optical three-wave-mixing process, in a pair of crystals and coupled into a silica-on-silicon waveguide chip fabricated by our collaborators at the University of Southampton. The output from the chip was measured with single-photon avalanche photodiodes.

How closely did our quantum machine match an ideal boson sampling device? To address this issue we compared our measurements to the predictions of a classical computer, which is able to handle small boson sampling tasks. By extending the model of our machine to include a number of small, independently measured imperfections, such as rare multi-pair photon emission from a source, we verified that the machine ran as expected. In terms of quantum optics, our findings extend the well-studied Hong-Ou-Mandel quantum interference of two photons to processes with three and four photons. In terms of computation, we demonstrated the feasibility of running small-scale boson sampling tasks with the current experimental state of the art.

A striking feature of the boson sampling problem is that it appears to be amenable to the tools of complexity theorists as well as those of quantum experimenters. Meeting these disparate requirements is the crucial challenge to achieving a direct test of quantum computational power. Future work on boson sampling will benefit from an on-going effort to understand how unavoidable experimental imperfections relate to computational complexity. Meanwhile quantum optics labs, including our own, will continue to work towards experiments with increasing numbers of single photons. Extending our initial studies to ten photons should provide clear evidence for the computational power of this simple quantum machine, and a calculation with tens of photons could reach the frontier of quantum complexity which is inaccessible by classical computation.

References
[1] Scott Aaronson and Alex Arkhipov. “The Computational Complexity of Linear Optics”. Proceedings of the ACM Symposium on the Theory of Computing (ACM, New York, 2011), pp. 333-342. Download.
[2] Justin B. Spring, Benjamin J. Metcalf, Peter C. Humphreys, W. Steven Kolthammer, Xian-Min Jin, Marco Barbieri, Animesh Datta, Nicholas Thomas-Peter, Nathan K. Langford, Dmytro Kundys, James C. Gates, Brian J. Smith, Peter G. R. Smith, Ian A. Walmsley. “Boson Sampling on a Photonic Chip”. Science, 339, 798 (2013). Abstract.
[3] Matthew A. Broome, Alessandro Fedrizzi, Saleh Rahimi-Keshari, Justin Dove, Scott Aaronson, Timothy C. Ralph, Andrew G. White. “Photonic Boson Sampling in a Tunable Circuit”. Science, 339, 794 (2013). Abstract.
[4] Max Tillmann, Borivoje Dakić, René Heilmann, Stefan nolte, Alexander Szameit, Philip Walther. “Experimental Boson Sampling”. ArXiv:1212.2240 [quant-ph] (2012).
[5] Andrea Crespi, Roberto Oselame, Roberta Ramponi, Daniel J. Brod, Ernesto Galvão, Nicolò Spagnolo, Chiara Vitelli, Enrico Maiorino, Paolo Mataloni, Fabio Sciarrino. “Experimental Boson Sampling in Arbitrary Integrated Photonic Circuits”. ArXiv:1212.2783 [quant-ph] (2012).

Quantum Flutter: A Dance of an Impurity and a Hole in a Quantum Wire

[Clockwise from Top left]: Charles J. M. Mathy, Eugene Demler, Mikhail B. Zvonarev.

Authors: 
Charles J. M. Mathy^1,2, Mikhail B. Zvonarev^2,3,4, Eugene Demler²

Affiliation:
¹ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, USA
²Department of Physics, Harvard University, Cambridge, Massachusetts, USA
³Université Paris-Sud, Laboratoire LPTMS, UMR8626, Orsay, France,
⁴CNRS, Orsay, France.

What happens when a particle moves through a medium at a velocity comparable to the speed of sound? The consequences lie at the heart of several striking phenomena in physics. In aerodynamics, for example, an object experiencing winds close to the speed of sound may experience a vibration that grows with time called flutter, which can ultimately have dramatic consequences such as the destruction of aeroplane wings or the iconic Tacoma Narrows bridge collapse. Other examples of physics induced by fast motion include acoustic shock waves and Cerenkov radiation. What we addressed in our work [1] was the effect of fast disturbances in strongly interacting quantum systems of many particles, in a case where the particles are effectively restricted to move in one dimension known as a quantum wire.

When the interactions between particles are weak, quantum systems can sometimes be described by a simple hydrodynamic equation. For example, the Gross-Pitaevskii Equation (GPE) describes the evolution of a weakly coupled gas of bosons at low temperatures when it forms a Bose-Einstein condensate. The GPE is analogous to equations found in hydrodynamics, which explains why one can see analogs of classical hydrodynamical effects such as shock waves and solitons in these systems [2,3]. But what if the interactions are too strong and such an approximation breaks down?

