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Journal articles on the topic 'Quantum feedback control'

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Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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1

James, M. R. "Optimal Quantum Control Theory." Annual Review of Control, Robotics, and Autonomous Systems 4, no. 1 (May 3, 2021): 343–67. http://dx.doi.org/10.1146/annurev-control-061520-010444.

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This article explains some fundamental ideas concerning the optimal control of quantum systems through the study of a relatively simple two-level system coupled to optical fields. The model for this system includes both continuous and impulsive dynamics. Topics covered include open- and closed-loop control, impulsive control, open-loop optimal control, quantum filtering, and measurement feedback optimal control.

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2

DONG, DAO-YI, CHEN-BIN ZHANG, ZONG-HAI CHEN, and CHUN-LIN CHEN. "INFORMATION-TECHNOLOGY APPROACH TO QUANTUM FEEDBACK CONTROL." International Journal of Modern Physics B 20, no. 11n13 (May 20, 2006): 1304–16. http://dx.doi.org/10.1142/s0217979206033942.

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Quantum control theory is profitably reexamined from the perspective of quantum information, two results on the role of quantum information technology in quantum feedback control are presented and two quantum feedback control schemes, teleportation-based distant quantum feedback control and quantum feedback control with quantum cloning, are proposed. In the first feedback scheme, the output from the quantum system to be controlled is fed back into the distant actuator via teleportation to alter the dynamics of system. The result theoretically shows that it can accomplish some tasks such as distant feedback quantum control that Markovian or Bayesian quantum feedback can not complete. In the second feedback strategy, the design of quantum feedback control algorithms is separated into a state recognition step, which gives "on-off" signal to the actuator through recognizing some copies from the cloning machine, and a feedback (control) step using another copies of cloning machine. A compromise between information acquisition and measurement disturbance is established, and this strategy can perform some quantum control tasks with coherent feedback.

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3

Dong, Dao-yi, Zong-hai Chen, Chen-bin Zhang, and Chun-lin Chen. "Feedback control of quantum system." Frontiers of Physics in China 1, no. 3 (September 2006): 256–62. http://dx.doi.org/10.1007/s11467-006-0032-x.

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4

CHEN, ZONGHAI, CHENBIN ZHANG, and DAOYI DONG. "QUANTUM CONTROL BASED ON QUANTUM INFORMATION." International Journal of Modern Physics B 21, no. 07 (March 20, 2007): 969–77. http://dx.doi.org/10.1142/s0217979207036928.

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Quantum control strategy is discussed from the perspective of quantum information. First, the constraints imposed on quantum control by quantum theory are analyzed. Then some quantum control schemes based on quantum information are discussed, such as teleportation-based distant quantum control, quantum feedback control using quantum cloning and state recognition, quantum control based on measurement and Grover iteration. Finally, some applications of quantum control theory in quantum information and quantum computation such as quantum error correction coding, universality analysis of quantum computation, feedback-induced entanglement enhancement, etc., are presented and the potential applications of quantum control are also prospected.

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5

Emary, Clive. "Delayed feedback control in quantum transport." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1999 (September 28, 2013): 20120468. http://dx.doi.org/10.1098/rsta.2012.0468.

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Feedback control in quantum transport has been predicted to give rise to several interesting effects, among them quantum state stabilization and the realization of a mesoscopic Maxwell's daemon. These results were derived under the assumption that control operations on the system are affected instantaneously after the measurement of electronic jumps through it. In this contribution, I describe how to include a delay between detection and control operation in the master equation theory of feedback-controlled quantum transport. I investigate the consequences of delay for the state stabilization and Maxwell's daemon schemes. Furthermore, I describe how delay can be used as a tool to probe coherent oscillations of electrons within a transport system and how this formalism can be used to model finite detector bandwidth.

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6

Song, Jie, Yan Xia, and Xiu-Dong Sun. "Noise-induced quantum correlations via quantum feedback control." Journal of the Optical Society of America B 29, no. 3 (February 8, 2012): 268. http://dx.doi.org/10.1364/josab.29.000268.

