Single-Photon Sources Combine High Purity, Indistinguishability and Efficiency All Together

From left to right: Chao-Yang Lu, Jian-Wei Pan, Sven Höfling and Christian Schneider.

Authors: Chao-Yang Lu¹, Christian Schneider², Sven Höfling^1,2,3,  Jian-Wei Pan¹

Affiliation:
¹CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.
²Technische Physik, Physikalisches Institat and Wilhelm Conrad Rontgen-Center for Complex Material Systems, Universitat Wurzburg, Germany.
³SUPA, School of Physics and Astronomy, University of St. Andrews, UK.

One-sentence summary: A single-photon source has been demonstrated which, for the first time, combines the features of high efficiency and near-perfect levels of purity and indistinguishabilty, opening the way to scalable multi-photon experiments on a semiconductor chip.

Spontaneous parametric down conversion has served as an excellent workhorse for fundamental test of quantum mechanics, quantum teleportation and optical quantum computing [1]. In this nonlinear optics process, the emission of photon pairs is probabilistic (with a probability of p) and inevitably accompanied by higher-order emission events (on the order of p²), which strongly limit the scalability for optical quantum information processing. So far, up to eight-photon entanglement—created from four independent photon pairs—have been demonstrated [2].

Past 2Physics article by Chao-Yang Lu and/or Jian-Wei Pan :
March 22, 2015: "Quantum Teleportation of Multiple Properties of A Single Quantum Particle" by Chao-Yang Lu and 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.

In an attempt to overcome this obstacle, increasing attention has turned to single quantum emitters, such as self-assembled semiconductor quantum dots (QD), trapped atoms or ions, single defects in diamond or monolayer, and single molecules. In the past two decades, although many previous proof-of-principle experiments have established photon antibunching — an unambiguous evidence for single-photon emission, a scalable extension to multiple photonic quantum bits remain elusive.

To be useful for multi-photon applications such as Boson sampling, a perfect single quantum emitters should fulfill the following wish list: (1) High quantum efficiency: The decay of excited states should predominantly result in an emitted photon. (2) Deterministic generation: Upon a pulsed excitation, the source should deterministically emit one photon in a push-button fashion. (3) High purity: The emission should have a vanishing multi-photon probability. (4) High indistinguishability: Individual photons emitted at different trials should be quantum mechanically identical to each other. (5) High collection efficiency: The radiated photons should be extracted with a high efficiency to a single spatial mode.

Past 2Physics article by Sven Höfling :
May 17, 2015: "A Current Out Of Fluctuations" by Pierre Pfeffer, Fabian Hartmann, Sven Höfling, Martin Kamp, Lukas Worschech.

Among the discovered single quantum emitters so far, QDs have the highest quantum efficiency in solid state and narrowest linewidth at cryogenic temperature, and thus are promising as deterministic single-photon emitters. However, despite the extensive efforts, simultaneously fulfilling all the five criteria in the wish list proved challenging. Most previous experiments either relied on non-resonant excitation of a QD-microcavity that degraded the photon purity and indistinguishability [3,4], or used resonant excitation of a QD in a planar cavity that limited the extraction efficiency [5].

Figure 1: (a) Scanning electron microscopy image of a typical QD micropillar. (b) Numerical simulation of the photon emission from the QD-micropillar. (c) The photons collected into the first lens per pulse versus single-photon purity versus pump power.

Recently, the USTC-Wurzburg joint team exploited s-shell pulsed resonant excitation of a Purcell-enhanced QD-micropillar to deterministically generate resonance fluorescence single photons [6] which for the first time combines all the features in the wish list. The experiments were performed on an InAs/GaAs QD embedded inside a 2.5 micron diameter micropillar cavity (see Fig.1a) with a quality factor of 6124 and a Purcell factor of 6.3. Great efforts are made to find a single perfect QD at a sweet point where at 7.8 K the QD is to spatially coupled and spectrally resonant to the micropillar. At pi pulse, we detect 3.7 million single photon counts per second. The overall system efficiency is 4.6%. After correcting for detection efficiency and optical loss, we estimate that 66% of the generated single photons are collected into the first objective lens. Figure 1c summarizes the combined performance of the efficiency and single-photon purity as a function of pump power. It should be noted that the high generation and extraction efficiency are obtained with little compromise of the single-photon purity (g²(0) ≤ 0.009).

The overall system efficiency 4.6% — the highest reported in QDs — can be improved using techniques such as orthogonal excitation and detection of RF, near-unity-efficiency superconducting nanowire single-photon detection, and antireflection coatings of the optical elements. At this stage already, the performance of the single-photon source is already about ten time brighter than the triggered single-photon source used in eight-photon entanglement, but requires a pump power that is 7 orders of magnitude lower.

Figure 2: Quantum interference between two single photons separated by ~13 ns where the photon polarization set at cross (a) and parallel (b). A zoom-in near the zero time delay is shown in (c).

Another crucial demand is that the photons should possess a high degree of indistinguishability. We note that the pulsed resonant excitation is more critically needed for QDs with large Purcell factors where the reduced radiative lifetime approaches the time jitter. The single photons' indistinguishability is tested using two-photon Hong-Ou-Mandel interference. Figure 2a and 2b show histograms of normalized two-photon counts for orthogonal and parallel polarization at an emission time separation of ~13 ns, respectively. An almost vanishing zero-delay peak is observed for two photons with identical polarization (see Fig. 2c for a zoom-in). We obtain a degrees of indistinguishability to be 0.978.

Such a single-photon source can be readily used to perform multi-photon experiments on a solid-state platform. Immediate applications include implementation of Boson sampling [7] — an intermediate quantum computation where it is estimated that with 20-30 single photons one can demonstrate complex tasks that is difficult for classical computers. In addition to the photonic applications, the high-efficiency fluorescence extraction would also allow a fast high-fidelity single-shot readout of single electron spins, and efficiently entangling distant QD spins.

References:
[1] Jian-Wei Pan, Zeng-Bing Chen, Chao-Yang Lu, Harald Weinfurter, Anton Zeilinger, Marek Żukowski, "Multi-photon entanglement and interferometry", Review of Modern Physics, 84, 777–838 (2012). Abstract.
[2] Xing-Can Yao, Tian-Xiong Wang, Ping Xu, He Lu, Ge-Sheng Pan, Xiao-Hui Bao, Cheng-Zhi Peng, Chao-Yang Lu, Yu-Ao Chen, Jian-Wei Pan, "Observation of eight-photon entanglement", Nature Photonics, 6, 225–228 (2012). Abstract.
[3] Charles Santori, David Fattal, Jelena Vučković, Glenn S. Solomon, Yoshihisa Yamamoto, "Indistinguishable photons from a single-photon device", Nature, 419, 594–597 (2002). Abstract.
[4] Stefan Strauf, Nick G. Stoltz, Matthew T. Rakher, Larry A. Coldren, Pierre M. Petroff, Dirk Bouwmeester, "High-frequency single-photon source with polarization control", Nature Photonics, 1, 704 (2007). Abstract.
[5] Yu-Ming He, Yu He, Yu-Jia Wei, Dian Wu, Mete Atatüre, Christian Schneider, Sven Höfling, Martin Kamp, Chao-Yang Lu, Jian-Wei Pan, "On-demand semiconductor single-photon source with near-unity indistinguishability", Nature Nanotechnology, 8, 213–217 (2013). Abstract.
[6] Xing Ding, Yu He, Z.-C. Duan, Niels Gregersen, M.-C. Chen, S. Unsleber, S. Maier, Christian Schneider, Martin Kamp, Sven Höfling, Chao-Yang Lu, Jian-Wei Pan, "On-Demand Single Photons with High Extraction Efficiency and Near-Unity Indistinguishability from a Resonantly Driven Quantum Dot in a Micropillar", Physical Review Letters, 116, 020401 (2016). Abstract.
[7] Scott Aaronson, Alex Arkhipov, The computational complexity of linear optics, Proceedings of the 43rd annual ACM symposium on Theory of computing, 2011, San Jose (ACM, New York, 2011), p. 333. Full Article.

