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2Physics Quote:
"Beyond the fundamental interest on the limit of quality-factors given a certain volume, there is a sustained interest in reducing the footprint of many cavity-based devices for future Photonic Integrated Circuits or PICs. Tailoring the optical potential further, for example by moving away from perfectly periodic structures, opens the possibility improving the field confinement and thus shrink devices."
-- Thomas Lepetit and Boubacar Kanté (Read full article: "Novel Electromagnetic Cavities: Bound States in the Continuum" )

Sunday, March 29, 2015

Photo-activated Biological Processes As Quantum Measurements

Birgitta Whaley (left) and Atac Imamoglu

Authors: Atac Imamoglu1, Birgitta Whaley2

1Institute of Quantum Electronics, ETH Zurich, Switzerland,
2Berkeley Quantum Information and Computation Center, Department of Chemistry, University of California, Berkeley, USA.

Image credit: Ilya Sinayskiy
Our current understanding of the physical world around us is based on quantum mechanics. It is natural in this framework to argue that at the molecular level, biological processes are also governed by the laws of quantum mechanics. This reasoning in turn implies that at short enough length and/or time scales the dynamics can exhibit counter-intuitive features, such as the molecule/system being in a coherent superposition of distinguishable states. A key question of fundamental interest is whether there are biological systems for which these microscopic dynamical quantum features help or enable the biological function [1-3]. Two processes that have been extensively studied in this context are light harvesting in photosynthesis and sensing of the inclination of the earth’s magnetic field by migrating birds.

Past 2Physics article by Atac Imamoglu :
December 23, 2012: "Observation of Entanglement Between a Quantum Dot Spin and a Single Photon" by Wei-bo Gao, Parisa Fallahi, Emre Togan, Javier Miguel-Sanchez, Atac Imamoglu.

Our work brings a new perspective to the analysis of these processes by embedding them in a quantum measurement context, where the biological system is modelled as a measurement device that is subject to the laws of quantum mechanics (i.e., a quantum meter) [4]. The function of this quantum meter is to measure an external classical stimulus, which is thereby equivalent to the biological sensing of this stimulus. We have analyzed several photo-activated biological processes within this formulation and find that these processes fall into two distinct classes.

In the first category, the measurement interaction induces changes in the system state at a rate that is proportional to the strength of the external stimulus. In this case, we find that while the presence of quantum coherence during the measurement interaction may result in a small enhancement of the rate that increases at most linearly with the increasing coherence time, it is however not essential for the biological function that results from the sensing of this stimulus.

By contrast, in the second category, the measurement interaction does not directly lead to an excitation rate that is proportional to the strength of the external stimulus. Instead, it is the quantum coherent evolution after the optical excitation that controls the sensitivity of the biological system to the stimulus. Most importantly, in this category, unless there is some quantum coherent dynamics after the photoactivation, there is vanishing sensitivity to the signal to be measured. Another difference is that depending on the specific nature of this coherent evolution, more detailed information about the signal than just its strength can be transmitted to the biological receptors.

The extensively studied process of photosynthesis [see, e.g., 1-3, 5-7] as well as the process of human vision [8,9] both belong to the first category. In contrast, the proposed hypothesis of a radical pair mechanism [10,11] for sensing of the inclination of the earth’s magnetic field by migratory birds belongs to the second category. An essential component of this mechanism is the coherent oscillation between singlet and triplet radical pairs in which the paired electrons are separated by several nanometers and are thus formally entangled over non-trivial distances. The chemical reactivity of the radical pair is different in the singlet and triplet states, resulting in a chemical signature of the non-equilibrium quantum dynamics induced by the quantum coherent dynamics.

While much indirect chemical evidence exists for this hypothesis, experimental validation in birds is challenging and, despite many plausibility arguments, no clear evidence for the validity of this hypothesis in migratory birds has been established thus far. It therefore remains an intriguing and open question today, as to whether there are biological sensing processes that can function only if quantum coherence is preserved on some extended time scale.

[1] Graham R. Fleming, Gregory D. Scholes, Yuan-Chung Cheng, “Quantum effects in biology”, Procedia Chemistry, 3, 38 (2011). Abstract.
[2] Neill Lambert, Yueh-Nan Chen, Yuan-Chung Cheng, Che-Ming Li, Guang-Yin Chen, Franco Nori, “Quantum biology”, Nature Physics, 9, 10 (2013). Abstract.
[3] M. Mohseni, Y. Omar, G. Engel, M. Plenio (Eds.), "Quantum effects in biology" (Cambridge University Press, 2014). 
[4] A. Imamoglu, K. B. Whaley, “Photo-activated biological processes as quantum measurements”, Physical Review E, 91,022714 (2015). Abstract.
[5] Rienk van Grondelle, Vladimir I. Novoderezhkin, “Quantum effects in photosynthesis”, Procedia Chemistry, 3, 198 (2011). Abstract.
[6] Konstantin E. Dorfman, Dmitri V. Voronine, Shaul Mukamel, Marlan O. Scully, “Photosynthetic reaction center as a quantum heat engine”, Proceedings of the National Academy of Sciences of USA, 110, 2746 (2013). Abstract.
[7] Aurélia Chenu, Gregory D. Scholes, “Coherence in energy transfer and photosynthesis”, Annual Review of Physical Chemistry, 66, 69 (2015). Abstract.
[8] F. Rieke, D. A. Baylor, “Single-photon detection by rod cells of the retina”, Review of Modern Physics, 70, 1027 (1998). Abstract.
[9] Philipp Kukura, David W. McCamant, Sangwoon Yoon, Daniel B. Wandschneider, Richard A. Mathies,”Structural observation of the primary isomerization in vision with femtosecond-stimulated Raman”, Science, 310, 1006 (2005). Abstract.
[10] Thorsten Ritz, Salih Adem, Klaus Schulten, “A model for photoreceptor-based magnetoreception in birds”, Biophysical Journal, 78, 707 (2000). Full Article.
[11] Kiminori Maeda, Alexander J. Robinson, Kevin B. Henbest, Hannah J. Hogben, Till Biskup, Margaret Ahmad, Erik Schleicher, Stefan Weber, Christiane R. Timmel, P.J. Hore, “Magnetically sensitive light-induced reactions in cryptochrome are consistent with its proposed role as a magnetoreceptor”, Proceedings of the National Academy of Sciences, 109, 4774 (2012). Abstract.

