Airborne Demonstration of a Quantum Key Distribution Receiver Payload

Christopher J. Pugh (left) and Thomas Jennewein

Authors: Christopher J. Pugh^1,2, Brendon L. Higgins^1,2,  Thomas Jennewein^1,2

Affiliation:
¹Institute for Quantum Computing, University of Waterloo, Ontario, Canada
²Dept of Physics and Astronomy, University of Waterloo, Ontario, Canada.

Quantum safe cryptography has truly been thrust into the limelight recently, especially after the NSA announced “The Information Assurance Directorate (IAD) will initiate a transition to quantum resistant algorithms in the not too distant future,” in August of 2015. Previous to this announcement, there has been a multitude of work done in accomplishing the quantum key distribution (QKD) protocol [1], a symmetric key algorithm, which has been proven to be cryptanalytically secure, even against quantum computer attacks. One major concern with QKD is the distances over which secure keys can be generated. In optical fibers this is known to have an upper limit around a few hundred kilometers due to absorption in the fibers. For free space, we are limited in line of site as well as atmospheric turbulence.

Using satellites to assist in the key generation helps alleviate these distance concerns by linking multiple stations located on the ground which can be separated by much larger distances than allowed by ground links. Performing QKD with moving platforms are important to prove the viability of future satellite implementations. Demonstrations of QKD to aircraft, prior to this work, have operated in the downlink configuration [2,3], where the quantum source and transmitter are placed on the airborne platform. Most recently, the Chinese Micius satellite performed entanglement distribution to ground stations separated by at least 1200 kilometers which has shown the viability of using satellites for quantum information purposes [4]. While the downlink approach ultimately has the potential for higher key rate, it is more complex and is not as flexible as an uplink configuration, which places the quantum receiver on the airborne platform while keeping the quantum source at the ground station [5]. In September 2016, we successfully achieved a quantum uplink, generating quantum secure key, to an airplane [6].

Our experimental setup consists of a QKD source (in a trailer for temperature and humidity control) and transmitter located at a ground station at Smiths Falls—Montague Airport (Fig 1), and a QKD receiver located on a Twin Otter research aircraft from the National Research Council of Canada. Targeting and tracking were established using strong beacon lasers, an imaging camera, and tracking feedback to motors at each of the two sites. Once at the aircraft, the QKD signals were recorded for later processing to complete the QKD protocol and secure extract key.

In order to generate the photons for encoding the information, we use a weak coherent pulse source implementing polarization-encoded BB84 with decoy states [7] at a rate of 400 MHz. These signals are characterized at the source with an automated polarization compensation system to compensate for drifts due to the optical fiber portion of the transmission to the transmitting telescope.

Fig 1: Optical ground station located at Smiths Falls—Montague Airport. The airplane is shown in the background as the white dashed line in the sky.

At the receiver, the signal is coupled from the receiver telescope into a custom fine pointing unit which guides both the quantum and beacon signals with a fast-steering mirror. Inside the fine-pointing system, a dichroic mirror separates the quantum and beacon signals---the beacon is reflected towards a quad-cell photo-sensor, providing position feedback to guide the fast-steering mirror in a closed loop.

The quantum signal then passes into a custom integrated optical assembly, containing a passive-basis-choice polarization analysis module with a 50:50 beam splitter and polarizing beam splitters, resulting in four beams corresponding to the four BB84 measurement states (horizontal, vertical, diagonal, and anti-diagonal). These four modes are then coupled into multimode fibers and guided to Silicon avalanche photo diodes detectors. The detectors trigger low-voltage differential signalling pulses which are measured at a control and data processing unit based on Xiphos' Q7 processor card, which has recently flown on the GHGSat, with a custom daughter board.

The airplane flew two path types: circular arcs around the ground station, and lines past the ground station. The distances for each type of pass varied from 3 to 10 km. The circular paths were used for longer link times as well as to relax pointing requirements as the aircraft telescope would remain relatively still and the transmitter would observe a constant rate. The line passes are more representative of a satellite, showing different angular speeds for different portions of the pass.

Fig 2: The Smiths Falls—Montague Airport as seen from the airplane during a day test flight. The end of the telescope can be seen in the far left of the photo.

In total, we had successful quantum links in seven of 14 passes of the airplane over the ground station, generating asymptotic key in one pass and finite-size secure key in 5 passes, with one pass showing over 800 kbit. The loss in the various passes ranged from 34.4 to 51.1 dB. Angular speeds (at the transmitter) between 0.4 deg/s and 1.28 deg/s were achieved. A transmitter pointing at a typical low-Earth-orbit satellite with an altitude of roughly 600 kilometers would be tracking at an angular speed of approximately 0.7 deg/s whereas tracking the International Space Station would require approximately 1.2 deg/s.

Fig 3: (left to right) Christopher Pugh and Thomas Jennewein hold up a University of Waterloo/Institute for Quantum Computing sticker to be mounted on the NRC Twin Otter Research Aircraft. The QKD receiver can be seen in the open door of the airplane.

In this experiment, we have demonstrated the viability of components of a quantum receiver satellite payload by successfully performing quantum key distribution in an uplink configuration to an airplane. The major components in the receiver payload (fine pointing unit, integrated optics assembly, detector modules, control and data processing unit) have a clear path to flight for future satellite integration. Recently, the Canadian government and the Canadian Space Agency have announced the intent to build a quantum satellite and this work will be beginning shortly.

References:
[1] Charles H. Bennett and Gilles Brassard, “Quantum cryptography: Public key distribution and coin tossing”. In Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, pages 175-179 (IEEE Press, New York, 1984). Article.
[2] Sebastian Nauerth, Florian Moll, Markus Rau, Christian Fuchs, Joachim Horwath, Stefan Frick, Harald Weinfurter, “Air-to-ground quantum communication”. Nature Photonics, 7, 382 (2013). Abstract.
[3] Jian-Yu Wang, Bin Yang, Sheng-Kai Liao, Liang Zhang, Qi Shen, Xiao-Fang Hu, Jin-Cai Wu, Shi-Ji Yang, Hao Jiang, Yan-Lin Tang, Bo Zhong, Hao Liang, Wei-Yue Liu, Yi-Hua Hu, Yong-Mei Huang, Bo Qi, Ji-Gang Ren, Ge-Sheng Pan, Juan Yin, Jian-Jun Jia, Yu-Ao Chen, Kai Chen, Cheng-Zhi Peng, Jian-Wei Pan., “Direct and full-scale experimental verifications towards ground-satellite quantum key distribution”. Nature Photonics, 7, 387 (2013). Abstract.
[4] Juan Yin, Yuan Cao, Yu-Huai Li, Sheng-Kai Liao, Liang Zhang, Ji-Gang Ren, Wen-Qi Cai, Wei-Yue Liu, Bo Li, Hui Dai, Guang-Bing Li, Qi-Ming Lu, Yun-Hong Gong, Yu Xu, Shuang-Lin Li, Feng-Zhi Li, Ya-Yun Yin, Zi-Qing Jiang, Ming Li, Jian-Jun Jia, Ge Ren, Dong He, Yi-Lin Zhou, Xiao-Xiang Zhang, Na Wang, Xiang Chang, Zhen-Cai Zhu, Nai-Le Liu, Yu-Ao Chen, Chao-Yang Lu, Rong Shu, Cheng-Zhi Peng, Jian-Yu Wang, Jian-Wei Pan, “Satellite-based entanglement distribution over 1200 kilometers”. Science, 356:1140 (2017). Abstract.
[5] J-P Bourgoin, E Meyer-Scott, B L Higgins, B Helou, C Erven, H Hübel, B Kumar, D Hudson, I D'Souza, R Girard, R Laflamme, T. Jennewein, “A comprehensive design and performance analysis of low Earth orbit satellite quantum communication”. New Journal of Physics, 15, 023006 (2013). Abstract.
[6] Christopher J Pugh, Sarah Kaiser, Jean-Philippe Bourgoin, Jeongwan Jin, Nigar Sultana, Sascha Agne, Elena Anisimova, Vadim Makarov, Eric Choi, Brendon L Higgins, Thomas Jennewein, “Airborne demonstration of a quantum key distribution receiver payload”. Quantum Science and Technology, 2, 024009 (2017). Abstract.
[7] Hoi-Kwong Lo, Xiongfeng Ma, Kai Chen, “Decoy state quantum key distribution”. Physical Review Letters, 94, 230504 (2005). Abstract.