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7

van Handel, R., J. K. Stockton, and H. Mabuchi. "Feedback control of quantum state reduction." IEEE Transactions on Automatic Control 50, no. 6 (June 2005): 768–80. http://dx.doi.org/10.1109/tac.2005.849193.

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8

Ting, Julian Juhi-Lian. "Alternative method for quantum feedback control." Superlattices and Microstructures 32, no. 4-6 (October 2002): 331–36. http://dx.doi.org/10.1016/s0749-6036(03)00037-5.

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9

Dong, Daoyi, Chenbin Zhang, and Zonghai Chen. "QUANTUM FEEDBACK CONTROL USING QUANTUM CLONING AND STATE RECOGNITION." IFAC Proceedings Volumes 38, no. 1 (2005): 195–200. http://dx.doi.org/10.3182/20050703-6-cz-1902.00432.

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10

Vuglar, Shanon L., and Ian R. Petersen. "Quantum Noises, Physical Realizability and Coherent Quantum Feedback Control." IEEE Transactions on Automatic Control 62, no. 2 (February 2017): 998–1003. http://dx.doi.org/10.1109/tac.2016.2574641.

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11

Ma, Tiantian, Jun Jing, Yi Guo, and Ting Yu. "Quantum feedback control for qubit-qutrit entanglement." Quantum Information and Computation 16, no. 7&8 (May 2016): 597–614. http://dx.doi.org/10.26421/qic16.7-8-3.

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We study a hybrid quantum open system consisting of two interacting subsystems formed by one two-level atom (qubit) and one three-level atom (qutrit). The quantum open system is coupled to an external environment (cavity) via the qubit-cavity interaction. It is found that the feedback control on different parts of the system (qubit or qutrit) gives dramatically different asymptotical behaviors of the open system dynamics. We show that the local feedback control mechanism acting on the qutrit subsystem is superior than that on the qubit in the sense of improving the entanglement. Particularly, the qutrit-control scheme may result in an entangled steady state, depending on the initial state.

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12

Mitchison, Mark T., John Goold, and Javier Prior. "Charging a quantum battery with linear feedback control." Quantum 5 (July 13, 2021): 500. http://dx.doi.org/10.22331/q-2021-07-13-500.

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Energy storage is a basic physical process with many applications. When considering this task at the quantum scale, it becomes important to optimise the non-equilibrium dynamics of energy transfer to the storage device or battery. Here, we tackle this problem using the methods of quantum feedback control. Specifically, we study the deposition of energy into a quantum battery via an auxiliary charger. The latter is a driven-dissipative two-level system subjected to a homodyne measurement whose output signal is fed back linearly into the driving field amplitude. We explore two different control strategies, aiming to stabilise either populations or quantum coherences in the state of the charger. In both cases, linear feedback is shown to counteract the randomising influence of environmental noise and allow for stable and effective battery charging. We analyse the effect of realistic control imprecisions, demonstrating that this good performance survives inefficient measurements and small feedback delays. Our results highlight the potential of continuous feedback for the control of energetic quantities in the quantum regime.

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13

Serafini, Alessio. "Feedback Control in Quantum Optics: An Overview of Experimental Breakthroughs and Areas of Application." ISRN Optics 2012 (December 17, 2012): 1–15. http://dx.doi.org/10.5402/2012/275016.

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We present a broad summary of research involving the application of quantum feedback control techniques to optical setups, from the early enhancement of optical amplitude squeezing to the recent stabilisation of photon number states in a microwave cavity, dwelling mostly on the latest experimental advances. Feedback control of quantum optical continuous variables, quantum nondemolition memories, feedback cooling, quantum state control, adaptive quantum measurements, and coherent feedback strategies will all be touched upon in our discussion.

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14

Rigatos, Gerasimos G. "Gradient-based feedback control of quantum systems." Optical Memory and Neural Networks 21, no. 2 (April 2012): 77–85. http://dx.doi.org/10.3103/s1060992x12020087.

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15

Kashima, K., and N. Yamamoto. "Control of Quantum Systems Despite Feedback Delay." IEEE Transactions on Automatic Control 54, no. 4 (April 2009): 876–81. http://dx.doi.org/10.1109/tac.2008.2010969.