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Sunday, March 22, 2015

Quantum Teleportation of Multiple Properties of A Single Quantum Particle

Jian-Wei Pan (left) and Chao-Yang Lu

Authors: Chao-Yang Lu, Jian-Wei Pan

CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.

The science fiction dream of teleportation [1] is to transport an object by disintegrating in one place and reappearing intact in another distant location. If only classical information is of interest, or if the object could be fully characterized by classical information—which can in principle be precisely measured—the object can be perfectly reconstructed (copied) remotely from the measurement results. However, for microscopic quantum systems such as single electrons, atoms or molecules, their properties are described by quantum wave functions that can be in superposition states. Perfect measurement or cloning of the unknown quantum states is forbidden by the law of quantum mechanics.

In 1993, Bennett et al. [2] proposed a quantum teleportation scheme to get around this roadblock. Provided with a classical communication channel and shared entangled states as a quantum channel, quantum teleportation allows the transfer of arbitrary unknown quantum states from a sender to a spatially distant receiver, without actual transmission of the object itself. Quantum teleportation has attracted a lot of attention not only from the quantum physics community as a key element in long-distance quantum communication, distributed quantum networks and quantum computation, but also the general audience, probably because of its connection to the scientific fiction dream in Star Trek. An interesting question is frequently asked: “would it be possible in the future to teleport a large object, say a human?” Before attempting to seriously answer that question, let us take steps back, look at where we actually are and think about a much, much easier and fundamental question: have we teleported multiple, or all degrees of freedom (DOFs) that fully describe a single particle, thus truly teleporting it intact? The answer is NO.

Past 2Physics article by Chao-Yang Lu and/or Jian-Wei Pan :

January 04, 2015: "Achieving 200 km of Measurement-device-independent Quantum Key Distribution with High Secure Key Rate" by Yan-Lin Tang, Hua-Lei Yin, Si-Jing Chen, Yang Liu, Wei-Jun Zhang, Xiao Jiang, Lu Zhang, Jian Wang, Li-Xing You, Jian-Yu Guan, Dong-Xu Yang, Zhen Wang, Hao Liang, Zhen Zhang, Nan Zhou, Xiongfeng Ma, Teng-Yun Chen, Qiang Zhang, Jian-Wei Pan

June 30, 2013: "Quantum Computer Runs The Most Practically Useful Quantum Algorithm" by Chao-Yang Lu and Jian-Wei Pan.

Although extensive efforts have been undertaken in the experimental demonstrations of teleportation in various physical systems, including photons [3], atoms [4], ions [5], electrons [6], and superconducting circuits [7], all the previous experiments shared one fundamental limitation: the teleportation only transferred one degree of freedom (DOF). This is insufficient for complete teleportation of an object, which could naturally possess many DOFs. Even in the simplest case, for example, a single photon, the elementary quanta of electromagnetic radiation, has intrinsic properties including its frequency, momentum, polarization and orbital angular momentum. A hydrogen atom—the simplest atom—has principle quantum number, spin and orbital angular momentum of its electron and nuclear, and various couplings between these DOFs which can result in hybrid entangled quantum states.

Complete teleportation of an object would require all the information in various DOFs are transferred at a distance. Quantum teleportation is a linear operation applied to the quantum states, thus teleporting multiple DOFs should be possible in theory. Experimentally, however, it poses significant challenges in coherently controlling multiple quantum bits (qubits) and DOFs. Hyper-entangled states—simultaneous entanglement among multiple DOFs—are required as the nonlocal quantum channel for teleportation. Moreover, the teleportation also necessitates unambiguous discrimination of hyper-entangled Bell-like states from a total number of 4N (N is the number of the DOFs). Bell-state measurements would normally require coherent interactions between independent qubits, which can become more difficult with multiple DOFs, as it is necessary to measure one DOF without disturbing another one. With linear operations only, previous theoretical work has suggested that it was impossible to discriminate the hyper-entangled states unambiguously.

We have taken a first step toward simultaneously teleporting multiple properties of a single quantum particle [8]. In the experiment, we teleport the composite quantum states of a single photon encoded in both the polarization—spin angular momentum (SAM) — and the orbital angular momentum (OAM). We prepare hyper-entangled states in both DOFs as the quantum channel for teleportation. By exploiting quantum non-demolition measurement, we overcome the conventional wisdom to unambiguously discriminate one hyper-entangled state out of the 16 possibilities. We verify the teleportation for both spin-orbit product states and entangled state of a single photon, and achieve an overall fidelity of 0.63 that well exceeds the classical limit.
Figure 1: Scheme for quantum teleportation of the spin-orbit composite states of a single photon. Alice wishes to teleport to Bob the quantum state of a single photon 1 encoded in both its SAM and OAM. To do so, Alice and Bob need to share a hyper-entangled photon pair 2-3. Alice then carries out an h-BSM assisted by teleportation-based QND measurement with an ancillary entangled photon pair.