Solving Linear Equations on Scalable Superconducting Quantum Computing Chip

From left to right: Chao-Yang Lu, Jian-Wei Pan, Xiaobo Zhu, H. Wang, Ming-Cheng Chen

Authors: Ming-Cheng Chen¹, H. Wang², Xiaobo Zhu^1,3, Chao-Yang Lu¹, Jian-Wei Pan¹

Affiliation:
¹Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China,
²Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China,
³Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.

One-sentence summary:
Quantum solver of linear system is achieved on scalable superconducting quantum computing chip.

The most ambitious target of quantum computing is to provide both high-efficiency and useful quantum software for killer applications. After decades of intense research on quantum computing, several quantum algorithms are found to demonstrate speedup over their classical counterparts, such as quantum simulation of molecular or condensed system [1], Grover search on unstructured database [2], Shor's period finding to crack RSA cryptography [3], matrix inversion to solve linear systems [4] and sampling from a hard distribution [5, 6]. Among them, sampling from a hard distribution is the most radical example to show the pure quantum computing power beyond the reach of any modern conventional computer and achieve "quantum supremacy" in the near-term [7].

However, the high-efficiency quantum supremacy algorithms have not been found to have practical applications yet. And the Grover search and Shor's period finding algorithms are limited to specific applications. On the contrary, the linear equations quantum algorithm can be applied to almost all areas of science and engineering and recently it finds fascinating applications in data science as a basic subroutine, for instance, in quantum data fitting [8] and quantum support vector machine [9].

Matrix inversion quantum algorithm to solve linear systems [4] is proposed by Harrow, Hassidim and Lloyd (HHL) in 2009 to estimate some features of the solution with exponential speedup. The algorithm uses the celebrated quantum phase estimation technology to force the computation to work at the eigen-basis of system matrix and reduce the matrix inversion to simple eigenvalue reciprocal. A compiled version of the HHL algorithm was previously demonstrated with linear optics [10, 11] and liquid NMR [12] quantum computing platforms, however, both of which are considered not easily scalable to a large number of qubits. Recently, we report the new implementation of the HHL algorithm on solid superconducting quantum circuit system, which is deterministic and easy scalable to large scale.

We run a nontrivial instance of smallest 2×2 system on superconducting circuit chip with four X-shape transmon qubits [13] and tens of one- and two-qubit quantum gates. The chip was fabricated on a sapphire substrate and used aluminum material to define superconducting qubits, resonators and transmission lines. With careful calibration, the single-qubit rotating gates were estimated to be of 98% fidelity and two-qubit entangling gates were of above 95% fidelity. Figure 1 and Figure 2 illustrate the quantum chip and the working quantum circuits, respectively.

Fig. 1: False color photomicrograph of the superconducting quantum circuit for solving 2×2 linear equations. Shown are the four X-shape transmon qubits, marked from Q1 to Q4, and their corresponding readout resonators.

Fig. 2: (click on image to view with higher resolution) Compiled quantum circuits for solving 2×2 linear equations with four qubits. There are three subroutines and more than 15 gates as indicated.

The quantum solver was tested by 18 different input vectors and the corresponding output solution vectors were characterized using quantum state tomography. In our 2*2 instance, the output qubit was measured along X, Y and Z axes of the Bloch sphere, respectively. The estimated quantum state fidelities ranged from 84.0% to 92.3%. The collected data was further used to infer the quantum process matrix of the solver and yielded the process fidelity of 83.7%. Figure 3 and Figure 4 show the experimental quantum state fidelity distribution and the quantum process matrix, respectively.

Fig. 3: Experimental quantum state fidelity distribution of the output states corresponding to the 18 input states.

Fig. 4: The real parts of the experimental quantum process matrix (bars with color) and the ideal quantum process matrix (black frames). All imaginary components (data not shown) of quantum process are measured to be no higher than 0.015 in magnitude.

These experimental results indicate that our superconducting quantum linear solver for 2*2 system have successfully operated. To scale the solver for more complicated instance with high solution accuracy, further improvement of device design and fabrication to increase quantum bit coherent time and optimization of quantum control pulses to reduce the operating time and error rate are necessary. In superconducting quantum circuit platform, there have been vast efforts devoted to scale the circuit complexity and quality, which have extended the qubit coherent time 5~6 orders of magnitude [14] manipulated up to 10 qubits [15] in the past decades, and we can expect the continuous progress in next decade to reach a mature level.

References:
[1] I. M. Georgescu, S. Ashhab, Franco Nori, "Quantum simulation". Reviews of Modern Physics, 86, 153 (2014). Abstract.
[2] P. Shor, “Algorithms for quantum computation: discrete logarithms and factoring” in Proc. 35th Annu. Symp. on the Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society Press, Los Alamitos, California, 1994), p. 124–134. Abstract.
[3] Lov K. Grover, "A Fast Quantum Mechanical Algorithm for Database Search", Proceedings of 28th Annual ACM Symposium on Theory of Computing, pp. 212-219 (1996). Abstract.
[4]  Aram W. Harrow, Avinatan Hassidim, Seth Lloyd, “Quantum algorithm for linear systems of equations”. Physical Review Letters, 103, 150502 (2009). Abstract.
[5] A. P. Lund, Michael J. Bremner, T. C. Ralph, "Quantum sampling problems, BosonSampling and quantum supremacy." NPJ Quantum Information, 3:15 (2017). Abstract.
[6] Hui Wang, Yu He, Yu-Huai Li, Zu-En Su, Bo Li, He-Liang Huang, Xing Ding, Ming-Cheng Chen, Chang Liu, Jian Qin, Jin-Peng Li, Yu-Ming He, Christian Schneider, Martin Kamp, Cheng-Zhi Peng, Sven Höfling, Chao-Yang Lu, Jian-Wei Pan, "High-efficiency multiphoton boson sampling". Nature Photonics 11, 361 (2017). Abstract.
[7] John Preskill, "Quantum computing and the entanglement frontier". arXiv:1203.5813 (2012).
[8] Nathan Wiebe, Daniel Braun, Seth Lloyd, "Quantum algorithm for data fitting". Physical review letters 109, 050505 (2012). Abstract.
[9] Patrick Rebentrost, Masoud Mohseni, Seth Lloyd, "Quantum support vector machine for big data classification". Physical review letters 113, 130503 (2014). Abstract.
[10] X.-D. Cai, C. Weedbrook, Z.-E. Su, M.-C. Chen, Mile Gu, M.-J. Zhu, Li Li, Nai-Le Liu, Chao-Yang Lu, Jian-Wei Pan, "Experimental quantum computing to solve systems of linear equations". Physical review letters 110, 230501 (2013). Abstract.
[11] Stefanie Barz, Ivan Kassal, Martin Ringbauer, Yannick Ole Lipp, Borivoje Dakić, Alán Aspuru-Guzik, Philip Walther, "A two-qubit photonic quantum processor and its application to solving systems of linear equations". Scientific reports 4, 6115 (2014). Abstract.
[12] Jian Pan, Yudong Cao, Xiwei Yao, Zhaokai Li, Chenyong Ju, Hongwei Chen, Xinhua Peng, Sabre Kais, Jiangfeng Du, "Experimental realization of quantum algorithm for solving linear systems of equations". Physical Review A 89, 022313 (2004). Abstract.
[13] Jens Koch, Terri M. Yu, Jay Gambetta, A. A. Houck, D. I. Schuster, J. Majer, Alexandre Blais, M. H. Devoret, S. M. Girvin, R. J. Schoelkopf, "Charge-insensitive qubit design derived from the Cooper pair box". Physical Review A 76, 042319 (2007). Abstract.
[14] M. H. Devoret, R. J. Schoelkopf1, "Superconducting circuits for quantum information: an outlook". Science, 339, 1169 (2013). Abstract.
[15] Chao Song, Kai Xu, Wuxin Liu, Chuiping Yang, Shi-Biao Zheng, Hui Deng, Qiwei Xie, Keqiang Huang, Qiujiang Guo, Libo Zhang, Pengfei Zhang, Da Xu, Dongning Zheng, Xiaobo Zhu, H. Wang, Y.-A. Chen, C.-Y. Lu, Siyuan Han, J.-W. Pan, "10-qubit entanglement and parallel logic operations with a superconducting circuit". arXiv:1703.10302 (2017). 