Discovery of Weyl Fermions, Topological Fermi Arcs and Topological Nodal-Line States of Matter

Princeton University group (click on the picture to view with higher resolution), From left to right: Guang Bian, M. Zahid Hasan (Principal investigator), Nasser Alidoust, Hao Zheng, Daniel S. Sanchez, Suyang Xu and Ilya Belopolski. 

Author: M. Zahid Hasan

Affiliation: Department of Physics, Princeton University, USA

Link to Hasan Research Group: Laboratory for Topological Quantum Matter & Advanced Spectroscopy >>

The eponymous Dirac equation describes the first synthesis of quantum mechanics and special relativity in describing the nature of electron. Its solutions suggest three distinct forms of relativistic particles - the Dirac, Majorana and Weyl fermions [1-3]. In 1929, Hermann Weyl proposed the simplest version of the equation, whose solution predicted massless fermions with a definite chirality or handedness [3]. Weyl’s equation was intended as a model of elementary articles, but in nearly 86 years, no candidate Weyl fermions have ever been established in high-energy experiments. Neutrinos were once thought to be such particles but later found to possess a small mass. Recently, analogs of the fermion particles have been discovered in certain electronic materials that exhibit strong spin-orbit coupling and topological behavior. Just as Dirac fermions emerge as signatures of topological insulators [4], researchers have shown that electronic excitations in semimetals such as tantalum or niobium arsenides (TaAs and NbAs) behave like Weyl fermions [5-7]. And such a behavior is consistent with their topological semimetal bandstructures [8,9].

Past 2Physics article by M. Zahid Hasan:
July 18, 2009: "Topological Insulators : A New State of Quantum Matter"

In 1937 physicist Conyers Herring considered under what conditions electronic bands in solids have the same energy by accident in crystals that lack certain symmetries [10]. Near these accidental band touching points, the low-energy excitations, or electronic quasiparticles can be described by an equation that is essentially identical to the 1929 Weyl equation. In recent times, these touching points have been theoretically studied in the context of topological materials and are referred to as Weyl points and the quasiparticles near them are the emergent Weyl fermions [11]. In these solids, the electrons’ quantum-mechanical wave functions acquire a phase, as though they were moving in a superficial magnetic field that is defined in momentum space. In contrast to a real magnetic field, this fictional field (known as a Berry curvature) admits excitations that behave like magnetic monopoles. These monopoles are topological defects or singularities that locate at the Weyl points. So the real space Weyl points are associated with chiral fermions and in momentum space they behave like magnetic monopoles [11-17]. The fact that Weyl nodes are related to magnetic monopoles suggests they will be found in topological materials that are in the vicinity of a topological phase transition [14,15]. The surface of a topological insulator has a Fermi surface that forms a closed loop in momentum space; in a Weyl semimetal, these loops become non-closed arcs as some symmetry is lifted [11,12]. These Fermi arcs terminate at the location of the bulk Weyl points ensuring their topological nature [12]. Theory had suggested that Weyl semimetals should occur in proximity to topological insulators in which inversion or time-reversal symmetry was broken [12,14,16].

Building on these ideas, researchers, including the Princeton University group, used ab initio calculations to predict candidate materials [8,9] and perform angle-resolved photoemission spectroscopy to detect the Fermi arcs, characteristic of Weyl nodes, on the surface of TaAs and NbAs [5-7]. ARPES is an ideal tool for studying such a topological material as known from the extensive body of works on topological insulators [4]. The ARPES technique involves shooting high-energy photons on a material and measuring the energy, momentum and spin of the ejected electrons both from the surface and the bulk. This allows for the explicit determination of both bulk Weyl nodes and the Fermi-arc surface states (Figure 1).

Figure 1: (click on the image to view with high resolution) Weyl fermion and Fermi arcs (a) Schematic of the band structure of a Weyl fermion semimetal. (b) Correspondence of the bulk Weyl fermions to surface Fermi arc states. (c) ARPES mapping of TaAs Fermi surface. (d) Fermi arc surface states and Weyl nodes on the (001) surface of TaAs. (e) Linear dispersion of Weyl quasi-particles in TaAs. (Adapted form Ref. [5])

In the absence of spin-orbit coupling, the tantalum arsenide material is a nodal-line semimetal in which the bulk Fermi surface is a closed loop in momentum space [8,17,18]. With spin-orbit coupling turned on, the loop-shaped nodal line condenses into discrete Weyl points in momentum space [8]. In this sense the topological nodal-line semimetal can be thought of as a state where the Weyl semimetals originate from by further symmetry breaking (Figure 2). Such a state has been considered in theory previously [17] but it lacked concrete experimental realizations. Very recently, the first example of a topological nodal-line semimetal in the lead tantalum selenide (PbTaSe₂) materials has been reported experimentally [18]. Even though many predictions existed, no concrete experimentally realizable material was found. These findings suggest that Weyl semimetals [5-7] and nodal-line semimetals [17-18] are the first two examples of topological materials that are intrinsically gapless in contrast to topological insulators [4].

Figure 2: (click on the image to view with high resolution) Topological nodal-line semimetals (a) Schematic of a Weyl semimetal and a topological nodal-line semimetal. (b) ARPES mapping and theoretical simulation of (001)-surface band structure of PbTaSe₂ showing the loop-shaped bulk Fermi surface. (c) ARPES spectrum and theoretical band structure along some momentum space directions. (e) Calculated iso-energy band contour showing the nodal line and topological surface states. (Adapted from Ref. [18])

In the 1980s, Nielsen and Ninomiya suggested that exotic effects, like the ABJ (Adler-Bell-Jackiw) chiral anomaly—in which the combination of an applied electric and magnetic fields generates an excess of quasiparticles with a particular chirality—were associated with Weyl fermions and could be observable in 3D crystals [13]. A further correspondence has been established more recently with the increased understanding of materials with band structures that are topologically protected [11-17]. Unusual transport properties that are associated with Weyl fermions, such as a reduction of the electrical resistance in the presence of an applied magnetic field, have already been reported in the TaAs class of materials [19,20] (Figure 3). Weyl materials can also act as a novel platform for topological superconductivity leading to the realization of Weyl-Majorana modes potentially opening a new pathway for investigating qubit possibilities [21]. Weyl particles have also been observed in photonic (bosonic) crystals. In these systems the number of optical modes has an unusual scaling with the volume of the photonic crystal, which may allow for the construction of large-volume single-mode lasers [22]. Development in the last few months seems to suggest that Weyl particles are indeed associated with a number of unexpected quantum phenomena and these findings may lead to applications in next-generation photonics and electronics.