Figure 1 illustrates our linear optical scheme for teleporting the spin-orbit composite state. The h-BSM is implemented in a step-by-step manner. First, the two photons, 1 and 2, are sent through a polarizing beam splitter (PBS). Secondly, the two single photons out of the PBS are superposed on a beam splitter (BS, see Fig.1a). Only the asymmetric Bell state will lead to a coincidence detection where there is one and only one photon in each output, whereas for the three other symmetric Bell state, the two input photons will coalesce to a single output mode. In total, these two steps would allow an unambiguous discrimination of the two hyper-entangled Bell states. To connect these two interferometers, we exploit quantum non-demolition (QND) measurement—seeing a single photon without destroying it and keeping its quantum information intact. Interestingly, quantum teleportation itself can be used for probabilistic QND detection. As shown in Fig.1 left inset, another pair of photons entangled in OAM is used as ancillary. The QND is a standard teleportation itself.
Figure 2: Experimental setup for teleporting multiple properties of a single photon. Passing a femtosecond pulsed laser through three type-I β-barium borate (BBO) crystals generates three photon pairs, engineered in different forms. The h-BSM for the photons 1 and 2 are performed in three steps: (1) SAM BSM; (2) QND measurement; (3) OAM BSM.

Figure 2 shows the experimental setup for the realization of quantum teleportation of the spin-orbit composite state of a single photon. We prepare five different initial states to be teleported (see Fig. 3 left inset), which can be grouped into three categories: product states of the two DoFs in the computational basis, products states of the two DoFs in the superposition basis, and a spin-orbit hybrid entangled state. To evaluate the performance of the teleportation, we measure the teleported state fidelity
defined as the overlap of the ideal teleported state (|φ >) and the measured density matrix. The teleportation fidelities for |φ >A, |φ >B, |φ >C, |φ >D and |φ >E yield 0.68±0.04, 0.66±0.04, 0.62±0.04, 0.63±0.04, and 0.57±0.02, respectively. Despite these experimental noise, the measured fidelities of the five teleported states are all well beyond 0.40—the classical limit, defined as the optimal state estimation fidelity on a single copy of a two-qubit system. These results prove the successful realization of quantum teleportation of the spin-orbit composite state of a single photon. Furthermore, for the entangled state |φ >E, we emphasize that the teleportation fidelity exceeds the threshold of 0.5 for proving the presence of entanglement, which demonstrates that the hybrid entanglement of different DoFs inside a quantum particle can preserve after the teleportation.
Figure 3: Experimental results for quantum teleportation of spin-orbit entanglement of a single photon. The fidelities are above the classical limit and entanglement limit.

Our methods can in principle be generalized to more DOFs, for instance, involving the photon’s momentum, time and frequency. The efficiency of teleportation can be enhanced by using more ancillary entangled photons, quantum encoding, embedded teleportation tricks, and high-efficiency single-photon detectors. The multi-DOF teleportation protocol is by no means limited to this system, but can also be applied to other quantum systems such as trapped electrons, atoms, and ions, which can be expected to be tested in the near future. Besides the fundamental interest, the developed methods in this work on the manipulation of quantum states of multiple DOFs will open up new possibility in quantum technologies.

[1] Anton Zeilinger, "Quantum teleportation". Scientific American, 13, 34–43 (2003). Link.
[2] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, William K. Wootters, "Teleporting an unknown quantum state via dual classic and Einstein-Podolsky-Rosen channels". Physical Review Letters, 70, 1895–1899 (1993). Abstract.
[3] Dik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter, Anton Zeilinger, "Experimental quantum teleportation". Nature, 390, 575–579 (1997). Abstract.
[4] Xiao-Hui Bao, Xiao-Fan Xu, Che-Ming Li, Zhen-Sheng Yuan, Chao-Yang Lu, Jian-Wei Pan, "Quantum teleportation between remote atomic-ensemble quantum memories", Proceedings of the National Academy of Sciences of the USA, 109, 20347–20351 (2012). Abstract.
[5] M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, D. J. Wineland, "Deterministic quantum teleportation of atomic qubits". Nature, 429, 737–739 (2004). Abstract.
[6] W. Pfaff, B. J. Hensen, H. Bernien, S. B. van Dam, M. S. Blok, T. H. Taminiau, M. J. Tiggelman, R. N. Schouten, M. Markham, D. J. Twitchen, R. Hanson, "Unconditional quantum teleportation between distant solid-state quantum bits". Science, 345, 532–535 (2014). Abstract.
[7] L. Steffen, Y. Salathe, M. Oppliger, P. Kurpiers, M. Baur, C. Lang, C. Eichler, G. Puebla-Hellmann, A. Fedorov, A. Wallraff, "Deterministic quantum teleportation with feed-forward in a solid state system". Nature. 500, 319–322 (2013). Abstract.
[8] Xi-Lin Wang, Xin-Dong Cai, Zu-En Su, Ming-Cheng Chen, Dian Wu, Li Li, Nai-Le Liu, Chao-Yang Lu, Jian-Wei Pan, "Quantum teleportation of multiple degrees of freedom of a single photon". Nature, 518, 516-519 (2015). Abstract.


Sunday, March 15, 2015

Radioactive Iron - An Astrophysical Clock for Nucleosynthesis

Anton Wallner (photo credit: Stuart Hay, ANU)

Author: Anton Wallner1,2

1Dept of Nuclear Physics, Australian National University, Canberra, Australia,
2VERA Laboratory, Faculty of Physics, University of Vienna, Austria.

Massive stars may end their life in a supernova explosion - one of the most violent events in our galaxy. Supernovae are thus massive exploding stars that return a large fraction of the star’s material back to the interstellar medium. Nucleosynthesis in massive stars shapes therefore the elemental abundance pattern and the galactic chemical evolution, e.g. our solar system is the product of many preceding star generations [1].