Schmidt Decomposition Made Universal to Unveil the Entanglement of Identical Particles

From left to right: Stefania Sciara, Rosario Lo Franco, Giuseppe Compagno

Authors: Stefania Sciara^1,2, Rosario Lo Franco^2,3, Giuseppe Compagno²

Affiliation:
¹INRS-EMT, Varennes, Québec J3X 1S2, Canada,
²Dipartimento di Fisica e Chimica, Università di Palermo, Italy,
³Dipartimento di Energia, Ingegneria dell'Informazione e Modelli Matematici, Università di Palermo,  Italy.

The Schmidt decomposition is an important mathematical tool which has been already utilized during the early stages of quantum theory by Schrödinger in the context of quantum measurements [1-3]. This tool allows to determine the set of measurements on one part of the system such that the measurement outcome on the other part is determined, in the sense that to each outcome of the first measurement it corresponds a unique outcome for the second measurement. Schmidt decomposition has been shown to be at the heart of quantum information theory, quantifying entanglement in bipartite systems. It has been also widely employed in the context of Einstein-Podolski-Rosen (EPR) paradox, Bell non-locality and black-hole physics [2-4].

Every element of this decomposition consists unavoidably of two independent subsystems. Application of the Schmidt decomposition to identical particles is therefore hindered by the fact that overlapping particles can never be considered independent. In fact, despite its wide utilization in systems of distinguishable particles, the Schmidt decomposition has remained debated for identical particles [5,6]. For instance, it is well known that for distinguishable particles this tool assesses the entanglement of the system by the von Neumann entropy of the reduced density matrix, whose eigenvalues are the squares of the Schmidt coefficients appearing in the decomposition [3]. Differently, in the case of identical particles, it has been claimed that the relationship between the Schmidt coefficients and the eigenvalues of the reduced density matrix breaks down [6]. In strict connection with this issue, the partial trace operation to get the reduced state has not been considered suitable for quantifying the entanglement of pure states of identical particles [6-8].

We recall that, in Nature, particles are of different types, all particles of each type (electrons, protons, photons and so on) being identical. In the quantum world, the identity of particles gives rise to a new characteristic with respect to the classical world, that is the indistinguishability among particles of the same type [9,10]. This exclusive quantum trait leads to fundamental properties of matter such that particles can be of two classes, named bosons and fermions. Moreover, at variance with the case of distinguishable particles, when identical particles have wave functions that spatially overlap, they can never be taken as independent of each other [11,12].

The latter behavior is an essential requisite in determining features like quantum correlations (e.g., entanglement) among the particles themselves and in the theory of measurement [1]. Nevertheless, identical particles constitute the building blocks of quantum information and computation theory, being present in Bose-Einstein condensates [13,14], quantum dots [15,16], superconducting circuits [17] and optical setups [18,19]. It is thus important to have trustable methods and tools to characterize the quantum features of composite systems of identical particles under these general conditions.

A first step towards this goal has been provided by a recent non-standard approach [12] which deals with systems of identical particles within a particle-based description (that is, in terms of particle states) without resorting to the usual practice to assign fictitious labels to the particles [9,10], which render the latter distinguishable removing their indistinguishability. In this way, the ambiguity arising from the introduction of these labels in evaluating quantum correlations in identical particle systems is avoided. This method has, in fact, provided a way to calculate partial trace and von Neumann entropy for identical particles. Using this new approach, in a recent work [20] we have been able to demonstrate that the Schmidt decomposition is universal, meaning that it is also obtainable for an arbitrary state of indistinguishable particles (bosons or fermions) under general conditions of spatial overlap. Thanks to this achievement, the amount of entanglement present in identical particle systems in pure states can be evaluated by the von Neumann entropy of the reduced density matrix, as occurs in the case of distinguishable particles.

We have used the Schmidt decomposition to analyze some paradigmatic states of two identical particles to find the suitable measurement basis for unveiling their entanglement properties. These systems are illustrated in Figure 1 and represent simple yet effective examples which make it emerge the effect of particle identity. The first one is the well-known condition of two identical qubits with opposite pseudospins in spatially separated locations, denoted with left (L) and right (R) (see Fig. 1a).

Figure 1. (a) Two identical qubits in two spatially separated places with opposite pseudospins. (b) Two identical qubits in the same spatial mode with arbitrary pseudospins. (c) Two identical qutrits (three-level quantum systems) in the same spatial mode. The shaded ellipses indicate that the particles are entangled. Figure from Ref. [20].

Indeed, we have found that the Schmidt decomposition and the corresponding von Neumann entropy supply the results which are physically expected in this situation, such as zero entanglement for a product (separable) state of the two particles and maximal entanglement for a Bell state. We have also explicitly shown that nonlocal measurements induce entanglement in a state of distant identical particles. This means that, in principle, identical particles cannot be considered completely independent even when they are spatially separated. Application of the Schmidt decomposition to a system of two boson qubits in the same site (see Fig. 1b) has evidenced that the entanglement increases as the two internal states tend to be orthogonal, as displayed in the plot of Fig. 2. This finding is a generalization of a previous result obtained only for two identical qubits in the same spatial mode with orthogonal internal states (or pseudospins, that is θ = π in the plot of Fig. 2) [12].

Figure 2. Entanglement between the pseudospins of two identical particles in the same site, quantified by the von Neumann entropy, as a function of the angle θ between the directions of the two pseudospins (internal states). Figure from Ref. [20].