We have found a model that shows interesting physics induced by supersonic motion which goes beyond a hydrodynamical description [1]. The system is a one-dimensional gas of hardcore bosons known as a Tonks-Girardeau gas (TG) [4]. We start the system in its ground state and inject a supersonic impurity that interacts repulsively with the background particles. We obtained exact results on what happens next using an approach from mathematical physics called the Bethe Ansatz approach, coupled with large-scale computing resources [5]. Thus we track the impurity velocity as a function of time and find two main surprising features. Firstly, the impurity does not come to a complete stop, instead it only sheds part of its momentum and keeps on propagating at a reduced velocity forever (Fig 1a). Secondly, the impurity velocity oscillates a function of time, a phenomenon we call quantum flutter as it arises from nonlinear interactions of a fast particle with its environment (see Fig. 1b).

Figure 1: Impurity momentum evolution and quantum flutter:
a, Schematic picture of our setup. Top: We start with a one-dimensional gas of hardcore bosons of mass m known as a Tonks Girardeau (TG) gas (red arrows), in its ground state. We then inject an impurity also of mass m with finite momentum Q (green arrow). Middle: The impurity loses part of its momentum by creating a hole around itself (sphere) and emitting a sound wave in the background gas (blue arrow). However it retains a finite momentum Q_sat after this process and carries on propagating without dissipation. Bottom: legend of the different characters in the story.
b, Time evolution of the expected momentum of the impurity, <P̂_↓(t)>. The momentum decays to a finite value Q_sat, and shows oscillations around Q_sat at a frequency we call ω_osc. The background gas has density ρ_↑, and we define a Fermi momentum k_F = πρ_↑, a Fermi energy E_F = k_F²/(2m) where m is the mass of the particles, and a Fermi time t_F = 1/E_F. Inset: zoom into the plot of <P̂_↓(t)> showing the oscillations we call quantum flutter.
c, Time evolution of the density of the background gas in the impurity frame. More precisely, shown is the density-density correlation function G_↓↑(x,t) = <ρ_↓(0,t) ρ_↑(x,t)> in units of ρ_↑/L where L is the system size, and the position along the wire is written in units of the interparticle distance ρ_↑^-1 in the background gas. Here ρ_↑ is the density of the background gas, and ρ_↓ the density of the impurity. G_↓↑(x,t) is effectively the density of the background gas with respect to the impurity position. We see the formation of the correlation hole around x ρ_↑ = 0 (blue valley), and the emission of the sound wave (red ridge). Underneath a schematic illustration of the dynamics is given: the blue arrow represents the emitted sound wave, the sphere is the hole, and the green arrow the impurity (see a). Inside the correlation hole the impurity and hole are dancing, meaning that they are oscillating with respect to each other, the phenomenon we denote as quantum flutter.

Using the exact methods just mentioned we were able to look in detail at the dynamical processes underlying quantum flutter. The time evolution of the impurity in the gas of bosons can be broken down into several steps. First the impurity carves out a depletion of the gas around itself, called a correlation hole. It expels the background density into a sound wave that carries away a large part of the momentum of the impurity, but not of all it (fig 1c). In fact the impurity retains part of its momentum and no longer sheds momentum because of kinematic constraints: there are no sound waves it can emit in the background gas while conserving momentum and energy.

After formation of the correlation hole, the impurity momentum starts to oscillate. When the dynamics of a quantum system shows a feature that is periodic in time, typically the frequency of the feature corresponds to an energy difference between two states of the system. Examples include light emission of an atom, or spin precession in response to a magnetic field, which underlies Nuclear Magnetic Resonance. In our case, the two states are an exciton and a polaron. The exciton corresponds to the impurity binding to a hole, since if the impurity repels the background gas, it is attracted to a hole (i.e. a missing particle in the background). The polaron is an impurity dressed due to interactions with the background particles, which affects its properties such as its effective mass: it becomes heavier as it carries a cloud of displaced background particles around it [6]. Thus we arrive at the following picture, as shown schematically in Fig. 2: first the impurity causes the emission of a sound wave in the background gas and creation of a hole close to it. It can bind to this hole and form an exciton, or not bind to it and form a polaron instead. In fact the impurity does both in the sense that it forms a quantum superposition of a polaron and an exciton. This quantum superposition leads to oscillations in the impurity velocity, a phenomenon called quantum beating, which is analogous to Larmor precession of a spin in a magnetic field. The difference here is that the two states that are beating, the exciton and polaron, are strongly entangled many-particle states. That we observe long-lived quantum coherence effects in a system composed of infinitely many particles is surprising. Namely, typically such systems exhibit decoherence, such that if one puts a particle in a quantum superposition of two states, the superposition decays because of interactions with other particles.