Figure 3: (click on the image to view with high resolution) Signature of the chiral anomaly in the Weyl fermion semimetal TaAs. (a) Magneto-resistance (MR) data of the Weyl semimetal TaAs in the presence of parallel electric and magnetic fields at T = 2 K. The MR decreases as one increases the magnetic field. (b) MR as a function of angle between the electric and the magnetic fields. The negative magneto-resistance is quickly suppressed as one varies the direction of the magnetic ~B field away from that of the electric ~E field. The observed negative MR and its angular dependence serve as the key signature of the chiral anomaly. (c,d) Landau energy spectra of the left- and right-handed Weyl fermions in the presence of parallel electric and magnetic fields. (Adapted from Ref. [20])

References:
[1] Frank Wilczek “Why are there analogies between condensed matter and particle theory?” Physics Today, 51, 11–13 (1998). Abstract.
[2] Palash B. Pal, “Dirac, Majorana and Weyl fermions”, American Journal of Physics, 79, 485–498 (2011). Abstract.
[3] Hermann Weyl, “Elektron und Gravitation. I”, Zeitschrift für Physik, 56, 330 (1929). Abstract.
[4] M. Z. Hasan and C.L. Kane “Topological Insulators”, Review of Modern Physics, 82, 3045 (2010). Abstract.
[5] Su-Yang Xu, Ilya Belopolski, Nasser Alidoust, Madhab Neupane, Guang Bian, Chenglong Zhang, Raman Sankar, Guoqing Chang, Zhujun Yuan, Chi-Cheng Lee, Shin-Ming Huang, Hao Zheng, Jie Ma, Daniel S. Sanchez, BaoKai Wang, Arun Bansil, Fangcheng Chou, Pavel P. Shibayev, Hsin Lin, Shuang Jia, M. Zahid Hasan, “Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs in TaAs”,  Science, 349, 613 (2015). Abstract.
[6] Su-Yang Xu, Nasser Alidoust, Ilya Belopolski, Zhujun Yuan, Guang Bian, Tay-Rong Chang, Hao Zheng, Vladimir N. Strocov, Daniel S. Sanchez, Guoqing Chang, Chenglong Zhang, Daixiang Mou, Yun Wu, Lunan Huang, Chi-Cheng Lee, Shin-Ming Huang, BaoKai Wang, Arun Bansil, Horng-Tay Jeng, Titus Neupert, Adam Kaminski, Hsin Lin, Shuang Jia, M. Zahid Hasan, “Discovery of a Weyl Fermion state with Fermi arcs in NbAs”, Nature Physics, 11, 748 (2015). Abstract.
[7] B.Q. Lv, H.M. Weng, B.B. Fu, X.P. Wang, H. Miao, J. Ma, P. Richard, X.C. Huang, L.X. Zhao, G.F. Chen, Z. Fang, X. Dai, T. Qian, H. Ding, “Experimental Discovery of Weyl Semimetal TaAs”, Physical Review X, 5, 031013 (2015). Abstract; B.Q. Lv, N. Xu, H.M. Weng, J.Z. Ma, P. Richard, X.C. Huang, L.X. Zhao, G.F. Chen, C.E. Matt, F. Bisti, V.N. Strocov, J. Mesot, Z. Fang, X. Dai, T. Qian, M. Shi, H. Ding, "Observation of Weyl nodes in TaAs", Nature Physics, 11, 724 (2015). Abstract.
[8] Shin-Ming Huang, Su-Yang Xu, Ilya Belopolski, Chi-Cheng Lee, Guoqing Chang, BaoKai Wang, Nasser Alidoust, Guang Bian, Madhab Neupane, Chenglong Zhang, Shuang Jia, Arun Bansil, Hsin Lin, M. Zahid Hasan, “A Weyl Fermion Semimetal with Surface Fermi Arcs in the Transition Metal Monopnictide TaAs Class”, Nature Communications, 6, 7373 (2015). Abstract.
[9] Hongming Weng, Chen Fang, Zhong Fang, B. Andrei Bernevig, Xi Dai, “Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides”, Physical Review X, 5, 011029 (2015). Abstract.
[10] Conyers Herring, “Accidental Degeneracy in the Energy Bands of Crystals”, Physical Review, 52, 365-373 (1937). Abstract.
[11] Ashvin Vishwanath, “Viewpoint: Where the Weyl Things Are”, Physics, 8, 84 (2015). Full Text.
[12] Xiangang Wan, Ari M. Turner, Ashvin Vishwanath, Sergey Y. Savrasov, “Topological Semimetal and Fermi-Arc Surface States in the Electronic Structure of Pyrochlore Iridates”, Physical Review B, 83, 205101 (2011). Abstract.
[13] H. B. Nielsen, Masao Ninomiya, “The Adler-Bell-Jackiw Anomaly and Weyl Fermions in a Crystal”, Physics Letters B, 130, 389 (1983). Abstract.
[14] Shuichi Murakami, “Phase Transition Between the Quantum Spin Hall and Insulator Phases in 3D: Emergence of a Topological Gapless Phase”, New Journal of Physics, 9, 356 (2007). Full Text.
[15] Grigory E. Volovik, "The Universe in a Helium Droplet", Oxford University Press (2003).
[16] A.A. Burkov, Leon Balents, "Weyl semimetal in a Topological Insulator multilayer", Physical Review Letters, 107, 127205 (2011). Abstract.
[17] A. A. Burkov, M. D. Hook, Leon Balents, "Topological Nodal Semimetals", Physical Review B, 84, 235126 (2011). Abstract.
[18] Guang Bian, Tay-Rong Chang, Raman Sankar, Su-Yang Xu, Hao Zheng, Titus Neupert, Ching-Kai Chiu, Shin-Ming Huang, Guoqing Chang, Ilya Belopolski, Daniel S. Sanchez, Madhab Neupane, Nasser Alidoust, Chang Liu, BaoKai Wang, Chi-Cheng Lee, Horng-Tay Jeng, Chenglong Zhang, Zhujun Yuan, Shuang Jia, Arun Bansil, Fangcheng Chou, Hsin Lin, M. Zahid Hasan , "Topological Nodal-Line Fermions in Spin-Orbit Metal PbTaSe₂", Nature Communications", 7:10556 (2016). Abstract.
[19] Xiaochun Huang, Lingxiao Zhao, Yujia Long, Peipei Wang, Dong Chen, Zhanhai Yang, Hui Liang, Mianqi Xue, Hongming Weng, Zhong Fang, Xi Dai, Genfu Chen, "Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs", Physical Review X, 5, 031023 (2015). Abstract.
[20] Chenglong Zhang, Su-Yang Xu, Ilya Belopolski, Zhujun Yuan, Ziquan Lin, Bingbing Tong, Nasser Alidoust, Chi-Cheng Lee, Shin-Ming Huang, Hsin Lin, Madhab Neupane, Daniel S. Sanchez, Hao Zheng, Guang Bian, Junfeng Wang, Chi Zhang, Titus Neupert, M. Zahid Hasan, Shuang Jia, "Observation of the Adler-Bell-Jackiw chiral anomaly in a Weyl semimetal", arXiv:1503.02630 [cond-mat.mes-hall] (2015). [To appear in Nature Communications].
[21] Anffany Chen, M. Franz, "Superconducting proximity effect and Majorana flat bands in the surface of a Weyl semimetal", arXiv:1601.01727 [cond-mat.supr-con] (2016).
[22] Ling Lu, Zhiyu Wang, Dexin Ye, Lixin Ran, Liang Fu, John D. Joannopoulos, Marin Soljačić, “Experimental Observation of Weyl Points”, Science, 349, 622 (2015). Abstract.

Communicating Quantum States with Alice on a Satellite

Some authors of "Experimental Satellite Quantum Communications" [4] during a night shift: (Right to Left) Davide Bacco, Simone Gaiarin, Daniele Dequal, Giuseppe Vallone and Paolo Villoresi.

Authors: Giuseppe Vallone¹, Davide Bacco¹, Daniele Dequal¹, Simone Gaiarin¹, Vincenza Luceri², Giuseppe Bianco³, Paolo Villoresi¹

Affiliation:
¹Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Padova, Italy 
²e-GEOS spa, Matera, Italy 
³Matera Laser Ranging Observatory, Agenzia Spaziale Italiana, Matera, Italy.