Two identical (boson) qutrits, that is three-level quantum systems, constitute a system of interest being promising candidates for quantum processors thanks to their good capacity to store quantum information [21,22]. We consider the qutrits in the same site, that is under the condition of complete spatial overlap, as depicted in Fig. 1c. Our method easily determines the two-qutrit entanglement for given combinations of their internal states and provides a physical interpretation. We remark that the entanglement found for the two qutrits is different from that obtained for the same system by an alternative approach, based on a so-called subalgebra technique [8]. The origin of this difference in the entanglement measure requires further investigation, for instance by comparing the two theoretical approaches or by experimental verifications.

We now briefly discuss the practical aspect concerning the possibility to exploit the entanglement of identical particles, as identified by the Schmidt decomposition we have introduced. In the context of quantum information processing with distinguishable particles, a well-established resource theory is based on local operations and classical communication (LOCC), where each particle is individually addressed [1-3]. On the other hand, a peculiar trait of indistinguishable particles is that it is not possible to operate on a given individual particle. This characteristic in general hinders the manipulation of composite systems of identical particles for desired tasks of quantum information and computation. Nevertheless, it is known that the entanglement quantified by the von Neumann entropy can be extracted from the state of identical particles and then utilized in a conditional way by LOCC [23].

In conclusion, the universal character of the Schmidt decomposition shown in our work allows a faithful treatment of the entanglement of composite systems of identical particles and opens the way to more general investigations of collective properties of such systems.

References:
[1] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, Karol Horodecki, “Quantum entanglement”, Review of Modern Physics, 81, 865 (2009). Abstract.
[2] John Preskill, “Lectures notes for physics 229: Quantum information and computation” (1998) Link.
[3] Michael A. Nielsen and Isaac L. Chuang, “Quantum Computation and Quantum Information” (Cambridge University Press, Cambridge, 2000).
[4] E.D. Belokolos, M.V. Teslyk, “Scalar field entanglement entropy of a Schwarzschild black hole from the Schmidt decomposition viewpoint”, Classical and Quantum Gravity, 26, 235008 (2009). Abstract.
[5] R. Paškauskas, L. You, “Quantum correlations in two-boson wave functions”, Physical Review A, 64, 042310 (2001). Abstract.
[6] Malte C Tichy, Florian Mintert, Andreas Buchleitner, “Essential entanglement for atomic and molecular physics”, Journal of Physics B: Atomic, Molecular and Optical Physics. 44, 192001 (2011). Abstract.
[7] GianCarlo Ghirardi, Luca Marinatto, Tullio Weber, “Entanglement and properties of composite quantum systems: a conceptual and mathematical analysis”, Journal of Statistical Physics 108, 49 (2002). Abstract.
[8] A. Balachandran, T. Govindarajan, Amilcar R. de Queiroz, A. Reyes-Lega, “Entanglement and particle identity: A unifying approach”, Physical Review Letters, 110, 080503 (2013). Abstract.
[9] Asher Peres, “Quantum Theory: Concepts and Methods” (Springer, Dordrecht, The Netherlands, 1995).
[10] Claude Cohen-Tannoudji, Bernard Diu, Franck Laloe, “Quantum mechanics, Vol. 2” (Wiley-VCH, Paris, France, 2005).
[11] John Schliemann, J. Ignacio Cirac, Marek Kuś, Maciej Lewenstein, Daniel Loss, “Quantum correlations in two-fermion systems”, Physical Review A, 64, 022303 (2001). Abstract.
[12] Rosario Lo Franco, Giuseppe Compagno, “Quantum entanglement of identical particles by standard information-theoretic notions”, Scientific  Reports, 6, 20603 (2016). Abstract.
[13] Immanuel Bloch, Jean Dalibard, Wilhelm Zwerger, “Many-body physics with ultracold gases”, Review of Modern Physics, 80, 885 (2008). Abstract.
[14] Marco Anderlini, Patricia J. Lee, Benjamin L. Brown, Jennifer Sebby-Strabley, William D. Phillips,  J. V. Porto, “Controlled exchange interaction between pairs of neutral atoms in an optical lattice”, Nature 448, 452 (2007). Abstract.
[15] Michael H. Kolodrubetz, Jason R. Petta, “Coherent holes in a semiconductor quantum dot”, Science 325, 42–43 (2009). Abstract.
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[19] Christian Reimer, Michael Kues, Piotr Roztocki, Benjamin Wetzel, Fabio Grazioso, Brent E. Little, Sai T. Chu, Tudor Johnston, Yaron Bromberg, Lucia Caspani, David J. Moss, Roberto Morandotti, “Generation of multiphoton entangled quantum states by means of integrated fre-quency combs”, Science 351, 1176 (2016). Abstract.
[20] Stefania Sciara, Rosario Lo Franco, Giuseppe Compagno, “Universality of Schmidt decomposition and particle identity”, Scientific Reports, 7, 44675 (2017). Abstract.
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[23] N. Killoran, M. Cramer, M. B. Plenio, “Extracting entanglement from identical particles”, Physical Review Letters, 112, 150501 (2014). Abstract.

A Step Towards The Realization of A Quantum Network

Ataç Imamoglu (left) and Aymeric Delteil (right)

Authors : Aymeric Delteil, Zhe Sun, Stefan Fält, Atac Imamoglu

Affiliation: Institute of Quantum Electronics, ETH Zurich, Switzerland.

Quantum network architectures consist of local nodes comprising quantum memories that are interconnected using single photons propagating in photonic channels. In such networks, the ability to transfer a quantum bit of information (qubit) from one node to another plays a central role. In a practical implementation, the photonic qubits are generated through spontaneous emission from a matter qubit – embodied for instance by a single atom or ion, a point defect or a quantum dot in a solid-state matrix. The generated photons are then collected in a fiber and sent to another matter qubit using a photonic channel.

Since photonic channels are subject to imperfect collection efficiencies and photon losses, there is a finite probability that such a state transfer based on a single photonic qubit fails. It is therefore suitable to have a heralding signal testifying that the transfer has been successful. Although some basic elements towards such heralded quantum state transfer have already been demonstrated in previous work using various physical systems [1-4], a full node-to-node heralded transfer using single photon qubits has not been achieved to date, mainly due to the dominant role of photon losses.

Using self-assembled semiconductor quantum dots (QDs), we have demonstrated heralded absorption of a neutral (source) QD generated single photonic qubit, by a single-electron charged (target) QD that is located 5 m away [5]. The photonic qubit is thereby transferred and stored in the spin degree of freedom of the single host electron. A successful process is heralded by detection of a subsequent photon that carries no information about the qubit state, which is essential to preserve the coherent quantum superposition.

The principle of our experiment is depicted in fig. 1. The source QD (QD1) is neutral and can be prepared in an arbitrary superposition of two exciton states using a two-color laser beam. This quantum state is encoded in the color of a single photon (flying qubit) generated upon radiative recombination of the QD1 exciton. This flying qubit is collected into a fiber and transferred to the target QD. Amongst the wide variety of QDs that are randomly formed during the growth of the sample, the target QD has been carefully selected to have a specific energy level scheme presenting two transitions of identical energies, such that photons emitted after absorption of the photonic qubit carry no information about the decay path. As a consequence, if the spin state is initially prepared in the superposition state |up> + |down>, upon absorption of the photonic qubit and detection of the subsequent photon, the electron spin ends in the qubit state generated by the laser excitation of the source QD.

Figure 1 : (Click on the image to view with higher resolution) Principle of the state transfer protocol based on heralded absorption of a single photon qubit.