Figure 2: Origin of quantum flutter:
a, The quantum flutter oscillations originate from the formation of a superposition of entangled states of the impurity with its environment. After the impurity is injected in the system is creates a hole around itself. It can then bind to this hole and form an exciton, or not bind to it and form a state that is dressed with its environment called a polaron. In fact the system forms a coherent superposition of these two possibilities, which then leads a quantum beating and oscillations in the impurity momentum with a frequency given by the energy difference between these two possibilities.
b, Comparison between the frequency ω_osc of oscillations in the impurity momentum, and the energy difference between the polaron E(Pol(0)) and the exciton E(Exc(0)) (the zero between brackets refers to the exciton and polaron having momentum zero). The x-axis denotes the interaction strength between the impurity and the background particles: the interaction between a background particle at position x_i and the impurity at position x_↓ is a contact interaction of the form g δ(x_i - x_↓), and one defines the dimensionless interaction parameter γ = m g/ρ_↑. ℏω_osc and E(Pol(0))-E(Exc(0)) are in quantitative agreement, which motivates the interpretation of quantum flutter as quantum beating between exciton and polaron.

To see quantum flutter in the laboratory directly, one can use methods from the field of ultracold atoms, in which neutral atoms are cooled and trapped using a combination of lasers and magnetic fields. The trapping potential can be chosen to restrict the atoms to move along 1D tubes, and effectively behave like a TG gas [7,8]. The interaction between the particles can be tuned using a Feshbach resonance. Impurity physics in one-dimensional TG gases has already been studied [9,10,11]. The only added ingredient needed for quantum flutter is to create impurities at finite velocities, which can be done using two-photon Raman processes. Quantum flutter can be observed by measuring the expected impurity velocity as a function of time. Thus cold atom experiments could confirm our predictions, and one could vary different parameters of the model so see how robust quantum flutter is. Our preliminary calculations suggest that quantum flutter survives within a certain window of varying all the parameters in the theory such as the interaction between background particles, the relative mass of the impurity and the background particles, and the form of the interactions.

In summary, we have found an example of a system of many particles where injecting a supersonic impurity leads to the spontaneous formation of a long-lived quantum superposition state which travels through the system at a finite velocity. The question of which systems allow transport of quantum coherent states is important for quantum computing applications [12], and has surfaced in recent studies of quantum effects in biology [13]. Thanks to the advent of exact methods and the development of precise experiments in the study of many-particle quantum dynamics, we expect to see progress being made on this question in the near future.

References
[1] Charles J. M. Mathy, Mikhail B. Zvonarev, Eugene Demler. "Quantum flutter of supersonic particles in one-dimensional quantum liquids". Nature Physics, 8, 881 (2012). Abstract.
[2] A.M. Kamchatnov and L.P. Pitaevskii. "Stabilization of solitons generated by a supersonic flow of a bose-einstein condensate past an obstacle". Physical Review Letters, 100, 160402 (2008). Abstract.
[3] I. Carusotto, S.X. Hu, L.A. Collins, and A. Smerzi. "Stabilization of solitons generated by a supersonic flow of a bose-einstein condensate past an obstacle". Physical Review Letters, 97, 260403 (2006). Abstract.
[4] M. Girardeau. "Relationship between systems of impenetrable bosons and fermions in one dimension". Journal of Mathematical Physics, 1, 516 (1960). Abstract.
[5] Jean-Sébastien Caux. "Correlation functions of integrable models: a description of the abacus algorithm". Journal of Mathematical Physics, 50, 095214 (2009). Abstract.
[6] A.S. Alexandrov, S. Devreeze, and T. Jozef. "Advances in Polaron Physics". Springer Series in Solid-State Sciences, Vol. 159 (2010).
[7]  Toshiya Kinoshita, Trevor Wenger and David S. Weiss. "A quantum newton's cradle". Nature, 440, 900 (2006). Abstract.
[8] Toshiya Kinoshita, Trevor Wenger and David S. Weiss. "Observation of a one-dimensional tonks-girardeau gas". Science, 305, 1125 (2004). Abstract.
[9] Stefan Palzer, Christoph Zipkes, Carlo Sias, Michael Köhl. "Quantum transport through a tonks-girardeau gas". Physical Review Letters, 103, 150601 (2009). Abstract.
[10] P. Wicke, S. Whitlock, and N.J. van Druten. "Controlling spin motion and interactions in a one-dimensional bose gas". ArXiv:1010.4545 [cond-mat.quant-gas] (2010).
[11] J. Catani, G. Lamporesi, D. Naik, M. Gring, M. Inguscio, F. Minardi, A. Kantian, and T. Giamarchi. "Quantum dynamics of impurities in a one-dimensional bose gas". Physical Review A, 85, 023623 (2012). Abstract.
[12] D.V. Averin, B. Ruggiero, and P. Silvestrini. "Macroscopic Quantum Coherence and Quantum Computing". Plenum Publishers, New York (2000).
[13] Gregory S. Engel, Tessa R. Calhoun, Elizabeth L. Read, Tae-Kyu Ahn, Tomá Manal, Yuan-Chung Cheng, Robert E. Blankenship, Graham R. Fleming. "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems". Nature, 446, 782 (2007). Abstract.