The exchange of quantum bits – or qubits – is a fundamental process in all Quantum Information protocols. The faithful transport of the fragile quantum content of a photon is needed inside the prototypes of photonic quantum computers as well for the teleportation of a given state.

Past 2Physics articles by this group:
August 31, 2014: "A True Randomness Generator Exploiting a Very Long and Turbulent Path" by Davide G. Marangon, Giuseppe Vallone, Paolo Villoresi.
November 24, 2013: "How to Realize Quantum Key Distribution with a Limited and Noisy Link" by Paolo Villoresi.
May 19, 2008: "The Frontier of Quantum Communication is the Space"
by Paolo Villoresi.

Image 1: The scenario where satellites uses Quantum Communications for distributing secure keys to a global communications network.

Moreover, in the relevant application of Quantum-Key-Distribution (QKD), which allows to create a private key between two terminals exploiting the laws of Quantum Physics, such exchange of qubits is expected to cover very long distances [1]. Indeed, in order to connect with secure communications two embassies, two corporate branches and so on, effective quantum communication schemes on a planetary scale are needed. The fibre channels were investigated first for the realization of QKD, such that now several commercial devices based on optical cables are already in operations. Fibers are very efficient up to about 100 km, and the present limit for QKD in fiber is 300 km as demonstrated in a recent experiment [2]; beyond that scale there is the need of quantum repeaters, which presently are in development in advanced research labs. A radically different approach is to go along a Space channels, and exploit a satellite as the sender or the receiver. From the link budget analysis and the effect of turbulence in the propagation, it is evident that the transmitter (Alice) is most conveniently located on the satellite and the receiver (Bob) on the ground [3,4,5].

The first attempt of quantum communication in Space, was made in 2008 by Villoresi et al [6,7], where photons launched from a ground station were reflected by CCRs (corner cube retroreflectors) and aimed back to the Earth. In that case it was used the Japanese satellite Ajisai for emulate an optical transmitter in space. In that work it was demonstrated the application of spectral, spatial and temporal filtering capable to point out the return photons with global losses in the up- and down-link as strong as 157 dB.

In the present experiment, reported recently in Ref. [8], we introduced novel schemes for temporal synchronization and the optical interface, realizing a significant improvement in SNR (signal to noise ratio), dark counts and total transmissivity. We proved that a generic qubit with polarization encoding preserves its characteristics in a channel starting from a source realized again by a retroreflector in orbit and measured on ground by a state analyzer connected to an astronomical telescope designed for satellite-laser ranging [9]. Moreover we were able to prove a communication protocol measuring not only one polarization degree, but a complete set of four polarization states required for protocols as QKD [5].

A very important parameter in QCs (Quantum communications) is represented by the QBER factor (Quantum bit error rate), defined as the number of wrong bits received in a slot time. In case this factor is too high (the threshold depends on the chosen protocol, and on the sending rate), the security of the generated key is not guaranteed [8]. In our experiment we showed, by using some LEO (Low Earth Orbit) satellites (Starlette, Stella, Larets, Jason-2), that our method and setup allows a secure communication in a very long distance scenario (~2000 km). The measured QBER in different runs results of the order of a few percent. It was possible to attest that even with high losses, variable attenuation, and high background a quantum key distribution system works, and an unconditionally secure key, needful for encryption, can be generated also in this case.

Image 2: Picture of the SLR laser and MLRO station situated in Matera.

For the first time qubits bouncing from space were measured and analyzed in different polarization states. Moreover, all the results were obtained with existing satellites naturally used for geodetic studies and other activities usually equipped with CCRs. The optical setup used in the experiment is yet completely integrable in a lot of OGS (optical ground station) and present an easy interface between quantum and classical signals. Furthermore, the technology of SLR and classical satellite communications was exploited for synchronizing the transmitter and the receiver, even though the synchronization process is not so easy with satellite in motion.

What’s next? The possibility of sending and receiving single photons in very long distances paves the way to a lot of future experiments and brings Quantum Physics and Quantum Communication in a privilege position. Firstly, the big effort made by the Governments and by the University is surely compensated. From a scientific point of view these experimental results are very fascinating because they allow new experiments based on this technology. In particular, QKD could be realized with a small and compact device capable of changing polarization of photons, creating a base element for quantum two-way protocols. Additionally, experiments like entanglement distribution involving long distances, Bell inequality and teleportation protocol could be possible in next few years.

With this experiment, it was demonstrated that, not only free-space quantum key distribution is a ready technology, but also the quantum satellite communication is nowadays possible and realizable. The results open the way to look towards a global space quantum network, where OGS could talk with satellite and vice-versa creating a global secure network.

Acknowledgments: The work was carried out within QuantumFuture, one of ten Strategic Projects funded by the University of Padova in 2009. Coordinated by Prof. Villoresi, the project has established the Quantum Communication Laboratory and engaged four research groups in a joint activity: Quantum Communications, Quantum Control Theory, Quantum Astronomy and Quantum Optics.

References:
[1] Valerio Scarani, Helle Bechmann-Pasquinucci, Nicolas J. Cerf, Miloslav Dušek, Norbert Lütkenhaus, Momtchil Peev, "The security of practical quantum key distribution", Review of Modern Physics, 81, 1301 (2009). Abstract.
[2] Boris Korzh, Charles Ci Wen Lim, Raphael Houlmann, Nicolas Gisin, Ming Jun Li, Daniel Nolan, Bruno Sanguinetti, Rob Thew, Hugo Zbinden, “Provably Secure and Practical Quantum Key Distribution over 307 km of Optical Fibre”. Nature Photonics, 9(3), 7. doi:10.1038/nphoton.2014.327 (2014). Abstract.
[3] Cristian Bonato, Markus Aspelmeyer, Thomas Jennewein, Claudio Pernechele, Paolo Villoresi, Anton Zeilinger, “In- fluence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Optics Express, 14,  10050 (2006). Full Article.
[4] Andrea Tomaello, Cristian Bonato, Vania Da Deppo, Giampiero Naletto, Paolo Villoresi, “Link budget and background noise for satellite quantum key distribution,” Advances in Space Research, 47, 802 (2011). Abstract.
[5] C. Bonato, A. Tomaello, V. Da Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New Journal of Physics, 11, 45017 (2009). Full Article.
[6] P Villoresi, T Jennewein, F Tamburini, M Aspelmeyer, C Bonato, R Ursin, C Pernechele, V Luceri, G Bianco, A Zeilinger and C Barbieri, "Experimental verification of the feasibility of a quantum channel between space and Earth", New Journal of Physics, 10, 033038 (2008). Full Article. 2Physics Article.
[7] Giuseppe Vallone, Davide Bacco, Daniele Dequal, Simone Gaiarin, Vincenza Luceri, Giuseppe Bianco, and Paolo Villoresi, “Experimental Satellite Quantum Communication” Phys. Rev. Lett. 115, 040502 (2015). Abstract.
[8] Davide Bacco, Matteo Canale, Nicola Laurenti, Giuseppe Vallone, Paolo Villoresi, "Experimental quantum key distribution with finite-key security analysis for noisy channels", Nature Communications, 4:2363, doi: 10.1038/ncomms3363 (2013). Abstract. 2Physics Article.
[9] http://ilrs.gsfc.nasa.gov/

Experimental Violation of Leggett-Garg Type Inequalities Using Quantum Memories

(From left to right) Zong-Quan Zhou, Chuan-Feng Li, Guang-Can Guo

Authors: Zong-Quan Zhou, Chuan-Feng Li, Guang-Can Guo

Affiliation: Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, China.