Implementing such an experiment is particularly challenging due to finite collection efficiencies and losses in the optical elements along the chain. One of the key elements that have allowed our realization is the use of a photonic structure enabling efficient extraction of the emitted photons. More specifically, the QDs are embedded in a planar cavity and the cavity output is collected using a solid immersion lens placed on top of the sample, ensuring that about 20% of the photons from each QD are collected by the first lens. The use of sensitive superconducting single photon detector with very low dark counts as well as crossed-polarization detection to suppress the strong pump laser light and background scattering have allowed us to demonstrate heralded absorption where we detected up to about 100 successful events per second. We demonstrated that the final state of the destination quantum dot spin is correlated with the initial state of the photon (or the target QD exciton) by measuring time-resolved photon coincidences.

Our scheme can be extended to realize spin-to-spin state transfer, or to generate heralded distant entanglement between two QD spins [6]. It can also be used to connect dissimilar physical systems in the context of hybrid quantum networks [7].

References:
[1] Stephan Ritter, Christian Nölleke, Carolin Hahn, Andreas Reiserer, Andreas Neuzner, Manuel Uphoff, Martin Mücke, Eden Figueroa, Joerg Bochmann, Gerhard Rempe, “An elementary quantum network of single atoms in optical cavities”, Nature, 484, 195 (2012). Abstract.
[2] Christoph Kurz, Michael Schug, Pascal Eich, Jan Huwer, Philipp Müller, Jürgen Eschner, “Experimental protocol for high-fidelity heralded photon-to-atom quantum state transfer”, Nature Communications, 5, 5527 (2014). Abstract.
[3] Norbert Kalb, Andreas Reiserer, Stephan Ritter, Gerhard Rempe, “Heralded Storage of a Photonic Quantum Bit in a Single Atom”, Physical Review Letters, 114, 220501 (2015). Abstract.
[4] Sen Yang, Ya Wang, D. D. Bhaktavatsala Rao, Thai Hien Tran, Ali S. Momenzadeh, M. Markham, D. J. Twitchen, Ping Wang, Wen Yang, Rainer Stöhr, Philipp Neumann, Hideo Kosaka, Jörg Wrachtrup, “High-fidelity transfer and storage of photon states in a single nuclear spin”, Nature Photonics, 10, 507 (2016). Abstract.
[5] Aymeric Delteil, Zhe Sun, Stefan Fält, Atac Imamoğlu, “Realization of a Cascaded Quantum System: Heralded Absorption of a Single Photon Qubit by a Single-Electron Charged Quantum Dot”, Physical Review Letters, 118, 177401 (2017). Abstract.
[6] D. Pinotsi and A. Imamoglu, “Single Photon Absorption by a Single Quantum Emitter”, Physical Review Letters, 100, 093603 (2008). Abstract.
[7] H. M. Meyer, R. Stockill, M. Steiner, C. Le Gall, C. Matthiesen, E. Clarke, A. Ludwig, J. Reichel, M. Atatüre, M. Köhl, “Direct Photonic Coupling of a Semiconductor Quantum Dot and a Trapped Ion”,  Physical Review Letters, 114, 123001 (2015). Abstract.

Ultrafast Quantum Simulator

Photos of some of the authors -- From Left to Right: (top row) Nobuyuki Takei,  Christian Sommer,  Claudiu Genes, Guido Pupillo; (bottom row)  Hisashi Chiba,  Matthias Weidemüller,  Kenji Ohmori.

Authors: Nobuyuki Takei^1,2, Christian Sommer^1,2,3, Claudiu Genes³, Guido Pupillo⁴, Haruka Goto¹, Kuniaki Koyasu^1,2, Hisashi Chiba^1,5, Matthias Weidemüller^6,7,8, Kenji Ohmori^1,2

Affiliation:
¹Department of Photo-Molecular Science, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, Japan,
²SOKENDAI (The Graduate University for Advanced Studies), Okazaki, Japan,
³Max Planck Institute for the Science of Light, Erlangen, Germany,
⁴IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, Strasbourg, France,
⁵Faculty of Engineering, Iwate University, Morioka, Japan,
⁶Physikalisches Institut, Universität Heidelberg, Heidelberg, Germany,
⁷Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, China,
⁸CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.

Link to Ohmori Group in Okazaki >>

The dynamics of interactions among large numbers of electrons govern a variety of important physical and chemical phenomena such as superconductivity, magnetism, and chemical reactions. An ensemble of many particles thus interacting with each other is referred to as a “strongly correlated system”. Understanding quantum mechanical behavior of a strongly correlated system is thus one of the central goals of modern sciences. It is extremely difficult, however, to predict theoretically the properties of a strongly correlated system even using the Japanese post-K supercomputer, which is expected to be one of the world’s fastest supercomputers planned to be completed by the year 2020. For example, the post-K cannot calculate even the ground-state energy by exact diagonalization, when the number of particles in the system is more than 30. It is in general more demanding to calculate the dynamics of the strongly correlated system.

Instead of calculating with a classical computer such as the post-K, an alternative concept has been proposed by Richard Feynman in 1980’s [1] and is now referred to as a “quantum simulator”, in which quantum mechanical particles such as atoms are assembled into an artificial strongly correlated system, whose properties are known and controllable [2,3]. It is then used to simulate and understand the properties of another strongly correlated system whose properties are not known. A quantum simulator could quickly simulate quantum mechanical behavior of a large number of particles that cannot be handled even by the post-K supercomputer, expected to become a next-generation simulation platform.

We have developed a completely new quantum simulator that can simulate the quantum mechanical dynamics of a strongly correlated system of more than 40 atoms within one nanosecond [4-6]. This has been realized by introducing a novel approach in which an ultrashort laser pulse whose pulse width is only 10 picoseconds is employed to control a high-density ensemble of atoms cooled to temperatures close to absolute zero. Furthermore we have succeeded in simulating the motion of electrons of this strongly correlated system that is modulated by changing the strength of interactions among many atoms in the ensemble.

In order to generate a strongly correlated system in which a large number of particles interact simultaneously with each other, it should be effective to assemble a quantum simulator with particles whose forces could reach as far as possible. A “Rydberg atom” is expected as the most promising candidate for that [7,8]. An atom usually has a diameter of about sub-nanometer, but can be irradiated with laser light to bring an electron that moves near its atom core to a high-energy orbital called a “Rydberg orbital”, whose diameter could be more than hundreds of nanometers. The atom thus generated is referred to as a Rydberg atom. Due to its long distance between the atom core with a positive charge and the Rydberg electron with a negative charge, a Rydberg atom generates an electric field that reaches a long distance. If one could build up an ensemble of Rydberg atoms, it should become a strongly correlated system in which those many Rydberg atoms interact simultaneously with each other. However, the strong electric field induced by a Rydberg atom shifts the energies of the Rydberg orbitals of its surrounding atoms as shown schematically in Fig. 1, so that conventional laser light cannot bring electrons of those surrounding atoms to their Rydberg orbitals. Accordingly there can be only one Rydberg atom within a sphere of a certain radius. This phenomenon is referred to as “Rydberg blockade” [7,8] and needs to be circumvented to generate a strongly correlated system of Rydberg atoms.

Figure 1: Mechanism of Rydberg blockade

Moreover there is another problem to be solved to realize such a Rydberg quantum simulator. Even if one could generate a strongly correlated system, the strong interaction among the Rydberg atoms would induce the temporal evolution of their quantum states on the timescale of 100 picoseconds, which is faster by a factor of more than hundred thousand than the timescale of a quantum simulator that has so far been considered.