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16

Vitali, David, Stefano Zippilli, Paolo Tombesi, and Jean-Michel Raimond. "Decoherence control with fully quantum feedback schemes." Journal of Modern Optics 51, no. 6-7 (April 2004): 799–809. http://dx.doi.org/10.1080/09500340408233597.

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17

Jacobs, Kurt. "Feedback control using only quantum back-action." New Journal of Physics 12, no. 4 (April 1, 2010): 043005. http://dx.doi.org/10.1088/1367-2630/12/4/043005.

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18

Kabuss, Julia, Florian Katsch, Andreas Knorr, and Alexander Carmele. "Unraveling coherent quantum feedback for Pyragas control." Journal of the Optical Society of America B 33, no. 7 (February 19, 2016): C10. http://dx.doi.org/10.1364/josab.33.000c10.

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19

Bhandari, Bibek, Robert Czupryniak, Paolo Andrea Erdman, and Andrew N. Jordan. "Measurement-Based Quantum Thermal Machines with Feedback Control." Entropy 25, no. 2 (January 20, 2023): 204. http://dx.doi.org/10.3390/e25020204.

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We investigated coupled-qubit-based thermal machines powered by quantum measurements and feedback. We considered two different versions of the machine: (1) a quantum Maxwell’s demon, where the coupled-qubit system is connected to a detachable single shared bath, and (2) a measurement-assisted refrigerator, where the coupled-qubit system is in contact with a hot and cold bath. In the quantum Maxwell’s demon case, we discuss both discrete and continuous measurements. We found that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further found that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we used continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We found that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.

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20

Li, J., and K. Jacobs. "The regime of good control." Quantum Information and Computation 9, no. 5&6 (May 2009): 395–405. http://dx.doi.org/10.26421/qic9.5-6-3.

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We derive the equations of motion describing the feedback control of quantum systems in the regime of ``good control", in which the control is sufficient to keep the system close to the desired state. One can view this regime as the quantum equivalent of the ``linearized" regime for feedback control of classical nonlinear systems. Strikingly, while the dynamics of a single qubit in this regime is indeed linear, that of all larger systems remains nonlinear, in contrast to the classical case. As a first application of these equations, we determine the steady-state performance of feedback protocols for a single qubit that use unbiased measurements.

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21

Chen, Chunlin, Lin-Cheng Wang, and Yuanlong Wang. "Closed-Loop and Robust Control of Quantum Systems." Scientific World Journal 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/869285.

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For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control asH∞control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention.

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22

Bardeen, Christopher J., Vladislav V. Yakovlev, Kent R. Wilson, Scott D. Carpenter, Peter M. Weber, and Warren S. Warren. "Feedback quantum control of molecular electronic population transfer." Chemical Physics Letters 280, no. 1-2 (November 1997): 151–58. http://dx.doi.org/10.1016/s0009-2614(97)01081-6.

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23

Qi, Bo. "On the quantum master equation under feedback control." Science in China Series F: Information Sciences 52, no. 11 (November 2009): 2133–39. http://dx.doi.org/10.1007/s11432-009-0206-6.

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24

Zhang, GuoFeng, and Matthew R. James. "Quantum feedback networks and control: A brief survey." Chinese Science Bulletin 57, no. 18 (May 3, 2012): 2200–2214. http://dx.doi.org/10.1007/s11434-012-5199-7.

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25

Weinacht, T. C., and P. H. Bucksbaum. "Using feedback for coherent control of quantum systems." Journal of Optics B: Quantum and Semiclassical Optics 4, no. 3 (April 3, 2002): R35—R52. http://dx.doi.org/10.1088/1464-4266/4/3/201.

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26

Xue, Shibei, Michael R. Hush, and Ian R. Petersen. "Feedback Tracking Control of Non-Markovian Quantum Systems." IEEE Transactions on Control Systems Technology 25, no. 5 (September 2017): 1552–63. http://dx.doi.org/10.1109/tcst.2016.2614834.

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27

BARCHIELLI, A., M. GREGORATTI, and M. LICCIARDO. "QUANTUM TRAJECTORIES, FEEDBACK AND SQUEEZING." International Journal of Quantum Information 06, supp01 (July 2008): 581–87. http://dx.doi.org/10.1142/s0219749908003815.