Evidence of Majorana States in an Al Superconductor – InAs Nanowire Device

[From left to right] Moty Heiblum, Yuval Oreg, Anindya Das, Yonathan Most, Hadas Shtrikman, Yuval Ronen

Authors: Yuval Ronen, Anindya Das, Yonatan Most, Yuval Oreg, Moty Heiblum, and Hadas Shtrikman

Affiliation: Dept. of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

When a bridge between fields in physics is created, exciting physics can emerge. In 1962 Anderson walked on a bridge connecting condensed matter physics with particle physics, by introducing the Anderson mechanism in superconductivity to explain the Meissner effect. A similar idea was used on the other side of the bridge by Higgs in 1964, to explain the mechanism that generates the mass of elementary particles known as the Higgs mechanism. Nowadays, another bridge is formed between these two fields emanating from an idea first originated by Ettore Majorana in 1937 – where spin 1/2 particles can be their own anti-particles[1]. Back then, Majorana suggested the neutrino as a possible candidate for his prediction, and experiments such as double-beta decay are planned to test his prediction.

A link between Majorana’s prediction of new elementary particles and the field of condensed matter physics was formed already more than a decade ago. Quasi-particle excitations, which are equal to their anti-quasi-particle excitations, are predicted to be found in the solid. Specifically, in vortices that live in an esoteric two-dimensional P-wave spinless superconductor. Moreover, these excitations are expected to be inherently different from their cousins the elementary particles: they have non-abelian statistics. The non-abelian statistics is one of the beautiful triumphs of the physics of condensed matter.

This so far unobserved quasi-particle, that has non-abelian statistics, has for a while been a ‘holy grail’ in the fractional quantum Hall effect regime; with filling factor 5/2 being the most promising candidate for its observation. Lately, another realization of Majorana quasi-particles is pursued. It follows a 1D toy model presented by Kitaev in 2001, showing how one can isolate two Majorana states at two widely separated ends of a 1D P-wave spinless superconductor [2]. These two Majorana states are expected to sit in the gap of the superconductor (at the Fermi energy) for a wide range of system parameters. Seven years later, Fu and Kane [3] found that a P-wave spinless superconductor can be induced by an S-wave superconductor in proximity to a topological insulator, occurring in a semiconductor with an inversion gap. It was thus not long before two theoretical groups [4,5] provided a prescription for how to turn a 1D semiconductor nanowire into an effective Kitaev 1D spinless P-wave superconductor.

The prescribed system is a semiconductor nanowire, with strong spin-orbit coupling, coupled to an S-wave superconductor (a trivial superconductor, with Cooper pairs in a singlet state). Electrons from the semiconductor undergo Andreev reflections, a process which induces S-wave superconductivity in the nanowire. The induced superconductivity opens gaps in the nanowire spectrum around the Fermi energy, at momentums k=0 and k=k_F (the Fermi momentum), due to the two spin bands being separated by spin-orbit coupling. An applied magnetic field quenches the gap at k=0 while hardly affecting the gap at k_F (the Zeeman splitting competes with superconductivity at k=0, where spin-orbit coupling, being proportional to k, plays no role), creating an effective gap different from the one induced by superconductivity. A gate voltage is used to tune the chemical potential into the effective gap. When the Zeeman energy is equal to the induced superconducting gap, the effective gap at k=0 closes; it then reopens upon further increase of the magnetic field, bringing the nanowire into a so called ‘topological phase’. Kitaev’s original toy model of a 1D P-wave superconductor is then implemented (Fig. 1).