Extraterrestrial material in the form of interstellar dust can also enter the solar system and may be deposited on Earth [2]. Their nucleosynthetic history is locked in its isotopic signatures. Interstellar matter will contain stable isotopes but also freshly produced radionuclides. Thus, the existence of fresh radionuclides in the interstellar medium serves as radioactive clocks for their recent production.

Radioactive iron-60 (Fe-60) is a radionuclide with a half-life of about 2 million years. It is predominantly formed in massive stars at the end of their lives just before and during a supernova and then distributed by the explosion into the interstellar space. Fe-60 is thus an ideal candidate to monitor supernova explosions and recent element synthesis.

Since this radioactive iron is not naturally present on Earth, trace amounts of this isotope are a particularly sensitive astrophysical marker. Supernova-produced iron from the interstellar medium can be captured by the Earth on its way through the Milky Way. If one finds this radioactive iron-60 in the terrestrial environment (apart from artificial production), it must come from cosmic explosions; more precisely from the last few million years, otherwise it would have long since decayed.

With its half-life in the million year range, Fe-60 is suitable for dating astrophysical events, such as supernova explosions. The usability of this isotope, in particular as an astrophysical clock, was however limited, because the lifetime of this nuclide was not exactly known - an important prerequisite to serve as a chronometer. There were two measurements so far, one from 1984 [3] and another very precise one from 2009 [4], but both were almost a factor of 2 different.

Iron-60 – a monitor for element synthesis and nearby supernova explosions

This isotope has a variety of applications in astrophysics. The main reason is, it is observed in space through its radioactive decay and it is not naturally present on Earth.

Researchers can virtually monitor live nucleosynthesis in massive stars, e.g. active regions of element formation and also the distribution of ejected stellar material in the Milky Way. Iron-60 can be observed directly in our Milky Way via space-born satellites through its decay and the characteristic radiation emitted (similar to another radioactive isotope, Al-26) [5,6]. These observations clearly demonstrate its presence in the interstellar medium. Such radionuclides were produced 'recently", i.e. within a few half-lives. As their decay is observed, one needs the half-life to calculate the number of atoms present in the interstellar medium.

Knie et al., in a pioneering work at the Technical University of Munich, Germany, found Fe-60 at the ocean floor in a manganese crust indicating a possible near-Earth supernova activity about 2 to 3 million years ago [7,8]. Iron-60 was present at the birth of our solar system, more than four billion years ago. This is evidenced today in pre-solar material by overabundances of Fe-60’s decay products [9].

Establishing a connection between these observations of the radioactive decay of Fe-60 and the number of iron-60 atoms, however, requires a precise knowledge of its life-time, that is, its half-life.

How to measure a half-life of millions of years?

Firstly, one needs a sufficient number of atoms. We, a team of scientists from Australia, Switzerland and Austria [10] used artificially produced iron-60 extracted from nuclear waste of an accelerator facility in Switzerland. This iron fraction was separated by specialists in Switzerland and then analyzed for its Fe-60 content. The number of radioactive atoms must be measured in absolute terms, and this is a difficult task and was probably the reason for the discrepancy in earlier measurements.

Figure caption: Identification spectra with a clear separation of the main background Ni-60 from Fe-60: single atom counting of Fe-60 at the ANU - each point represents a single atom. Combining up to 5 different detector signals results in an unsurpassed sensitivity of Fe-60/Fe = 4 X 10-17 (A. Wallner et al., [10]).

We used a very sensitive method to accurately determine the low number of Fe-60 atoms in their sample: accelerator mass spectrometry (AMS) [11,12], a technique that counts atoms directly and that is used for example, also for radiocarbon dating. The Fe-60 measurements were carried out at the Heavy Ion Accelerator Facility at the Australian National University in Canberra, one of the world's most sensitive facilities to detect tiny traces of rare elements in our environment. With this extremely sensitive facility no background could influence our results. Further, we counted Fe-60 relative to another radioactive iron isotope, namely Fe-55. Fe-55 is well known and easier to measure. By using the same measurement setup for Fe-60 and Fe-55, we are confident that potential unknown errors were minimized in our work.

The new value for the half-life of Fe-60 [10] shows a good agreement with the precise measurement by Rugel et al. from the year 2009 [4]. According to our result, they had done a very good job! Combining both measurements, this allows now the use of Fe-60 as a precise cosmic clock. It eliminates a long-standing discrepancy and thus establishes this radionuclide as a precise astrophysical chronometer.

As another additional outcome we encourage other groups to repeat such kind of measurements. With respect to the difficulty of performing measurements of long half-lives, independent and complementary techniques are essential for settling open and difficult-to-solve questions.