In order to create a Rydberg quantum simulator that can simulate a strongly correlated system, therefore, a totally new concept and technique have been needed to solve those two essential problems: (1) how to circumvent Rydberg blockade?; (2) how to observe the system on the timescale faster by a factor of hundred thousand than the one considered for a quantum simulator so far?

We have succeeded in solving those two essential problems for the first time. Figure 2a schematically shows a property of laser light that has so far been used typically for the development of a quantum simulator. It shines continuously as shown in Fig. 2(a-1) and is produced by a so-called “continuous wave laser”. This laser light has an extremely narrow range of wavelength (energy) as shown in Fig. 2(a-2). Therefore it cannot bring an electron to the Rydberg orbital that is shifted energetically in the surrounding atom as shown in Fig. 1. Instead of using this continuous wave laser, therefore, we has introduced a pulsed laser light that shines only during ~ 10 picoseconds as shown in Fig. 2(b-1). This pulsed laser light has its wavelength range broader than that of the continuous wave laser by a factor of more than one million as shown in Fig. 2(b-2). It can therefore bring an electron to the Rydberg orbital even if its energy is shifted in the surrounding atom. Moreover the temporal width of the laser pulse is one tenth of the timescale expected for the temporal evolution of the system, so that the evolution should be able to be observed in real time.

Figure 2: Properties of conventional laser light that has so far been used for the development of a quantum simulator (a-1, a-2) and of the one newly introduced in our work (b-1, b-2).

The experiment was performed with rubidium atoms. Figure 3 shows a schematic of the experiment. An ensemble of ~ 10⁶ rubidium atoms was cooled down to an ultralow temperature around 70 microK with laser cooling techniques and trapped in a laser tweezer. These atoms were irradiated with an “ultrashort laser pulse 1” whose pulse width was ~ 10 picoseconds, and its wavelength range was appropriately manipulated with a special technique. The temporal evolution of the atoms after laser pulse 1 was observed with another “ultrashort laser pulse 2”. The delay of laser pulse 2 from laser pulse 1 was controlled ultra-precisely on the 10 attosecond timescale with a special device, so that the evolution was observed on this timescale. It was then observed in real time that the electrons of many Rydberg atoms, which were generated with laser pulse 1 that circumvented Rydberg blockade, oscillated with a period of one femtosecond, and the timing of those oscillations was gradually shifted on the timescale of 10 attoseconds due to the simultaneous interactions among more than 40 Rydberg atoms. Furthermore this timing shift has successfully been accelerated by enlarging the Rydberg orbitals or by decreasing the distances among Rydberg atoms to increase the strength of the interactions.

Figure 3: Schematic of the experimental setup.

We have thus introduced ultrashort laser pulses into a quantum simulator for the first time and succeeded in developing a totally new quantum simulator. This ultrafast quantum simulator can simulate the dynamics of a large number of particles interacting with each other that cannot be handled by even a world’s fastest supercomputer such as the post-K. The simulation has been completed in 1 nanosecond.

It has been demonstrated that our ultrafast quantum simulator can quickly simulate the dynamics of a strongly correlated system of a large number of particles interacting with each other, which cannot be handled by even the post-K supercomputer. The ultrafast quantum simulator is expected to develop into a future simulation platform that could contribute to designing superconducting and magnetic materials and drug molecules, whose functionalities are governed by strongly correlated electrons. It is also expected to serve as a fundamental tool to investigate the origins of physical properties of matter such as superconductivity and magnetism as well as the mechanism of a chemical reaction that proceeds in a complex environment such as a liquid.

References:
[1] Richard P. Feynman, “Simulating physics with computers”, International Journal of Theoretical Physics 21, 467 (1982). Abstract.
[2] Immanuel Bloch, Jean Dalibard, Wilhelm Zwerger, “Many-body physics with ultracold gases”, Reviews of Modern Physics 80, 885 (2008). Abstract.
[3] I. M. Georgescu, S. Ashhab, Franco Nori, “Quantum simulation”, Reviews of Modern Physics 86, 153 (2014). Abstract.
[4] Nobuyuki Takei, Christian Sommer, Claudiu Genes, Guido Pupillo, Haruka Goto, Kuniaki Koyasu, Hisashi Chiba, Matthias Weidemüller,  Kenji Ohmori, “Direct observation of ultrafast many-body electron dynamics in an ultracold Rydberg gas”, Nature Communications 7, 13449 (2016). Abstract.
[5] Christian Sommer, Guido Pupillo, Nobuyuki Takei, Shuntaro Takeda, Akira Tanaka, Kenji Ohmori, Claudiu Genes, “Time-domain Ramsey interferometry with interacting Rydberg atoms”, Physical Review A 94, 053607 (2016). Abstract.
[6] Kenji Ohmori, “Optically Engineered Quantum States in Ultrafast and Ultracold Systems”, Foundations of Physics, 44, 813 (2014). Abstract.
[7] M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms”, Reviews of Modern Physics, 82, 2313 (2010). Abstract.
[8] Daniel Comparat, Pierre Pillet, “Dipole blockade in a cold Rydberg atomic sample”, Journal of the Optical Society of America, B 27, A208 (2010). Abstract.

Experimental Simulation of the Exchange of Majorana Zero Modes

From left to right: (top row) Jin-Shi Xu, Kai Sun, Yong-Jian Han; (bottom row) Chuan-Feng Li, Jiannis K. Pachos, and Guang-Can Guo.

Authors: Jin-Shi Xu^1,2, Kai Sun^1,2, Yong-Jian Han^1,2, Chuan-Feng Li^1,2, Jiannis K. Pachos³, Guang-Can Guo^1,2

Affiliation:
¹Key Laboratory of Quantum Information, Department of Optics and Optical Engineering, University of Science and Technology of China, China,
²Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, China,
³School of Physics and Astronomy, University of Leeds, UK.

The exchange character of identical particles plays an important role in physics. For bosons, such an exchange leaves their quantum state the same, while a single exchange between two fermions gives a minus sign multiplying their wave function. A single exchange between two Abelian anyons gives rise to a phase factor that can be different than 1 or -1, that corresponds to bosons or fermions, respectively. More exotic exchanging character are possible, namely non-Abelian anyons. These particles have their quantum state change more dramatically, when an exchange between them takes place, to a possibly different state. Such non-Abelian anyons are the Majorana fermions that were first proposed by the physicist Majorana [1].

Majorana zero modes (MZMs) are quasiparticle excitations of topological phases of matter that have the same exchange character of the Majorana fermions, that is, they are non-Abelian anyons. When two MZMs are exchanged, the process cannot be described only by a global phase multiplying their wave function. Instead, their internal states, corresponding to degenerate ground states of the topological system, are transformed by a unitary operator. In addition, states encoded in the ground-state space of systems with MZMs are naturally immune to local errors. The degeneracy of the ground state, driven by the corresponding Hamiltonian, cannot be lifted by any local perturbation. Therefore, the encoded quantum information is topologically protected. These unusual characteristics imply that MZMs may potentially provide novel and powerful methods for quantum information processing [2]. Rapid theoretical developments have greatly reduced the technological requirements and made it possible to experimentally observe MZMs. However, until now, only a few positive signatures of the formation of MZMs have been reported in solid-state systems. The demonstration of the essential characteristic of non-Abelian exchange and the property of topological protection of MZMs is a considerable challenge.