Figure 1: Energy dispersion of the InAs nanowire excitations (Bogoliubov-de Gennes spectrum), in proximity to the Al superconductor. Heavy lines show electron-like bands and light lines show hole-like bands. Opposite spin directions are denoted in blue and magenta (red and cyan) for the spin-orbit effective field direction (perpendicular direction), where a relative mixture denotes intermediate spin directions. (a) Split electronic spin bands due to spin-orbit coupling in the InAs wire. Spin-orbit energy defined as Δ_so, with the chemical potential μ measured with respect to the spin bands crossing at p=0. (b) With the application of magnetic field, B, perpendicular to the spin-orbit effective magnetic field, B_so a Zeeman gap, E_z= gμ_BB/2, opens at p=0. (c) Light curves for the hole excitations are added, and bringing into close proximity a superconductor opens up superconducting gaps at the crossing of particle and hole curves. The overall gap is determined by the minimum between the gap at p=0 and the gap at p_F, while for μ=0 and E_z close to Δ_ind the gap at p=0 is dominant. (d) As in (c) but E_z is increased so that the gap at p_F is dominant. (e) B is rotated to a direction of 30^o with respect to B_so. The original spin-orbit bands are shifted in opposite vertical directions, and the B component, which is perpendicular to B_so is diminished. (f) The evolution of the energy gap at p=0 (dotted blue), at p_F (dotted yellow), and the overall energy gap (dashed black) with Zeeman energy, E_z, for μ=0. The overall gap is determined by the minimum of the other two, where the p=0 gap is dominant around the phase transition, which occurs at E_z=Δ_ind. At high E_z the p_F gap, which is decreasing with E_z, becomes dominant.

Seventy five years after Majorana’s monumental paper, we may be close to a realization of a quasi-particle that is identical to its anti-quasi-particle, possessing non-abelian statistics. Several experimental groups [6,7,8] follow the prescribed recipe for a 1D P-wave spinless superconductor[4,5], with our group being one of them. A zero energy conductance peak, at a finite Zeeman field, had been seen now in InSb and InAs nanowires in proximity to Nb and Al superconductors, respectively. This peak is considered a signature for the existence of a Majorana quasi-particle, since the Majorana resides at the Fermi energy.

Figure 2: Structure of the Al-InAs structures suspended above p-type silicon covered with 150nm SiO₂. (a) Type I device, the nanowire is supported by three gold pedestals, with a gold ‘normal’ contact at one edge and an aluminum superconducting contact at the center. The conductive Si substrate serves as a global gate (GG), controlling barrier as well as the chemical potential of the nanowire. Two narrow local gates (RG and LG), 50nm wide and 25nm thick, displaced from the superconducting contact by 80nm, also strongly influence the barrier height as well as the chemical potential in the wire. (b) Type II device, similar to type I device, but without the pedestal under the Al superconducting contact. This structure allows control of the chemical potential under the Al contact. (c) SEM micrograph of type II device. A voltage source, with 5 Ohm resistance, provides V_SD, and closes the circuit through the ‘cold ground’ (cold finger) in the dilution refrigerator. Gates are tuned by V_GG and V_RG to the desired conditions. Inset: High resolution TEM image (viewed from the <1120> zone axis) of a stacking faults free, wurtzite structure, InAs nanowire, grown on (011) InAs in the <111> direction. TEM image is courtesy of Ronit Popovitz-Biro. (d) An estimated potential profile along the wire. The two local gates (LG and RG) and global gate (GG) determine the shape of the potential barriers; probably affect the distance between the Majoranas.

Our work, with MBE grown InAs nanowire in proximity to an Al superconductor [8] (Fig 2), demonstrated a zero bias peak and several more interesting features in the parameters' space. First, the closing of the gap at k=0 was clearly visible when the Zeeman energy was equal to the induced gap. Second, splitting of the zero-bias-peak was observed at low and high Zeeman field; likely to result from spatial coupling of the two Majorana states. Third, the zero-bias-peak was found to be robust in a wide range of chemical potential (assumed to be within the k=0 gap). While these observations agree with the presence of a Majorana quasi-particle (though the peak height is much smaller than expected, maybe due to the finite temperature of the experiment), the available data does not exclude other effects that may result with a similar zero bias peak (such as, interference, disorder, multi-bands, Kondo correlation).

Quoting Wilczek: “Whatever the fate of these particular explorations, there is no doubt that Majorana's central idea, which long seemed peripheral, has secured a place at the core of theoretical physics"[9].