[1] R. Diehl, D.H. Hartmann and N. Prantzos (eds.), "Astronomy with Radioactivities", Lecture Notes in Physics, vol. 812, Springer, Berlin (2011). Google Books Preview.
[2] A. Wallner, T. Faestermann, C. Feldstein, K. Knie, G. Korschinek, W. Kutschera, A. Ofan, M. Paul, F. Quinto, G. Rugel, P. Steier, "Abundance of live 244Pu in deep-sea reservoirs on Earth points to rarity of actinide nucleosynthesis", Nature Communications, 6:5956; DOI: 10.1038/ncomms6956 (2015). Full Article.
[3] Walter Kutschera, Peter J. Billquist, Dieter Frekers, Walter Henning, Kenneth J. Jensen, Ma Xiuzeng, Richard Pardo, Michael Paul, Karl E. Rehm, Robert K. Smither, Jan L. Yntema, Leonard F. Mausner, "Half-life of 60Fe", Nuclear Instruments and Methods in Physics Research, Section B, 5, 430 (1984). Abstract.
[4] G. Rugel, T. Faestermann, K. Knie, G. Korschinek, M. Poutivsev, D. Schumann, N. Kivel, I. Günther-Leopold, R. Weinreich, and M. Wohlmuther, "New Measurement of the 60Fe Half-Life", Physical Review Letters, 103, 072502 (2009). Abstract.
[5] W. Wang, M. J. Harris, R. Diehl, H. Halloin, B. Cordier, A.W. Strong, K. Kretschmer, J. Knödlseder, P. Jean, G. G. Lichti, J. P. Roques, S. Schanne, A. von Kienlin, G. Weidenspointner, and C. Wunderer, "SPI observations of the diffuse 60Fe emission in the galaxy", Astronomy & Astrophysics, 469, 1005 (2007). Abstract.
[6] Roland Diehl, "Nuclear astrophysics lessons from INTEGRAL", Reports on Progress in Physics. 76, 026301 (2013). Abstract.
[7] K. Knie, G. Korschinek, T. Faestermann, E. A. Dorfi, G. Rugel, A. Wallner, "60Fe Anomaly in a Deep-Sea Manganese Crust and Implications for a Nearby Supernova Source", Physical Review Letters, 93, 171103 (2004). Abstract.
[8] C. Fitoussi, G. M. Raisbeck, K. Knie, G. Korschinek, T. Faestermann, S. Goriely, D. Lunney, M. Poutivtsev, G. Rugel, C. Waelbroeck, A. Wallner, "Search for Supernova-Produced 60Fe in a Marine Sediment", Physical Review Letters, 101, 121101 (2008). Abstract.
[9] A. Shukolyukov, G.W. Lugmair, "60Fe in eucrites", Earth and Planetary Science Letters, 119, 159 (1993). Abstract ; A. Shukolyukov, G.W. Lugmair, "Live iron-60 in the early solar system", Science, 259, 1138 (1993). Abstract.
[10] A. Wallner, M. Bichler, K. Buczak, R. Dressler, L. K. Fifield, D. Schumann, J. H. Sterba, S. G. Tims, G. Wallner, W. Kutschera, “Settling the half-life of 60Fe – fundamental for a versatile astrophysical chronometer”, Physical Review Letters, 114, 041101 (2015). Abstract.
[11] Hans-Arno Synal, "Developments in accelerator mass spectrometry", International Journal of Mass Spectrometry, 349–350, 192 (2013). Abstract.
[12] Walter Kutschera, "Applications of accelerator mass spectrometry", International Journal of Mass Spectrometry, 349–350, 203 (2013). Abstract.

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Sunday, February 22, 2015

Nonlocality and Conflicting Interest Games

[From Left to Right] Anna Pappa, Niraj Kumar, Thomas Lawson, Miklos Santha, Shengyu Zhang, Eleni Diamanti, Iordanis Kerenidis

Authors: Anna Pappa1,2, Niraj Kumar1,3, Thomas Lawson1, Miklos Santha2,4, Shengyu Zhang5, Eleni Diamanti1, Iordanis Kerenidis2,4

1LTCI, CNRS–Télécom ParisTech, Paris, France, 
2LIAFA, CNRS–Université Paris 7, France, 
3Indian Institute of Technology, Kanpur, India, 
4CQT, National University of Singapore, Singapore, 
5Department of Computer Science and Engineering and ITCSC, The Chinese University of Hong Kong, Shatin, Hong Kong.

Nonlocality is a fundamental property of quantum mechanics that has puzzled researchers since the early formulations of quantum theory. Consider two parties, Alice and Bob, with inputs xA and xB respectively, who are positioned far from each other, and are asked to produce one output each (yA for Alice and yB for Bob). Even if the two players have pre-agreed on some local hidden variables, there exist quantum correlations that cannot be reproduced by any such set of variables [1,2]. These correlations allow the two parties to perform several computational tasks more efficiently, e.g. they can win specific games with probabilities strictly higher than allowed by any classical theory.

Till now, all known examples of quantum games considered players that have common interests, meaning that they either jointly win or lose the game. A famous such example is the CHSH game [3; CHSH stands for first letters of last names of the authors of this paper], where the players win if their outputs are different when both input bits are equal to 1, and if they are the same otherwise. It can be shown that classical resources provide a winning probability of 0.75, while the sharing of a maximally entangled pair can boost the winning probability to approximately 0.85. Another important type of games is conflicting interest games. A typical example is the “Battle of the Sexes”, where Alice and Bob want to meet, but Alice wants to go to the ballet, while Bob prefers theater. In case both go to the ballet, Alice is very pleased and Bob is fine with it; if they go to the theater, Bob is very pleased and Alice is fine with it, while if they go to different places, they are both very unhappy.

In our recent work [4], we examine whether the nonlocal feature of quantum mechanics can offer an advantage similar to the one observed in the CHSH game, but for games with conflicting interests. In order to observe a quantum advantage, we will study games with incomplete information (or Bayesian games), where each party receives some input unknown to the other party [5]. We present a Bayesian game with conflicting interests, and we show that there exist quantum strategies with average payoff for the two players strictly higher than that allowed by any classical strategy. The payoffs of the players for different inputs can be viewed as a table: the rows correspond to the outputs/actions of Alice (yA), while the columns to the outputs/actions of Bob (yB).
The players are interested in maximizing their average payoff over the probability distribution of their inputs, and they may use some advice from a third party (source) in order to achieve their goal. This advice can be in the form of classical bits or quantum states. In general, the classical bits received by the two players can be correlated between them (for example they can be either 00 or 11), and the quantum states may be entangled. By examining all possible strategies with classical advice, it is not difficult to verify that in our game, the sum of the average payoffs of the two players cannot be more than 1.125.