Recently, we use a photonic quantum simulator to experimentally investigate the exchange of MZMs supported in the 1D Kitaev Chain Model (KCM) [3]. The Fock space of the Majorana system is mapped to the space of the quantum simulator by employing two steps. First, we perform the mapping of the Majorana system to a spin-1/2 system via the Jordan-Wigner (JW) transformation. Then we perform the mapping of the spin system to the spatial modes of single photons. In this way, we are able to demonstrate the exchange of two MZMs in a three-site Kitaev chain encoded in the spatial modes of photons. We further demonstrate that quantum information encoded in the degenerate ground state is immune to local phase and flip noise errors.

We consider a three-fermion KCM which is the simplest model that supports isolated two MZMs. Six Majorana fermions are involved and the exchange of two isolated Majoranas can be realized by a set of projective measurement, which can be expressed as imaginary-time evolution (ITE) operators with a sufficiently large evolution time. These processes depend on the corresponding Hamiltonians. Figure 1 shows the exchanging process.

Figure 1: The exchange of Majorana zero modes. The spheres with numbers at their centers represent the Majorana fermions at the corresponding sites. A pair of Majorana fermions bounded by an enclosing ring represents a normal fermion. The wavy lines between different sites represent the interactions between them. The interactions illustrated in a, b, c and d represent different Hamiltonians, respectively. The figure is adapted from Reference [3].

We transformed the KCM to a spin model through the JW transformation. Although these two models have some different physics, they share the same spectra in the ferromagnetic region and their corresponding quantum evolution are equivalent. The geometric phases obtained from the exchanging evolution are invariant under the mapping. As a result, the well-controlled spin system offers a good platform to determine the exchanging matrix and investigate the exchange behavior of MZMs.

In our experiment, the states of three spin-1/2 sites correspond to an eight-dimension Hilbert space, which are encoded in the optical spatial modes of a single photon. To complete the exchange, we implement the ITE by designing appropriate dissipative evolution. The ground state information of the corresponding Hamiltonian is preserved but the information of the other states is dissipated. We use beam-displacers to prepare the initial states and the dissipative evolution is accomplished by passing the photons through a polarization beam splitter. In our case, the optical modes with horizontal polarization are preserved which represent the ground states of the Hamiltonian. The optical modes with vertical polarization are discarded.

Figure 2 shows the experimental results of simulating the exchanging evolution. States encoded in the two-dimension degeneracy space are represented in Bloch spheres. The final states (Figure 2b) after the exchanging evolution are obtained by rotating the initial states (Figure 2a) counterclockwise along the X axis through an angle of π/2. We obtain the exchanging matrix through the quantum process tomography [4]. The real and imaginary parts of the exchanged operator are presented in Figures 2c and d. Compare with the theoretical operation, the fidelity is calculated to be 94.13±0.04%.

Figure 2: Experimental results on simulating the exchanging evolution. a. The six experimental initial states in the Bloch sphere. b. The corresponding experimental final states after the braiding evolution. The final states are shown to be rotated along the X axis by π/2 from the initial states. c. Real (Re) and d. Imaginary (Im) parts of the exchange operator with a fidelity of 94.13±0.04%. The figure is adapted from Reference [3].

Figures 3a and b show the real and imaginary parts of the flip-error protection operator with a fidelity of 97.91±0.03%. Figures 4c and d show the real and imaginary parts of the phase-error protection operator with a fidelity of 96.99±0.04%. The high fidelity reveals the protection from the local flip error and phase error of the information encoded in the ground state space of the Majorana zero modes. The total operation behaves as an identity, thus demonstrating immunity against noise.

Figure 3: Experimental results on simulating local noises immunity. a. Real (Re) and b. Imaginary (Im) parts of the flip-error protection operator, with a fidelity of 97.91±0.03%. c. Real (Re) and d. Imaginary (Im) parts of the phase-error protection operator, with a fidelity of 96.99±0.04%. The high fidelity reveals the protection from the local flip error and phase error of the information encoded in the ground state space of the Majorana zero modes. The figure is adapted from Reference [3].

In our experiment, the optical quantum simulator provides a versatile medium that can efficiently simulate the Kitaev chain model that supports MZMs at its endpoints. It also opens the way for the efficient realization and manipulation of MZMs in complex architectures. The gained know-how can be picked up by other technologies that offer scalability, like ion traps or optical lattices. This work achieves the realization of non-Abelian exchanging and may provide a novel way to investigate topological quantities of quantum systems.

References:
[1] Ettore Majorana, "Symmetrical theory of electrons and positrons", Nuovo Cimento 14, 171 (1937). Abstract.
[2] Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, "Non-Abelian anyons and topological quantum computation". Review of Modern Physics, 80, 1083 (2008). Abstract.
[3] Jin-Shi Xu, Kai Sun, Yong-Jian Han, Chuan-Feng Li, Jiannis K. Pachos, Guang-Can Guo, "Simulating the exchange of Majorana zero modes with a photonic system". Nature Communications", 7, 13194 (2016). Abstract.
[4] J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, A. G. White, "Quantum process tomography of a Controlled-NOT gate". Physical Review Letters, 93, 080502 (2004). Abstract.

Carbon Nanotubes as Exceptional Electrically Driven On-Chip Light Sources

From left to right: (top row) Felix Pyatkov, Svetlana Khasminskaya, Valentin Fütterling; (bottom row) Manfred M. Kappes, Wolfram H. P. Pernice, Ralph Krupke

Authors: Felix Pyatkov^1,2, Svetlana Khasminskaya¹, Valentin Fütterling¹, Randy Fechner¹, Karolina Słowik^3,4, Simone Ferrari^1,5, Oliver Kahl^1,5, Vadim Kovalyuk^1,6, Patrik Rath^1,5, Andreas Vetter¹, Benjamin S. Flavel¹, Frank Hennrich¹, Manfred M. Kappes^1,7, Gregory N. Gol’tsman⁶, Alexander Korneev⁶, Carsten Rockstuhl^1,3, Ralph Krupke^1,2, Wolfram H.P. Pernice⁵

Affiliation:
¹Institute of Nanotechnology, Karlsruhe Institute of Technology, Germany
²Department of Materials and Earth Sciences, Technical University of Darmstadt, Germany
³Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Germany
⁴Institute of Physics, Nicolaus Copernicus University, Poland
⁵Department of Physics, University of Münster, Germany
⁶Department of Physics, Moscow State Pedagogical University, Russia
⁷Institute of Physical Chemistry, Karlsruhe Institute of Technology, Germany

Carbon nanotubes (CNTs) belong to the most exciting objects of the nanoworld. Typically, around 1 nm in diameter and several microns long, these cylindrically shaped carbon-based structures exhibit a number of exceptional mechanical, electrical and optical characteristics [1]. In particular, they are promising ultra-small light sources for the next generation of optoelectronic devices, where electrical components are interconnected with photonic circuits.

Few years ago, we demonstrated that electically driven CNTs can serve as waveguide-integrated light sources [2]. Progress in the field of nanotube sorting, dielectrophoretical site-selective deposition and efficient light coupling into underlying substrate has made CNTs suitable for wafer-scale fabrication of active hybrid nanophotonic devices [2,3].

Recently we presented a nanotube-based waveguide integrated light emitters with tailored, exceptionally narrow emission-linewidths and short response times [4]. This allows conversion of electrical signals into well-defined optical signals directly within an optical waveguide, as required for future on-chip optical communication. Schematics and realization of this device is shown in Figure 1. The devices were manufactured by etching a photonic crystal waveguide into a dielectric layer following electron beam lithography. Photonic crystals are nanostructures that are also used by butterflies to give the impression of color on their wings. The same principle has been used in this study to select the color of light emitted by the CNT. The precise dimensions of the structure were numerically simulated to tailor the properties of the final device. Metallic contacts in the vicinity to the waveguide were fabricated to provide electrical access to CNT emitters. Finally, CNTs, sorted by structural and electronic properties, were deposited from a solution across the waveguide using dielectrophoresis, which is an electric-field-assisted deposition technique.