References:
[1] Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract.
[2] A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article.
[3] Liang Fu and Charles Kane, "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator", Physical Review Letters 100, 096407 (2008). Abstract.
[4] Roman M. Lutchyn, Jay D. Sau and Sankar Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Physical Review Letters, 105, 077001 (2010). Abstract.
[5] Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
[6] V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science 336, 1003 (2012). Abstract. 2Physics Article.
[7] M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, H. Q. Xu, "Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device", arXiv: 1204.4130 (2012).
[8] Anindya Das, Yuval Ronen, Yonathan Most, Yuval Oreg, Hadas Shtrikman, Moty Heiblum, "Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions", Nature Physics, 8, 887–895 (2012). Abstract.
[9] Frank Wilczek, "Majorana Returns", Nature Physics, 5, 614 (2009). Abstract.

Observation of Entanglement Between a Quantum Dot Spin and a Single Photon

[From left to right] Parisa Fallahi, Atac Imamoglu, Javier Miguel-Sanchez, Wei-bo Gao, Emre Togan















Authors: Wei-bo Gao, Parisa Fallahi, Emre Togan, Javier Miguel-Sanchez, Atac Imamoglu

Affiliation: Institute of Quantum Electronics, ETH Zurich, Switzerland

Entanglement deepens our understanding of fundamental physics. A well-known example is the study of non-local interpretations of quantum mechanics by testing the violation of Bell’s inequality [1]. In the practical side, an interface between a stationary qubit (spin) and a flying qubit (photon) is a basic element to build a distributed quantum network. Moreover, such a network can be used for building a quantum computer, that offers significant speedups in solving certain technologically relevant classes of problems. A realization of distributed quantum computation will use few-qubit quantum processor nodes (spins) connected by photons [2]. A particularly interesting platform is a spin based semiconductor system in which photonic circuits that interconnect the nodes can be fabricated on the same semiconductor chip [3].

In the past few years, considerable efforts have been made to demonstrate entanglement between a spin and a photon. In 2004, the first observation of entanglement between a single trapped atom and a single photon was realized in the group of C. Monroe in Michigan [4]. In 2006 and 2007, the entanglement between a neutral atom and a single photon was realized in the groups of H. Weinfurter [5] G. Rempe [6] in Germany. In 2010, entanglement between an N-V center and a single photon was reported [7]. Despite the appeal of semiconductor based systems the realization of spin-photon entanglement in these systems had been very challenging mainly due to fast transitions and strong decoherence of the quantum dot spins and has only been achieved in 2012. In our work as well as the complementary work of the Yamamoto group at Stanford, the difficulty of measurement was overcome and the first semiconductor spin-photon entanglement was reported [8, 9].

Our experiment focuses on a single electron spin trapped in an InGaAs self-assembled quantum dot. A magnetic field of 0.7 Tesla applied perpendicular to the sample growth direction. The ground states of the quantum dot are identified by the orientation of the electron spin. The basic principle behind the deterministic generation of a spin–photon entangled state is straightforward: following the excitation of the quantum dot into an excited (trion) state, radiative recombination will project the system into an entangled state where the color and polarization of the emitted photon are entangled with the spin of the electron in the ground state. Our measurement process entails suppression of the laser background using cross polarized excitation and collection, thus erasing the polarization information of the quantum dot photons. We therefore focus on the entanglement between the spin qubit and the color (frequency) of the photonic qubit.

To demonstrate entanglement we measure both classical and quantum correlations between the electron spin and the color of the emitted photon. Quantum correlations are demonstrated through observation of oscillations in the emitted photon counts conditioned on detecting a spin in a superposition of up and down spins. By reversing the spin projection direction, we observe a Pi-phase change in the oscillation. These oscillations originate from a phase shift between the two components of the entangled state as the time between photon emission and spin measurement is changed. We calculate an overall entanglement fidelity with a lower bound of 0.67±0.05 , which is above 0.5 and thus constitutes a proof for entanglement in our system.

Semiconductor quantum dots have many advantages compared to the other candidates for optically accessible qubits. For example, majority of the photons are emitted into the zero phonon line making them bright, narrow bandwidth single-photon sources. Also fast spin manipulation of the spin states (~4ps) is possible, and the spontaneous emission time is short (~600ps), making a repetition rate of 76MHz possible in our experiment. There are, however, also drawbacks: the dephasing time of the spin states is about 1ns, limiting the useful time window in the entanglement generation. Moreover, lack of a cycling transition, reduces the likelihood of being able to determine the spin state at a single experimental run, limiting efficient scaling to more spins. Luckily these drawbacks can be overcome by using coupled quantum dot systems that have much richer transition structure and the spin qubits can be more robust against the noisy environment [10]. We aim to achieve spin-spin entanglement in the coupled quantum dot systems in the near future.