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Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light emitted by a two-level atom, stimulated by a coherent monochromatic laser. In the presence of a Wiseman-Milburn feedback scheme, based on the homodyne detection of a fraction of the emitted light, we analyze the squeezing dependence on the various control parameters.

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28

Wang, Shi, and Matthew R. James. "Quantum feedback control of linear stochastic systems with feedback-loop time delays." Automatica 52 (February 2015): 277–82. http://dx.doi.org/10.1016/j.automatica.2014.11.014.

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29

WISEMAN, H. M. "FEEDBACK IN OPEN QUANTUM SYSTEMS." Modern Physics Letters B 09, no. 11n12 (May 20, 1995): 629–54. http://dx.doi.org/10.1142/s0217984995000590.

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Open quantum systems continually lose information to their surroundings. In some cases this information can be readily retrieved from the environment and put to good use by engineering a feedback loop to control the system dynamics. Two cases are distinguished: one where the feedback mechanism involves a measurement of the environment, and the other where no measurement is made. It is shown that the latter case can always replicate the former, but not vice versa. This emphasizes the quantum nature of the information being fed back. Two approaches are used to describe the feedback: quantum trajectories (which apply only for feedback based on measurement) and quantum Langevin equations (which can be used in either case), and the results are shown to be equivalent. The obvious applications for the theory are in quantum optics, where the information is lost by radiation damping and can be retrieved by photodetection. A few examples are discussed, one of which is particularly interesting as it has no classical counterpart.

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30

Cardona, Gerardo, Alain Sarlette, and Pierre Rouchon. "Continuous-time Quantum Error Correction with Noise-assisted Quantum Feedback." IFAC-PapersOnLine 52, no. 16 (2019): 198–203. http://dx.doi.org/10.1016/j.ifacol.2019.11.778.

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31

Doherty, Andrew C., A. Szorkovszky, G. I. Harris, and W. P. Bowen. "The quantum trajectory approach to quantum feedback control of an oscillator revisited." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (November 28, 2012): 5338–53. http://dx.doi.org/10.1098/rsta.2011.0531.

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We revisit the stochastic master equation approach to feedback cooling of a quantum mechanical oscillator undergoing position measurement. By introducing a rotating wave approximation for the measurement and bath coupling, we can provide a more intuitive analysis of the achievable cooling in various regimes of measurement sensitivity and temperature. We also discuss explicitly the effect of backaction noise on the characteristics of the optimal feedback. The resulting rotating wave master equation has found application in our recent work on squeezing the oscillator motion using parametric driving and may have wider interest.

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32

Gough, John E. "Principles and applications of quantum control engineering." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (November 28, 2012): 5241–58. http://dx.doi.org/10.1098/rsta.2012.0370.

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This is a brief survey of quantum feedback control and specifically follows on from the two-day conference Principles and applications of quantum control engineering, which took place in the Kavli Royal Society International Centre at Chicheley Hall, on 12–13 December 2011. This was the eighth in a series of principles and applications of control to quantum systems workshops.

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33

Ge, Shuzhi Sam, Thanh Long Vu, and Tong Heng Lee. "Quantum Measurement-Based Feedback Control: A Nonsmooth Time Delay Control Approach." SIAM Journal on Control and Optimization 50, no. 2 (January 2012): 845–63. http://dx.doi.org/10.1137/100801287.

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34

Lib, Ohad, Giora Hasson, and Yaron Bromberg. "Real-time shaping of entangled photons by classical control and feedback." Science Advances 6, no. 37 (September 2020): eabb6298. http://dx.doi.org/10.1126/sciadv.abb6298.

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Quantum technologies hold great promise for revolutionizing photonic applications such as cryptography. Yet, their implementation in real-world scenarios is challenging, mostly because of sensitivity of quantum correlations to scattering. Recent developments in optimizing the shape of single photons introduce new ways to control entangled photons. Nevertheless, shaping single photons in real time remains a challenge due to the weak associated signals, which are too noisy for optimization processes. Here, we overcome this challenge and control scattering of entangled photons by shaping the classical laser beam that stimulates their creation. We discover that because the classical beam and the entangled photons follow the same path, the strong classical signal can be used for optimizing the weak quantum signal. We show that this approach can increase the length of free-space turbulent quantum links by up to two orders of magnitude, opening the door for using wavefront shaping for quantum communications.