On the other hand, if we consider the case where quantum advice is given to the two players in the form of a maximally entangled state (Bell pair), the players can use projective measurements on their part of the state [6], in order to boost the sum of their average payoffs to 1.28, which is higher than any strategy with classical advice can achieve. It is very interesting to note here that the strategy that attains this payoff is also a quantum equilibrium, meaning that no player can gain a higher payoff by choosing a different strategy unilaterally.

Finally, we have demonstrated our game in practice, using the commercial entangled photon source quED by QuTools and taking a large number of independent runs of the game, in order to estimate each player’s average payoff. We found that the joint payoff is 1.246, which is well above the classical bound of 1.125, and slightly below the maximum value allowed by quantum strategies (1.28), because of experimental noise.

In conclusion, we demonstrated that the nonlocal feature of quantum mechanics can offer an advantage in a scenario where the two parties have conflicting interests. We examined a Bayesian game that attains higher payoffs for both players when using quantum advice compared to any classical strategy, and we experimentally verified the quantum advantage, by playing the game using a commercial photon source.

[1] John Bell, "On the Einstein Podolsky Rosen paradox". Physics, 1, 195-200 (1964). Full Article.
[2] Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, Stephanie Wehner, “Bell nonlocality”, Review of Modern Physics, 86, 419 (2014). Abstract.
[3] John F. Clauser, Michael A. Horne, Abner Shimony, Richard A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories”. Physical Review Letters, 23, 880–884 (1969). Abstract.
[4] Anna Pappa, Niraj Kumar, Thomas Lawson, Miklos Santha, Shengyu Zhang, Eleni Diamanti, Iordanis Kerenidis, "Nonlocality and Conflicting Interest Games", Physical Review Letters, 114, 020401 (2015). Abstract.
[5] J. C. Harsanyi, Management Science, 14 (3), 159-183 (Part I), 14 (5): 320-334 (Part II), 14 (7): 486-502 (Part III) (1967/1968).
[6] Richard Cleve, Peter Høyer, Ben Toner, John Watrous, "Consequences and limits of nonlocal strategies", Proceedings of the 19th Annual IEEE Conference on Computational Complexity, pages 236–249 (2004). Full Article.


Sunday, February 15, 2015

Homeostasis and dynamic phase transition in a simple model of cells with chemical signaling:
Can renormalization group teach us something nontrivial about biology?

Anatolij Gelimson (left) and Ramin Golestanian

Authors: Anatolij Gelimson, Ramin Golestanian

Affiliation: Rudolf Peierls Centre for Theoretical Physics, University of Oxford, United Kingdom.

The motility of bacteria or cells in response to chemicals (chemotaxis) has attracted a lot of interest in biological and medical research [2]. It plays a crucial role in cancer metastasis [3], the early stages of bacterial colony formation, wound healing and development of embryos [2]. However, the underlying mechanisms of these important processes are not fully understood due to the high complexity of these living many-body systems.

Figure 1: The interplay between the two general processes growth and chemotaxis (figure 1) leads to a variety of collective phenomena.

In our recent publication [1] in Physics Review Letters we have developed a simple model to shed some light on these interacting cells, also taking into account cellular growth and death. To study it, we have applied the method of so-called Dynamical Renormalization Groups common for the theory of phase transitions [4]. Similar to physical systems, it turns out that details of the microscopic behavior of cells do not impact the collective behavior on a large scale, whereas the interplay between the two general processes growth and chemotaxis (figure 1) leads to a variety of collective phenomena, which includes a sharp transition from a phase that has moderate controlled growth and death, and regulated chemical interactions, to a phase with strong uncontrolled growth/death and no chemical interactions [1]. Remarkably, for a range of parameters, the transition point shows nontrivial collective motion, which can even be described analytically. [1]

Bacteria such as E. coli have developed an elaborate run-and-tumble search strategy for the needed chemicals by coupling sensing of the chemicals to their motility machinery [5]. In eukaryotic cells, the chemotaxis mechanism is even more complex, often involving thousands of molecular motors or actin polymerization [6].

However, if one regards the effects of these microscopic mechanisms on a more macroscopic level, the resulting motion of bacteria and cells can effectively be modeled as a directed motion towards (or away from) increasing concentrations of chemicals [7]. On this coarse-grained level of description, the motion of bacteria in a field of chemicals is therefore somewhat analogous to the motion of particles in a gravitational or electrical field [8, 9].

But other than in non-active matter, distinctive features of a living system are also growth and death, which we need to take into account in a generic model for the formation of cellular or bacterial aggregations [10]. Interestingly, it turns out that the interplay between chemotactic interactions and growth-death processes leads to a range of different collective behaviors of cells.

We have studied our cellular model with the method of Dynamical Renormalization groups [4]. The basic idea behind it is simple: while microscopically a large number of particles, cells or bacteria might show very complicated behavior with a variety of different interactions, on a more macroscopic level only very few of these interactions will actually determine the collective effects. The so-called renormalization is basically a systematic way of observing a many-particle system from a coarser and coarser level. Coarsening the system will result in make some interactions disappear, whereas others will become stronger. In Physics, this development is called a flow in parameter space. [4]

Figure 2

In our model we have found a threshold in growth and chemotactic strength at which the flow in parameter space changes, which corresponds to a critical change of the macroscopic behavior of cells (figure 2). Below the threshold, the bacteria show jamming and aggregation due to chemotaxis. But above the threshold, chemotaxis becomes irrelevant and the behavior of cells is dominated by uncontrolled growth and death [1].

This threshold could potentially be tested experimentally and also contribute towards answering of fundamentally challenging questions in metastatic growth or bacterial colony formation. The hope is that our research will help understand what controls the communication between strongly dividing cells that are far apart and their collective behavior. The method of Dynamical Renormalization groups we have applied is very generic and could be powerful to shed light on more complex scenarios, like for example adhesive metastatic cells or chemical-dependent cell growth.