Link to the Group of Quantum Network >>

Ever since the birth of quantum mechanics we faced the difficulty to reconcile the superposition behavior of quantum particles and our intuitive experience in dealing with macroscopic objects which should occupy definite states at all times and independently of the observers. Leggett and Garg subsequently formulated the question qualitatively by means of the derivation of a series of inequalities based upon the premises of macroscopic realism and noninvasive measurability [1]. In practice, the main experimental challenge comes from the implementation of truly noninvasive measurements [2]. To avoid the requirement of performing noninvasive measurements, a different type of Leggett-Garg inequalities (LGtI) has been derived from the stationary assumption [3,4], which includes the time translational invariance of the probabilities and Markovianity of the system evolution [2]. If stationarity does hold for the considered system, these inequalities provide a quantitative way to witness the persistence of coherent effects, that is, they allow for benchmarking ‘quantumness’.

Figure 1: Single photons excited the superposition states of two pieces of Nd:YVO₄ crystals. The horizontally (H) and vertically (V) polarized components of a single photon are converted to collective excitation of billions of atoms in the first crystal and second crystal, respectively. The two crystals have thicknesses of 3 mm and are separated by a distance of 2 mm.

Zong-Quan Zhou, Chuan-Feng Li and Guang-Can Guo from the University of Science and Technology of China, and Susana Huelga from the Ulm University have reported in Physical Review Letters [5] that they are able to violate the LGtI in a light-matter interfaced system. By separately benchmarking the Markovian character of the evolution and the translational invariance of the conditional probabilities, the observed violation of the LGtI is attributed to the quantum coherent character of the process.

In the experiment, narrowband single photons are generated from nonlinear crystal through the spontaneous parametric down-conversion process. Then the H+V-polarized single photons are employed to excite the superposition states of the collective excitation of two solid-state quantum memories. The group developed a novel technique, the polarization-dependent atomic-frequency-comb (AFC) technique, to control the dynamical evolution of the collective atomic states. A frequency detuning of δ is introduced between the H-polarized and V-polarized AFC, which determines the state evolution speed. Finally, the atomic states are read out through the AFC echo emission and analyzed with polarization-dependent single-photon detections. The recorded state evolution is shown in Figure 2(a) which is nearly perfect unitary evolution. The calculated LGtI is shown in Figure 2(b) and shows a violation of the classical bound by 6.9 standard errors. The stationary assumption was independently verified for the experimental setup. Therefore, the experimental violation of LGtI demonstrates that the dynamics of a collective excitation which is distributed across two macroscopically separated crystals can be well described by quantum mechanics, while a classical description is excluded.

Figure 2: (a) Time evolution of the probabilities to find the system in atomic state D and A for an AFC excitation initially prepared in state D and with AFC detuning δ of 5 MHz. Here D is defined as an atomic state of “first crystal excited + second crystal excited” and A is the orthogonal state, “first crystal excited - second crystal excited”. (b). The envelope evolution of LGtI. The solid lines are the ideal quantum mechanical predictions. The blue dashed line represents the lower bound of -1, as predicted by classical incoherent theories.

This is a coherent evolution of microscopic excitation in macroscopic objects and represents an interesting exploration of the crossover between quantum and classical regimes. These results provide a general procedure to benchmark quantumness when temporal correlations can be independently assessed and confirm the persistence of quantum coherence effects in systems of increasing complexity. Further efforts to combine the multi-photon entanglement [6,7] and the atomic memory could lead to a test of LGtI with quantum superposition states of larger macroscopicity [8].

Reference:
[1] A. J. Leggett, Anupam Garg, “Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks?”, Physical Review Letters, 54, 857 (1985). Abstract.
[2] Clive Emary, Neill Lambert, Franco Nori, “Leggett-Garg Inequality”, Reports on Progress in Physics, 77, 016001 (2014). Abstract.
[3] S. F. Huelga, T. W. Marshall, E. Santos , “Proposed test for realist theories using Rydberg atoms coupled to a high-Q resonator”, Physical Review A, 52, R2497 (1995). Abstract.
[4] Susana F. Huelga, Trevor W. Marshall, Emilio Santos, “Temporal Bell-type inequalities for two-level Rydberg atoms coupled to a high-Q resonator”, Physical Review A, 54, 1798 (1996). Abstract.
[5] Zong-Quan Zhou, Susana, F. Huelga, Chuan-Feng Li, Guang-Can Guo, “Experimental detection of quantum coherent evolution through the violation of Leggett-Garg-type inequalities”, Physical Review Letters, 115, 113002 (2015). Abstract.
[6] A. I. Lvovsky, R. Ghobadi, A. Chandra, A. S. Prasad and C. Simon,, “Observation of micro-macro entanglement of light”, Nature Physics, 9, 541 (2013). Abstract.
[7] N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. T. Thew, N. Gisin, “Displacement of entanglement back and forth between the micro and macro domains”, Nature Physics, 9, 545 (2013). Abstract.
[8] A. J. Leggett, “Macroscopic Quantum Systems and the Quantum Theory of Measurement”, Progress of Theoretical Physics Supplements, 69, 80 (1980). Full Article.

How Time Dilation Affects Quantum Superpositions

(From left to right) Igor Pikovski, Magdalena Zych, Fabio Costa, Časlav Brukner
(Click on the image to see their faces with better resolution)

Authors: Igor Pikovski^1,2,3,4, Magdalena Zych^1,2,5, Fabio Costa^1,2,5, Caslav Brukner^1,2

Affiliation:
¹Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Austria,
²Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Vienna, Austria,
³ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, USA,
⁴Department of Physics, Harvard University, Cambridge, Massachusetts, USA,
⁵Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland, Australia.

Can gravity affect quantum systems? Quantum theory and gravity seem to apply to very different physical regimes. It is often argued that gravity is irrelevant on very small scales, where typical quantum phenomena are observed. A well-known argument compares the forces between an electron and a proton: gravity is roughly 10³⁹ times weaker than electromagnetism. But this is not the full story. As has been shown in numerous experiments, gravity can indeed influence a quantum wave function of the smallest particles. Newtonian gravity from Earth can induce a quantum phase-shift for a particle that is in a superposition between two different heights. This was first demonstrated with Neutrons in the famous COW (Colella-Overhauser-Werner) experiment in 1975 [1].

Past 2Physics article by this group:
January 15, 2012: "Quantum Complementarity Meets Gravitational Redshift" by Magdalena Zych, Fabio Costa, Igor Pikovski, Časlav Brukner.

What about Einstein’s gravity? If the Newtonian potential can influence a quantum wave function, what can one expect from post-Newtonian effects stemming from general relativity? It turns out that novel phenomena arise, with no classical analogue. A few years ago, we studied how time dilation affects a single clock in superposition [2] (see also 2Physics article “Quantum Complementarity Meets Gravitational Redshift”). Classically, two clocks placed at different heights will experience different proper times, and thus will be time dilated with respect to each other. But in quantum theory, an additional effect arises: If a single clock is brought into superposition of two heights, its internal degrees of freedom (or clock states) get entangled with its position. This entanglement affects the superposition of heights. If the two amplitudes are brought together to interfere, the interference pattern will be affected due to quantum complementarity: As the internal clock states record time, they gain “which-way information” and thus destroy the quantum coherence. This interplay has been recently demonstrated in an experiment with a BEC, where the time delay of spin precession was simulated by inhomogeneous magnetic fields [3] (see also 2Physics article “One Clock in Two Places Simultaneously”).