References:
[1] Alain Aspect, Philippe Grangier, and Gérard Roger, "Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: a new violation of Bell’s inequalities", Physical Review Letters, 49, 91–94 (1982). Abstract.
[2] H. J. Kimble, "Quantum Internet", Nature 453, 1023 (2008). Abstract.
[3] K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, "Quantum nature of a strongly coupled single quantum dot-cavity system", Nature, 445, 896–899 (2007). Abstract.
[4] B. B. Blinov, D. L. Moehring, L.-M. Duan, C. Monroe, "Observation of entanglement between a single trapped atom and a single photon", Nature 428, 153–157 (2004). Abstract.
[5] Jürgen Volz, Markus Weber, Daniel Schlenk, Wenjamin Rosenfeld, Johannes Vrana, Karen Saucke, Christian Kurtsiefer, Harald Weinfurter, "Observation of entanglement of a single photon with a trapped atom", Physical Review Letters, 96, 030404 (2006). Abstract.
[6] Tatjana Wilk, Simon C. Webster, Axel Kuhn, Gerhard Rempe, "Single-atom single-photon quantum interface", Science, 317, 488–490 (2007). Abstract.
[7] E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, M. D. Lukin, "Quantum entanglement between an optical photon and a solid state spin qubit", Nature, 466, 730–734 (2010). Abstract.
[8] W. B. Gao, P. Fallahi, E. Togan, J. Miguel-Sanchez, A. Imamoglu, "Observation of entanglement between a quantum dot spin and a single photon", Nature, 491, 426–430 (2012). Abstract.
[9] Kristiaan De Greve, Leo Yu, Peter L. McMahon, Jason S. Pelc, Chandra M. Natarajan, Na Young Kim, Eisuke Abe, Sebastian Maier, Christian Schneider, Martin Kamp, Sven Höfling, Robert H. Hadfield, Alfred Forchel, M. M. Fejer, Yoshihisa Yamamoto, "Quantum-dot spin–photon entanglement via frequency down conversion to telecom wavelength", Nature, 491, 421–425 (2012). Abstract.
[10] K. M. Weiss, J. M. Elzerman, Y. L. Delley, J. Miguel-Sanchez, A. Imamoğlu, "Coherent Two-Electron Spin Qubits in an Optically Active Pair of Coupled InGaAs Quantum Dots", Physical Review Letters, 109, 107401 (2012). Abstract.

Quantum Statistics From Outside Space And Time

[From left to right] 
Front row: Yeong-Cherng Liang (Geneva), Jean-Daniel Bancal (then Geneva, now Singapore); 
Middle row: Antonio Acin (Barcelona), Nicolas Gisin (Geneva); 
Back row: Valerio Scarani (Singapore), Stefano Pironio (Brussels).







Authors:
Jean-Daniel Bancal^1,5, Stefano Pironio², Antonio Acin^3,4, Yeong-Cherng Liang¹, Valerio Scarani⁵, Nicolas Gisin¹

Affiliations:
¹Group of Applied Physics, University of Geneva, Switzerland
²Laboratoire d’Information Quantique, Université Libre de Bruxelles, Belgium
³ICFO-Institut de Ciències Fotòniques, Castelldefels (Barcelona), Spain
⁴ICREA-Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain
⁵Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore

Quantum theory predicts what nature does with unparalleled scope and accuracy. In the new perspective of quantum information, one can add that quantum theory predicts what nature can do for you. But the theory is silent about how nature does it. This silence is at the heart of the uneasiness that some scientists and most laypersons have felt, and continue feeling, when confronted with quantum physics.

Einstein, for one, believed that this silence was only a temporary feature of the then-newly born formalism. He was confident that, with time, someone would find an explanation for quantum phenomena in terms of mechanisms in space-time. However, the passing of time brought physics further from Einstein’s wishes: in 1964, John Bell proved that quantum theory is incompatible with pre-established agreement. Indeed, some predictions of the theory violate a criterion called Bell inequality. Whenever this happens, we are certain that the results of measurements were certainly not pre-recorded in the physical systems. This violation has been clearly observed in several experiments, since Aspect’s pioneering one in 1982.