Figure 1: (a) Schematic view of the multilayer device structure consisting of two electrodes (yellow) and a photonic waveguide (purple) that is etched into the Si3N4 layer. Its central part is underetched into the SiO2 layer to a depth of 1.5 µm and photonic crystal holes are formed. The carbon nanotube bridges the electrodes on top of the waveguide. (b,c) False colored scanning electron microscope images of the device. The figure is adapted from Reference [4].

The functionality of the device was verified with optical microscopy and spectroscopy, which allowed detection of light emitted by the CNT and also of the light coupled into the waveguide. An electrically biased CNT generates photons, which efficiently couple into the photonic crystal waveguide, as shown in Figure 2a. The emitted light propagates along the waveguide and is then coupled out again using on-chip grating couplers. Because of the photonic crystal the emission spectrum of the CNT is extremely sharp (Figure 2b) and the emission wavelength can be tailored by our manufacturing process. In addition, the nanotube responds very quickly to electrical signals and hence acts as a transducer for generating optical pulses in the GHz range (Figure 2c). The modulation rates of these CNT-based transducers can in principle be pushed to much higher frequencies up to 100 GHz using more advanced nanostructures.

Figure 2: (click on the image to view with higher resolution) CCD camera image of the electrically biased device. Light emission is observed from the nanotube and from the on-chip grating couplers, both connected with the emitter via the waveguide. (b) Emission spectra simultaneously measured at the grating coupler. (c) A sequence of the driving electrical pulses as well as the recorded waveguided emission pulses (red) in GHz frequency range. The figure is adapted from Reference [4].

Nanophotonic circuits are promising candidates for next-generation computing devices where electronic components are interconnected optically with nanophotonic waveguides. The move to optical information exchange, which is already routinely done in our everyday life using optical fibers, also holds enormous benefit when going to microscopic dimensions – as found on a chip. Essential elements for such opto-electronic devices are nanoscale light emitters which are able to convert fast electrical signals into short optical pulses. Using such ultrafast transducers will allow for reducing power requirements and eventually speed up current data rates. For achieving ultimately compact devices the emitter should be as small as possible and interface efficiently with sub-wavelength optical devices. It would also have to operate at a chosen design wavelength and at high speed.

CNTs integrated into a photonic crystal nanobeam waveguides fulfill these requirements and constitute a promising new class of transducers for on-chip photonic circuits. These novel emitters are particularly interesting because of their simplicity. In contrast to conventional laser sources, CNTs are made entirely from carbon, which is available in abundance and does not require expensive fabrication routines as needed for III-V technologies. Moreover, CNTs can also be readily combined with existing CMOS technology, which makes them attractive for a wide range of applications.

So far we spoke about traditional computers based on binary logic. Going beyond classical computation, quantum computers that exploit the enormous potential of quantum mechanics for complex calculations and cryptography hold promise to revolutionize current information processing approaches. Optical quantum systems that employ single photons to realize quantum bits (qubits) belong to the prominent candidates for such future quantum information processing systems. To build a photonic quantum computer, sources of single photons (e.g. single molecules, quantum dots and semiconducting CNTs [5]), optical quantum gates and single photon detectors are needed. These devices are capable of very fast and reliable emission and detection of distinct photons.

An experimental approach, which allows for showing that a light source emits one photon at a time, consists of measuring intensity correlations in the emitted light. We performed this experiment on a solid silicon-based chip with an electrically driven CNT -- actings as a non-classical light source, waveguides, and two detectors for single photons [6]. The nanophotonic circuit shown in Figure 3 includes these three components: a CNT, a dielectric waveguide for the low-loss light propagation and a pair of superconducting nanowires for the efficient detection of light. A single chip carries dozens of such photonic circuits. The device fabrication process was similar to the realization of photonic crystal waveguides, except that now travelling-wave nanowire detectors were also formed on top of the waveguide.

Figure 3: (click on the image to view with higher resolution) (a,b) Schematics and optical image of device with an electrically driven light emitting nanotube in the middle (E) and single-photon superconducting NbN-detectors at the ends (D) of waveguide. The figure is adapted from Reference [6].

The functionality of the device was verified at cryogenic conditions with a setup which allowed the ultra-fast detection of light that was emitted by the CNT and then coupled into the waveguide. An electrically biased semiconducting CNT generates single photons, which can propagate bidirectionally within the waveguide towards the highly sensitive detectors. The intensity of the emitted light was measured as a function of the electrical bias current through the nanotube (Figure 4a). If only one photon at a time is emitted, the simultaneous detection of two photons with both detectors is highly unlikely. This can be derived from the dip in the second-order correlation function shown in Figure 4b. The low probability of simultaneous many-photon detection underlines the non-classical nature of the light source, which is the first step towards a true single-photon emitter. In essence, we thus realized a fully-integrated quantum photonic circuit with a single photon source and detectors, both of which are electrically driven and scalable.

Figure 4: (a) Measurement of the CNT emission intensity in dependence of bias current. Within the marked region semiconducting CNTs reveal non-classical emitting properties. (b) A measured second order correlation function. The minimum value significantly below unity represents the low possibility for simultaneous emission of two photons. The figure is adapted from Reference [6].

References:
[1] Phaedon Avouris, Marcus Freitag, Vasili Perebeinos, "Carbon-Nanotube Photonics and Optoelectronics", Nature Photonics, 2, 341-350 (2008). Abstract.
[2] Svetlana Khasminskaya, Felix Pyatkov, Benjamin S. Flavel, Wolfram H. P. Pernice, Ralph Krupke ,"Waveguide-Integrated Light-Emitting Carbon Nanotubes", Advanced Materials, 26, 3465-3472 (2014). Abstract.
[3] Randy G. Fechner, Felix Pyatkov, Svetlana Khasminskaya, Benjamin S. Flavel, Ralph Krupke, Wolfram H. P. Pernice, "Directional Couplers with Integrated Carbon Nanotube Incandescent Light Emitters", Optics Express, 24, 966-974 (2016). Abstract.
[4] Felix Pyatkov, Valentin Fütterling, Svetlana Khasminskaya, Benjamin S. Flavel, Frank Hennrich, Manfred M. Kappes, Ralph Krupke, Wolfram H. P. Pernice, "Cavity-Enhanced Light Emission from Electrically Driven Carbon Nanotubes", Nature Photonics, 10, 420-427 (2016). Abstract.
[5] Alexander Högele, Christophe Galland, Martin Winger, Atac Imamoğlu, "Photon Antibunching in the Photoluminescence Spectra of a Single Carbon Nanotube", Physical Review Letters, 100, 217401 (2008). Abstract.
[6] Svetlana Khasminskaya, Felix Pyatkov, Karolina Słowik, Simone Ferrari, Oliver Kahl, Vadim Kovalyuk, Patrik Rath, Andreas Vetter, Frank Hennrich, Manfred M. Kappes, Gregory N. Gol’tsman, Alexander Korneev, Carsten Rockstuhl, Ralph Krupke, Wolfram H.P. Pernice "Fully Integrated Quantum Photonic Circuit with an Electrically Driven Light Source", Nature Photonics (2016). Abstract.