Figure 1: The gravitational field causes time dilation, clocks closer to Earth run slower than clocks further away. For a quantum superposition of a single clock at two heights, the clock states and its position become entangled.

In our latest work, we showed that the effect of time dilation on quantum systems is very general and affects the quantum coherence of any composite quantum system [4]. Time dilation is universal: it affects any system regardless of its structure or composition. Clocks are affected by time dilation as much as the heart beat or the half-life of a decaying particle. Also composite quantum systems are affected, as they usually have a finite temperature: It means that there is always some internal dynamics present within the system, which can be affected by time dilation. If such a composite system is brought into superposition between different heights above Earth, as in the above example with a clock, time dilation will correlate all internal dynamics with the height of the system. And this causes decoherence of the center-of-mass, just as in the case with an actual clock. In practice, any system is affected that has some internal energy spread. If the center-of-mass of such a system is brought into superposition and a sufficient difference in proper times is accumulated along the superposed paths, quantum coherence will be lost because of the relative time delay of the internal dynamics of the system. Needless to say, time dilation can be caused by a gravitational field but also by any acceleration or by velocities. There is no “external” environment, only the presence of time dilation causes the system’s center-of-mass to decohere due to the dynamics of its own composition.

Figure 2: A complex molecule in superposition in a gravitational field. Because of time dilation, the frequencies of the individual atoms depend on the height of the molecule. This causes decoherence of quantum superpositions of the center-of-mass of the molecule.

One may expect this effect to be vanishingly small. After all, it is very hard to detect time dilation on Earth. But it turns out that already on mesoscopic scales, the effect is strong: If a gram-scale object at room temperature is put into a superposition of height difference of 1µm, then time dilation will cause decoherence after about 1ms. This is because many internal degrees of freedom contribute to the effect. Each individually is affected by time dilation only a tiny bit, but for a larger composite system, the effect can become significant. For quantum systems, it is of course very challenging to prepare such large superpositions, and other decoherence effects will also be of importance. But there is a parameter range at superfluid temperatures, where experiments with very large molecules or microspheres could in principle observe the predicted phenomena in the future. But importantly, the effect is universal and any internal dynamics will contribute to decoherence. Thus one can think of other possible experiments with internal dynamics other than thermal, such as nuclear dynamics or some fast chemical processes.

All of these will contribute to the rate of decoherence; one can be creative in designing a clever experiment. In fact, one could also use such setups to reverse the logic: observing coherence of the center-of-mass might be a key to shed light on unknown internal dynamics. Maybe the best possible way for experimental verification will turn out to take an actual clock and put it in superposition -- as we proposed in [2] and which has recently been shown to work in an analogue experiment [3]. Future experiments should be able to verify decoherence due to time dilation, which follows only from quantum theory and general relativity as we know them.

Finally, what do we actually learn from this study? In our work, we do not treat the gravitational field quantum-mechanically, thus there is no direct connection to “quantum gravity”. Yet, we study how quantum mechanical test systems behave on a background space-time, as opposed to classical test particles, and new effects arise. We discovered a new decoherence mechanism, but the most exciting aspect of the work is that the interplay between quantum theory and gravity has novel phenomena to offer. Our work shows one example, but this research direction is still widely unexplored: Many more possible effects and experiments on the interplay between these two great theories are waiting to be discovered!

References:
[1] Roberto Colella, Albert W. Overhauser, Samuel A. Werner. “Observation of Gravitationally Induced Quantum Interference”, Physical Review Letters, 34, 1472 (1975). Abstract.
[2] Magdalena Zych, Fabio Costa, Igor Pikovski, Časlav Brukner. “Quantum interferometric visibility as a witness of general relativistic proper time”, Nature Communications, 2, 505 (2011). Abstract. 2Physics Article.
[3] Yair Margalit, Zhifan Zhou, Shimon Machluf, Daniel Rohrlich, Yonathan Japha, Ron Folman. “A self-interfering clock as a 'which path' witness”, published online in 'Science Express' (August 6, 2015). Abstract. 2Physics Article.
[4] Igor Pikovski, Magdalena Zych, Fabio Costa, Časlav Brukner, “Universal decoherence due to gravitational time dilation”, Nature Physics ,11, 668-672 (2015). Abstract.

Universal Linear Optics

The Bristol team : (from left to right) Anthony Laing, Chris Sparrow, Jacques Carolan and Christopher Harrold.

Authors: Christopher Harrold¹ and Chris Sparrow^1,2

Affiliation:
¹Centre for Quantum Photonics, H. H. Wills Physics Laboratory, and Department of Electrical and Electronic Engineering, University of Bristol, UK.
²Department of Physics, Imperial College London, UK.

In our recent work [1], we demonstrate a single reprogrammable optical circuit that is sufficient to implement all possible linear optical protocols up to the size of the circuit.

Since 1897, when it was shown by the German mathematician Adolf Hurwitz, it has been known that any unitary matrix can be built up from smaller 2 X 2 matrices [2]. Then in 1994 Reck et al. showed that any arbitrary unitary can be realised via some physical process [3]. In particular, they showed that if we use a certain arrangement of reconfigurable linear optical elements, we can perform any unitary matrix.

This network can be implemented as a sequence of ≈ m²/2 two-mode primitives with two free parameters. These primitives are built out of variable reflectivity beam splitters and phase shifters. The beam splitters are comprised of a phase shifter sandwiched between two directional couplers, known as a Mach-Zehnder interferometer (MZI). By tuning the phase inside the interferometer we can arbitrarily split the light between the two outputs of the interferometer. A phase shifter placed on the output of the interferometer allows us to tune the phase of the resulting state. The phase shifters are resistive heaters patterned above a small region of waveguide. A change in temperature changes the local refractive index in the waveguide with respect to another and thus realises a phase shift. Cascading these primitive units into the triangular arrangement, together with full control over these phase shifters allows us to configure any linear optical unitary on six modes.

Our device was fabricated by Japanese company Nippon Telegraph and Telephone (NTT), the world’s leading telecommunications company. The six-mode universal system consists of 15 MZIs with 30 thermo-optic phase shifters integrated into a single photonic chip that is electrically and optically interfaced for arbitrary setting of all phase shifters. Once calibrated, we could implement any unitary we wanted and switch between experiments that typically would have taken months to build in a matter of seconds.

Figure 1: A fully reconfigurable optical chip. The device allows us to implement any quantum information protocol in linear optics on up to 6 modes.

We realised heralded quantum logic gates [4] designed to be scalable for the circuit model of quantum computation (QC) for the first time in integrated photonics. We also implemented a heralded entangling gate and used measurements in different bases to verify the successful generation of an entangled state. Entangling gates such as the one implemented here are an essential requirement for one of the most promising routes to photonic QC, measurement based quantum computing [5, 6]. Not only were we able to perform these protocols, but importantly we were able to report experimental results with high fidelity.

We then turned our attention to a completely disparate aspect of linear optics and configured our device in order to perform boson sampling. Boson sampling is a computational task with one objective: sampling from a probability distribution governed by the output statistics of photons injected into a fixed linear optical network [7]. It provides a rapid route to demonstrate the intrinsic exponential advantage a quantum computer has over a classical one. We implemented 100 instances of the boson sampling problem, injecting up to three photons into our circuit and reproduced the expected theoretical probability distributions with exceptional fidelity. We also investigated techniques used to verify the successful implementation of Boson Sampling by implementing a family of unitaries known as the quantum complex Hadamards [8]. These sorts of techniques will be crucial in the future when the circuits and number of photons used mean that classical verification will be intractable even for the most powerful classical computers [9, 10]. Crucially, the reconfigurable circuit allows us to carry out Boson sampling and the verification protocols all on the same device.