[1] Anatolij Gelimson, Ramin Golestanian, "Collective Dynamics of Dividing Chemotactic Cells", Physical Review Letters, 114, 028101 (2015). Abstract.
[2] S.J. Singer, Abraham Kupfer, "The Directed Migration of Eukaryotic Cells", Annual Review of Cell Biology, 2, 337 (1986).
[3] Douglas Hanahan, Robert A. Weinberg, Cell, 144, 646 (2011). Full Article.
[4] Ernesto Medina, Terence Hwa, Mehran Kardar, Yi-Cheng Zhang, "Burgers equation with correlated noise: Renormalization-group analysis and applications to directed polymers and interface growth", Physical Review A, 39, 3053 (1989). Abstract.

[5] Howard C. Berg, "E. coli in Motion" (Springer-Verlag, New York, 2004).
[6] Herbert Levine, Wouter-Jan Rappel, "The physics of eukaryotic chemotaxis", Physics Today, 66 (issue 2), 24 (2013). Abstract.

[7] Evelyn F. Keller, Lee A. Segel, "Traveling bands of chemotactic bacteria: A theoretical analysis", Journal of Theoretical Biology, 30, 235 (1971). 
[8] Pierre-Henri Chavanis, Carole Rosier, Clément Sire, "Thermodynamics of self-gravitating systems", Physical Review E, 66, 
036105 (2002). Abstract. 

[9] Pierre-Henri Chavanis, Clément Sire, "Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions", Physical Review E, 69, 016116 (2004). 
[10] Martin Nowak, "Evolutionary Dynamics", Harvard University Press (2006).

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Sunday, February 08, 2015

Building A Better Quantum Interface

From left to right: (top row) Bernardo Casabone, Konstantin Friebe, Birgit Brandstätter, (bottom row) Klemens Schüppert, Rainer Blatt, Tracy E. Northup.

Author: Konstantin Friebe

Affiliation: Institut für Experimentalphysik, Universität Innsbruck, Austria.

One of the largest challenges in quantum information science stems from the fact that to date no truly scalable quantum computer has been built, i.e., current devices only contain a few quantum bits (qubits). However, in order to access regimes where the power of quantum computation really comes into play, one would need scalable architectures with many qubits.

One approach for solving this issue is called distributed quantum computing. It consists of many small-scale quantum computers that are linked via photonic channels in close analogy to the internet or the “cloud” [1]. In this way, many small quantum computers can be linked together to make one large computer.

In this approach, the challenge consists of faithfully transferring quantum information between remote small-scale quantum computers via photonic channels. Quantum interfaces for this purpose can be built using cavity quantum electrodynamics systems. In such a system, the stationary qubits for computation are kept inside a cavity, also known as an optical resonator, i.e., between two mirrors. These mirrors enhance the interaction between the stationary qubits and photons (“flying qubits”), so that faithful transfer of quantum information from matter to light becomes possible. In fact, the mirrors make it possible to generate a single information-carrying photon from a stationary qubit and to be able to send this photon to another quantum computer with high efficiency [2].
Figure 1: Schematic of the setup. Two calcium ions (green spheres) are trapped inside an optical resonator (mirrors). By addressing the ions with laser beams at wavelengths 729 nm (global 729, addressing 729) and 393 nm, it is possible to prepare them in an entangled state with controllable phase, and a single photon can be generated in the cavity (red standing wave profile). The polarisation of the photon carries one qubit of information. After the photon has left the resonator, it is analysed using waveplates (λ/2, λ/4) and a polarising beam splitter (PBS), which splits up the two orthogonal polarisations H (horizontal) and V (vertical). The photon is then detected at one of two avalanche photodiodes (APD1 and APD2). (This Figure is from reference [3]).

In our recent experiment at the University of Innsbruck, Austria, we trapped two calcium ions inside an optical resonator [3]. In this case, the ions constitute the small-scale quantum computer. Ions are well-suited for this task, as an extensive toolbox for their preparation, manipulation and readout exists. The two ions were laser-cooled and prepared in an entangled state by manipulating their electronic and motional states with a laser field. Entanglement means that the two ions have “lost their individuality” and have to be described as a collective system with collective qualities. In this case, it is the electronic states of the two ions that are entangled with one another. This entangled state can be characterized by a phase, i.e., a number between zero and 2π. By controlling the phase of the entangled state of the two ions, it was possible to either enhance the probability to generate a photon in the cavity (phase 0) or to suppress the generation of a photon (phase π). The first case is called superradiance, while the suppression is called subradiance.
Figure 2: Probability of detecting a photon as a function of the time after the photon generation is started. The blue circles show the photon detection probability for the superradiant case (entangled state with phase 0), while the brown diamonds represent the subradiant state (entangled state with phase π). For comparison, the case of the two individual ions is shown (open triangles). For the superradiant case, the photon is produced faster than for a single ion, while in the subradiant case, photon generation is suppressed. Lines are simulations. (This Figure is from reference [3]).

We next encoded one qubit of information in the state of two entangled ions, that is, we used two “physical qubits” as a single “logical qubit”. The information stored in this qubit was then mapped onto the polarisation state of a single photon. By analysing the polarisation of the photon after it had left the resonator, we were able to show that the transfer of information was more faithful if the two ions were in the state with phase 0 than for a single ion. The efficiency of the process was higher, too.
Figure 3: Process fidelity (upper panel), the measure for the faithfulness of the transfer of quantum information, and efficiency (lower panel) as a function of the time after the photon generation is started. Blue filled circles are data from the superradiant entangled state, while open black circles are data from a single ion. Both process fidelity and efficiency are higher for the case of two entangled ions in the superradiant state. Lines are simulations. (This Figure is adapted from reference [3]).