Past 2Physics article by Antonio Acín:
August 19, 2012: "Testing the Dimension of Classical and Quantum Systems" by Martin Hendrych, Rodrigo Gallego, Michal Mičuda, Nicolas Brunner, Antonio Acín, Juan P. Torres

The violation of Bell inequalities puts severe constraints on Einstein’s hope: any mechanism in space-time that reproduces quantum predictions must involve superluminal influences – exactly what Einstein wanted to avoid at all cost! The faster-than-light character comes from the fact that the predictions of quantum theory, as well as the observed experimental results, are unchanged if the measurement events are space-like separated.

For many physicists, once the obscene word “superluminal” is uttered, all speech must cease. Others, less definite at the moment of telling nature how to behave, were ready to give some credit to a mechanistic explanation, but under one condition: it must not be possible for us to use these influences to send actual messages faster than light. In other words, to be acceptable by the physics community, the hypothetical influences must at least be “hidden”. Abner Shimony coined the expression “peaceful coexistence” between relativity and the violation of Bell inequalities. There did not seem to be much more to be said on the topic, apart from noticing that the Bohmian presentation of quantum theory uses precisely hidden influences in the updating of its “quantum potential”.

In our recent work, we show that the constraint can be strengthened to the extreme: any finite-speed influence would lead to the possibility of sending messages faster than light, in blatant violation of relativity. The price to pay for peaceful coexistence is to accept influences that propagate at infinite speed, making the quantum universe fully connected, while conspiring to remain hidden from us.

In order to understand the generality of our result, let us first stress one point: if the goal would be to reproduce all the predictions of quantum theory as we know it, it is already obvious that the speed must be infinite. Indeed, finite-speed influences would certainly lead to deviations from quantum predictions, depending on the space-time configuration: for instance, if the measurement events cannot be connected by the influence, one should never observe a violation of Bell inequalities. In this work, we decided not to erect quantum theory to the rank of untouchable truth: we accepted finite-speed influences as working assumption, together with the required deviations from the predictions of our present-day formalism. We only assumed that, if the influences have the time to propagate from one measurement event to the next, quantum statistics are produced (because this is what is observed). Even in such a flexible scenario, we were able to prove that ultimately finite-speed influences cannot be hidden. Further, the conclusion can be reached using only observable statistics: it is not only theory-independent, but also “device-independent”.

Illustration of how to obtain a constraint on finite-speed models with three particles

The trick consists in devising a suitable multi-partite configuration, because no conclusion can be reached in the more familiar bipartite scenario. The idea of the argument can be sketched with three parties (see figure). The diagrams are drawn in the preferred frame in which the hypothetical influences propagate. Configuration (a) is such that the influences propagate from A to B, then from B to C: in this case, we request that quantum statistics are recovered. In configuration (b), A and B do not receive each other’s influence, while C receives the influences from both A and B. Now:

• On the one hand, according to the role of influences in this model, a possible violation of Bell inequalities by A and B in configuration (a) should cease if the observers change to configuration (b) e.g. by advancing B’s measurement. 
• On the other hand, for the influences to be hidden, the statistics AC and BC must be the same in both configurations.

The contradiction can be reached by finding marginal statistics AC and BC, whose possible three-partite extension are necessarily such that AB violates some Bell inequality. As it turns out, we have not found such an example with three parties, but a similar one involving four particles.

In conclusion: assuming that some quantum statistics can be observed, a classical mechanism that explains them must not only use superluminal influences: either it uses infinite-speed influences, or it allows us to send messages faster than light. Both alternatives are mind-boggling? Well, there is a reason why physicists prefer to skip the issue of “how nature does it”.

The history of an idea, with three references:

•  The idea is already ten years old, but at that time we did not have the mathematical tools to find a complete proof: Valerio Scarani, Nicolas Gisin, "Superluminal influences, hidden variables, and signaling", Physics Letters A, 295, 167 (2002). Abstract.
• We resumed working on this project in February 2011. Two weeks later appeared in the arXiv a nice breakthrough: Sandro Coretti, Esther Hänggi, Stefan Wolf, "Nonlocality is transitive", Physical Review Letters, 107, 100402 (2011).  Abstract. Wolf and coworkers had found a proof for “no-signaling statistics”. Those statistics cannot be obtained with quantum physics, so the final challenge remained open; nevertheless, this work showed that there is real hope of finding a proof. 
• Our proof for quantum statistics is: J-D. Bancal, S. Pironio, A. Acín, Y-C. Liang, V. Scarani, N. Gisin, "Quantum non-locality based on finite-speed causal influences leads to superluminal signaling", Nature Physics, 8, 867 (2012). Abstract.