The chip’s ability to implement arbitrary circuits promises to replace a multitude of existing prototype systems as well as providing a platform for those yet to be discovered. The results presented in [1] required ~ 1000 configurations of the device and point the way towards applications across quantum technologies.

References:
[1] Jacques Carolan, Christopher Harrold, Chris Sparrow, Enrique Martín-López, Nicholas J. Russell, Joshua W. Silverstone, Peter J. Shadbolt, Nobuyuki Matsuda, Manabu Oguma, Mikitaka Itoh, Graham D. Marshall, Mark G. Thompson, Jonathan C. F. Matthews, Toshikazu Hashimoto, Jeremy L. O’Brien, Anthony Laing, "Universal linear optics", Science, 349, 711 (2015). Abstract.
[2] A. Hurwitz, "über die Erzeugung der Invarianten durch Integration", Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, p.71 (1897). Full Article.
[3] Michael Reck, Anton Zeilinger, Herbert J. Bernstein, Philip Bertani, "Experimental realization of any discrete unitary operator", Physical Review Letters, 73, 58 (1994). Abstract.
[4] E. Knill, R. Laflamme, G.J. Milburn, "A scheme for efficient quantum computation with linear optics", Nature, 409, 46 (2001). Abstract.

[5] Robert Raussendorf, Hans J. Briegel, "A One-Way Quantum Computer", Physical Review Letters, 86, 
5188 (2001). Abstract.

[6] Daniel E. Browne, Terry Rudolph, "Resource-Efficient Linear Optical Quantum Computation", Physical Review Letters, 95, 010501 (2005). Abstract.

[7] Scott Aaronson, Alex Arkhipov, "The computational complexity of linear optics" in Proceedings of the ACM symposium on Theory of Computing, pp.333-342 (ACM, New York, 2011), Abstract.
[8] Anthony Laing, Thomas Lawson, Enrique Martín López, Jeremy L. O’Brien, "Observation of Quantum Interference as a Function of Berry’s Phase in a Complex Hadamard Optical Network", Physical Review Letters, 108, 260505 (2012). Abstract.
[9] Jacques Carolan, Jasmin D. A. Meinecke, Peter J. Shadbolt, Nicholas J. Russell, Nur Ismail, Kerstin Wörhoff, Terry Rudolph, Mark G. Thompson, Jeremy L. O'Brien, Jonathan C. F. Matthews, Anthony Laing, "On the experimental verification of quantum complexity in linear optics", Nature Photonics, 8, 621 (2014). Abstract.
[10] Malte Christopher Tichy, Markus Tiersch, Fernando de Melo, Florian Mintert, Andreas Buchleitner, "Zero-Transmission Law for Multiport Beam Splitters", Physical Review Letters, 104, 220405 (2010). Abstract.

One Clock in Two Places Simultaneously

Ron Folman (photo credit: Naomi Weisman)

Author: Ron Folman

Affiliation: Ben-Gurion University of the Negev, Beer Sheva, Israel.

Link to atom chip group >>

Introduction:

This story is about Einstein’s theory of general relativity (GR) [1] and quantum mechanics (QM) [2]. These two theories constitute the physics revolutions of the 20th century, and there are numerous attempts to unify them or, at the very least, understand how they work together. This story is also about time. Some would claim that we are still far from really understanding time [3].

GR came to life in 1915, and was successful in explaining minute anomalies in the orbits of Mercury and other planets. In 1919, Sir Arthur Eddington was able, during a total solar eclipse, to verify a prediction of the theory when he headed an expedition which confirmed the deflection of light by the Sun. Some predictions, such as gravitational waves, remain unobserved. Another of the verified predictions of GR is that time is affected by gravity; it ticks at different rates depending on how close you are to a massive object. This has been confirmed for several decades now by sending rockets with clocks to large heights and recently, as atomic clocks became much more accurate, even by simply moving a clock a few centimeters higher in a lab. This effect was nicely displayed in the recent movie 'Interstellar'.

GR was always considered strange and hard to fathom. It is rumored that in one of his lectures on GR, Sir Eddington was asked by Ludwik Silberstain: "Professor Eddington, you must be one of three persons in the world who understands general relativity." Eddington paused, unable to answer. Silberstein continued "Don't be modest, Eddington!" Finally, Eddington replied "On the contrary, I'm trying to think who the third person is." It is quite amazing to see how less than a century later GR is an important part of our day-to-day life, as it is an essential part in the GPS navigation system.

QM is thought by many to be even weirder. It took away determinism, it allowed non-locality, and it even allowed objects to be in two places (or two states, e.g., of energy or of spin) at the same time. This seemed so ridiculous that one of the fathers of QM, Erwin Schrödinger came up with a thought experiment in which a cat is alive and dead at the same time, theoretically made possible due to QM. Other contributors to the birth of QM disliked it just as much. Einstein said that “God does not play with dice” and Louis de-Broglie believed determinism will come back in a more comprehensive theory. Niels Bohr said: “For those who are not shocked when they first come across quantum theory cannot possibly have understood it”. Yet, the theory is successfully withstanding endless testing for almost a century now.

It is quite strange that these two successful theories have not been put together into one simple description of the universe. It remains to be seen what exactly the interplay between the two is: for example, some claim that the crucial process of decoherence, which is responsible for defining the border between the quantum realm and the classical world (as our day-to-day world of large objects is known), is powered by GR [4]. Some even claim that the process of “wave-function collapse” is driven by GR [5]. This process is responsible for the fact that out of many possible outcomes which exist according to QM, we see only one when we make a measurement.

The experiment :

In the experiment we conducted, published recently in Science [6], we wanted to study the interplay between the two theories. Specifically we wanted to see what would happen if we take one clock and put it in two places in which time ticks at different rates, simultaneously. We then put the clock together again and observed it.

In order to do this we used a device called an atom chip (see our website for many relevant papers). It is a powerful tool in manipulating the internal and external degrees of freedom of ultra-cold atoms. Every atom in a cloud of ultra-cold atoms (a Bose-Einstein condensate at -273 deg. Celsius) was put in two places simultaneously (known in scientific language as a spatial quantum superposition [7]), by utilizing a device called an interferometer. In parallel, every atom was turned into an atomic clock by manipulating its internal (spin) degrees of freedom.

As we did not have sensitive enough clocks to observe the minute effect of GR, we induced an artificial time difference between the two locations occupied by the single clock (these two copies of the single clock are referred to in scientific language as wave-packets). Our proof-of-principle experiment indeed shows (as predicted by [8]) that time differences have a major effect on the quantum outcome expected from an interferometer (called an “interference pattern”). Specifically, we showed that time may act as a “which path” witness as if we measured in which of the two locations the clock is. Once such a measurement is made, QM tells us that the special state of quantum superposition is destroyed and the clock can no longer be in two places at the same time (this is called “complementarity”). However, we have also showed that if the hands of the clock in one wave-packet are rotated enough so that they again overlap the hands of the clock in the other wave-packet, we again cannot differentiate between the two locations and the superposition, and consequently the interference pattern is restored.

Technically, we used very strong magnetic gradients to construct a Stern-Gerlach type of interferometer, and also used similar gradients to induce the relative time lag (using the Zeeman effect). The atoms are laser-cooled and then additionally cooled by forced evaporation. The atoms are isolated from the environment by the fact that the whole experiment is conducted in a vacuum chamber. The final outcome of the experiment is registered with a CCD camera observing the atoms.

We now have a new tool at our disposal to investigate time and the interplay between GR and QM. What we will find is an open question. Usually, new tools bring new insight. The next step should be to use more accurate clocks and to separate the clock into positions farther apart so that we are able to see the effect of GR.