In conclusion, by encoding quantum information in entangled states of more than one qubit, a better, i.e., more faithful quantum interface can be built, which is important for distributed quantum computing. Additionally, by choosing the phase π instead, qubits can be completely decoupled from the interface. This is interesting for future quantum computers consisting of long arrays of ions, where one might need a selective interface for just certain qubits, while the others remain undisturbed.

[1] H. J. Kimble, "The quantum internet", Nature, 453, 1023 (2008). Abstract
[2] T.E. Northup, R. Blatt, "Quantum information transfer using photons", Nature Photonics, 8, 356 (2014). Abstract
[3] B. Casabone, K. Friebe, B. Brandstätter, K. Schüppert, R. Blatt, T. E. Northup, "Enhanced quantum interface with collective ion-cavity coupling", Physical Review Letters, 114, 023602 (2015). Abstract.
[4] C. Russo, H. G. Barros, A. Stute, F. Dubin, E. S. Phillips, T. Monz, T. E. Northup, C. Becher, T. Salzburger, H. Ritsch, P. O. Schmidt, R. Blatt, "Raman spectroscopy of a single ion coupled to a high-finesse cavity", Applied Physics B, 95, 205 (2009). Abstract.


Sunday, January 25, 2015

Sound Velocity Bound and Neutron Stars

Paulo Bedaque (left) and Andrew W. Steiner (right)

Authors: Paulo Bedaque1, Andrew W. Steiner2,3,4 

1Department of Physics, University of Maryland, College Park, USA 
2Institute for Nuclear Theory, University of Washington, Seattle, USA
3Department of Physics and Astronomy, University of Tennessee, Knoxville, USA 
4Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA. 

Neutron stars are the final stage in the evolution of a star, the remnants of supernova explosion marking the end of the star’s life. They are incredibly compact objects: masses comparable to the Sun’s are compressed in a region of about 10 miles radius. At these densities, most matter is composed of neutrons. The repulsion between neutrons balances precariously against the strong gravitational fields generated by this high matter concentration: a little less repulsion or a little more mass leads to the collapse of the star into a black hole [1].

It has been possible to measure the mass of several neutron stars, and until recently, all accurate mass measurements were near 1.4 times the mass of our sun. However, within the past few years, two neutron stars have been discovered to have a mass around twice that of our sun [2]. What this discover means is that the neutron matter composing the star is stiffer than previously expected.

The speed of sound in air is about 346 meters per second, and it tends to increase with either the density or the temperature of the medium in which it travels. Since neutron stars contain the most dense matter in the universe one might wonder how fast the speed of sound is inside neutron stars.

Everywhere else in the universe [3], the speed of sound seems to be limited to the speed of light divided by the square root of 3, that is, v < 0.577 c (see, for example, the figures here: Link to plots >> ). At high enough densities or temperatures, the speed of sound approaches this limiting value. This result comes from quantum chromodynamics (QCD) [4] - the physical theory which describes how neutrons and protons (made of quarks) interact. At high enough densities and temperatures, QCD exhibits "asymptotic freedom", meaning that the interaction becomes weaker [5]. Unfortunately, neutron star densities are not large enough so that quarks are weakly interacting.

In a paper published in Physical Review Letters (as an 'Editor's suggestion') on January 21st [6], we showed that the speed of sound in neutron stars must exceed this value at some point inside a neutron star. The reason is that models where the speed of sound is smaller than the limiting value at all densities (those like the black lines in the figure) are too soft to produce neutron stars with masses twice the mass of the sun. Thus, the only alternative is that the speed of sound must look something like either the blue dotted or red dashed lines.

This result is important because it tells us more about how neutrons and protons interact, not only in neutron stars, but also here on earth [7]. It gives us more insight into how QCD behaves at high densities. Finally, it also helps us understand some of the more extreme neutron star-related processes like core-collapse supernovae, magnetar flares, and neutron star mergers.

Notes & References:
[1] See a diagram of stellar evolution from the Chandra X-ray observatory, their neutron star page, or the wikpedia entry on neutron stars.
[2] P.B. Demorest, T. Pennucci, S.M. Ransom, M.S.E. Roberts, J.W.T. Hessels, "A two-solar-mass neutron star measured using Shapiro delay". Nature, 467, 1081–1083 (2010). Abstract; John Antoniadis, Paulo C. C. Freire, Norbert Wex, Thomas M. Tauris, Ryan S. Lynch, Marten H. van Kerkwijk, Michael Kramer, Cees Bassa, Vik S. Dhillon, Thomas Driebe, Jason W. T. Hessels, Victoria M. Kaspi, Vladislav I. Kondratiev, Norbert Langer, Thomas R. Marsh, Maura A. McLaughlin, Timothy T. Pennucci, Scott M. Ransom, Ingrid H. Stairs, Joeri van Leeuwen, Joris P. W. Verbiest, David G. Whelan, "A Massive Pulsar in a Compact Relativistic Binary". Science, 340, 6131 (2013). Abstract.
[3] The only possible exception is matter inside the event horizon of a black hole, which is not causally connected with the rest of the universe anyway.
[4] See the Wikipedia article on Quantum Chromodynamics.
[5] This finding led to 2004 Nobel prize in physics for David J. Gross, H. David Politzer and Frank Wilczek.
[6] Paulo Bedaque, Andrew W. Steiner, "Sound Velocity Bound and Neutron Stars". Physical Review Letters, 114, 031103 (2015). Abstract. Also available at: arXiv:1408.5116 [nucl-th].
[7] Neutrons and protons are the basic building blocks of all atomic nuclei.

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