The Team :

The team included Ph.D. student Yair Margalit, post-doctoral fellows Dr. Zhifan Zhou and Dr. Shimon Machluf, and researchers Dr. Yonathan Japha and Dr. Daniel Rohrlich. In the picture are the first two authors of the paper: PhD student Yair Margalit (left) and post-doctoral fellow Zhifan Zhou (right).

Additional Thoughts :

It is perhaps appropriate to end a popular article with some broad thoughts and even speculations. It stands to reason that human kind knows much less than what it doesn’t know. Namely, we are just beginning to explore and understand the structure and dynamics of our world. History and Philosophy of science teach us that our understanding is constantly changing and no theory is the “end of the road”. Will we see extensions to GR or QM in our lifetime? Will they somehow be unified?

The atoms in our lab are our teachers; they are teaching us new things every day. As we build a better dictionary from atom language to human language we will be able to understand more. They are teaching us about our physical universe and about how to understand the strange mysteries of QM. They are teaching us technology (clocks, magnetic sensors, gravitational sensors, navigation, quantum communications and quantum computing). Eventually they may even teach us things that have to do directly with who we are. For example, is there such a thing as free will? On this latter topic I invite the reader to see a very short and simplified film I made [9].

It makes me envious but also very happy to know that some of the young readers of this article will know much more than I ever will. I encourage the young reader to take up the adventure wholeheartedly.

References:
[1] “General relativity turns 100”, Special issue, Science, 347 (March 2015). Table of contents.
[2] “Foundations of quantum mechanics”, Insight issue, Nature Physics, 10 (April 2014).  Table of contents.
[3] Lee Smolin, "Time Reborn" (Mariner Books, 2014).
[4] Igor Pikovski, Magdalena Zych, Fabio Costa, Časlav Brukner, “Universal decoherence due to gravitational time dilation”, Nature Physics, 11, 668-672 (2015). Abstract.
[5] Roger Penrose, "The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics", Chapter 6 (New York: Oxford U. Press, 1989) ; Lajos Diósi, “Gravity-related wave function collapse: mass density resolution”, Journal of Physics: Conference Series, 442, 012001 (2013). Full Article ; Angelo Bassi, Kinjalk Lochan, Seema Satin, Tejinder P. Singh, Hendrik Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests”, Review of Modern Physics, 85, 471 (2013). Abstract.
[6] Yair Margalit, Zhifan Zhou, Shimon Machluf, Daniel Rohrlich, Yonathan Japha, Ron Folman, “A self-interfering clock as a 'which path' witness”, published online in 'Science Express' (August 6, 2015). Abstract.
[7] This new terminology is meaningful as all attempts to interpret the reality of this situation with day-to-day language have led to some sort of contradiction. The strange reality of the quantum world can perhaps only be accurately described by mathematics. Using words, which originate in our day-to-day (“classical”) experience, always fails those who attempt to harness them for the description of the quantum world. Perhaps one may alternatively state that the clock is in a state where it somehow “feels” how time “ticks” in several places at once.
[8] Magdalena Zych, Fabio Costa, Igor Pikovski, Časlav Brukner, “Quantum interferometric visibility as a witness of general relativistic proper time”, Nature Communications, 2, 505 (2011). Abstract. 2Physics Article.
[9] “ ‘Are we alive?’ – a thought by Ron Folman”: YouTube Link.  

Efficient Photon Collection from a Nitrogen Vacancy Center in a Circular Bullseye Grating in Diamond

[From left to right] Luozhou Li, Edward Chen and Dirk Englund.

Authors: Luozhou Li, Edward Chen, Dirk Englund

Affiliation: Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA.

Link to Quantum Photonics Laboratory >>

The nitrogen-vacancy center (NV) [1] behaves much like an atom trapped in the diamond lattice. Because of the high band gap and the mostly spin-free composition of the diamond host, the NV is well isolated from the environment, so it shows well-behaved atom-like properties. Most importantly, it’s possible to optically prepare and measure the long-lived states of the associated electron and nuclear spins. NVs are potentially promising building blocks for a large-scale quantum network where the optical addressability of the NV allows flying qubits, or photons, to connect nodes of this network together. One of the fundamental bottlenecks for this to be made into a reality is the flux of photons collected from an NV, which determines how quickly the NV’s spin state can be measured and compared: the more fluorescent photons that are collected, the faster new connections can be made. The same photon collection limitation is also true for using the NV as a highly sensitive quantum sensor, where the sensitivity to electric, magnetic and temperature fields increase with increased photon collection. Thus, higher photon detection of the NV’s photoluminescence is of central importance to many NV quantum technologies, such as communication, computing, and even sensing.

In our recent work [2], we introduce a circular “bullseye” grating in diamond (Figure 1), which enables record-high photon collection from the nitrogen-vacancy (NV) color center. The bullseye grating consists of concentric slits etched into a diamond membrane [3], which itself is about half of a wavelength in thickness. The grating period satisfies the second-order Bragg condition, giving rise to the scattering of light out of the membrane. The scattered light from each grating interferes constructively out of the plane and into the far field, thereby enabling significantly higher collection efficiency. With this circular grating, we have shown that it’s possible to collect about an order of magnitude more fluorescence than is possible from an NV in un-patterned diamond.

Figure 1: (a) Illustration of an array of diamond bullseye gratings adjacent to a microwave strip line. (b) Schematic of the circular grating. ‘a’ denotes the lattice constant and ‘gap’ the air spacing between circular gratings. (c) Simulated electric field intensity (log scale) in the x = 0 plane with air above and glass below the diamond. A dipole emitter was placed in the center of the bullseye grating, and was oriented along the horizontal direction.

Achieving higher collection efficiency from the NV impacts several applications such as improved sensing of static or dynamic electromagnetic fields just outside the diamond, higher luminosity room-temperature single photon sources, and better quantum memories for quantum computing and networking. For example, NV researchers [4] have recently shown that the NV is even sensitive to changes of single proton spins, paving the way for magnetic resonance imaging of individual molecules in liquid — and this application would be improved by better fluorescence collection from the NV.

The efficient photon collection should allow for a range of new measurements, such as non-demolition measurements of NV spins — i.e., you could make a measurement and then act back on the NV spin state. We’re also using the efficient collection for medium-scale quantum registers, which would contain on the order of tens of qubits each, and for quantum sensing.

References:
[1] Marcus W. Doherty, Neil B. Manson, Paul Delaney, Fedor Jelezko, Jörg Wrachtrup, Lloyd CL Hollenberg, "The nitrogen-vacancy colour centre in diamond." Physics Reports, 528, 1-45 (2013). Abstract.
[2] Luozhou Li, Edward H. Chen, Jiabao Zheng, Sara L. Mouradian, Florian Dolde, Tim Schröder, Sinan Karaveli, Matthew L. Markham, Daniel J. Twitchen, and Dirk Englund, "Efficient photon collection from a nitrogen vacancy center in a circular bullseye grating." Nano letters, 15, 1493 (2015). Abstract.
[3] Luozhou Li, Igal Bayn, Ming Lu, Chang-Yong Nam, Tim Schröder, Aaron Stein, Nicholas C. Harris, Dirk Englund. "Nanofabrication on unconventional substrates using transferred hard masks." Scientific reports, 5, Article number 7802 (2015). Article.
[4] A. O. Sushkov, I. Lovchinsky, N. Chisholm, R. L. Walsworth, H. Park, M. D. Lukin, "Magnetic resonance detection of individual proton spins using quantum reporters." Physical Review Letters, 113, 197601 (2014). Abstract.