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35

Belavkin, V. P. "Quantum demolition filtering and optimal control of unstable systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (November 28, 2012): 5396–407. http://dx.doi.org/10.1098/rsta.2011.0517.

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A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton–Jacobi–Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton–Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

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36

Wang, Chang, and Mao-Fa Fang. "Quantum discord of two-qutrit system under quantum-jump-based feedback control." Chinese Physics B 28, no. 12 (November 2019): 120302. http://dx.doi.org/10.1088/1674-1056/ab4e83.

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37

Grigoletto, Tommaso, and Francesco Ticozzi. "Stabilization Via Feedback Switching for Quantum Stochastic Dynamics." IEEE Control Systems Letters 6 (2022): 235–40. http://dx.doi.org/10.1109/lcsys.2021.3065603.

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38

Jacobs, K. "Feedback control for communication with non-orthogonal states." Quantum Information and Computation 7, no. 1&2 (January 2007): 127–38. http://dx.doi.org/10.26421/qic7.1-2-8.

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Communicating classical information with a quantum system involves the receiver making a measurement on the system so as to distinguish as well as possible the alphabet of states used by the sender. We consider the situation in which this measurement takes an appreciable time. In this case the measurement must be described by a continuous measurement process. We consider a continuous implementation of the optimal measurement for distinguishing between two non-orthogonal states, and show that feedback control can be used during this measurement to increase the rate at which the information regarding the initial preparation is obtained. We show that while the maximum obtainable increase is modest, the effect is purely quantum mechanical in the sense that the enhancement is only possible when the initial states are non-orthogonal. We find further that the enhancement in the rate of information gain is achieved at the expense of reducing the total information which the measurement can extract in the long-time limit.

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39

Barkemeyer, Kisa, Regina Finsterhölzl, Andreas Knorr, and Alexander Carmele. "Revisiting Quantum Feedback Control: Disentangling the Feedback‐Induced Phase from the Corresponding Amplitude." Advanced Quantum Technologies 3, no. 2 (October 11, 2019): 1900078. http://dx.doi.org/10.1002/qute.201900078.

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40

Harraz, Sajede, and Shuang Cong. "State Transfer via On-Line State Estimation and Lyapunov-Based Feedback Control for a N-Qubit System." Entropy 21, no. 8 (July 31, 2019): 751. http://dx.doi.org/10.3390/e21080751.

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In this paper, we propose a Lyapunov-based state feedback control for state transfer based on the on-line quantum state estimation (OQSE). The OQSE is designed based on continuous weak measurements and compressed sensing. The controlled system is described by quantum master equation for open quantum systems, and the continuous measurement operators are derived according to the dynamic equation of system. The feedback control law is designed based on the Lyapunov stability theorem, and a strict proof of proposed control laws are given. At each sampling time, the state is estimated on-line, which is used to design the control law. The simulation experimental results show the effectiveness of the proposed feedback control strategy.

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41

Liu, Cheng-Cheng, Ting-Sheng Wei, Jia-Dong Shi, Zhi-Yong Ding, Juan He, Tao Wu, and Liu Ye. "Optimal measurement-based feedback control on noisy quantum systems." Laser Physics Letters 18, no. 11 (October 15, 2021): 115203. http://dx.doi.org/10.1088/1612-202x/ac2b95.

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42

Hu, Juju, Qin Xue, and Yinghua Ji. "Identification of open quantum system: Via closed feedback control." International Journal of Modern Physics B 33, no. 27 (October 30, 2019): 1950327. http://dx.doi.org/10.1142/s0217979219503272.

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For stochastic quantum systems with given dissipations, the identification method of Hamiltonian is given in this paper. First, the stability of the system is realized through designing a real-time feedback control method. Second, by using Routh–Hurwitz stability criterion, the intervals of the element values of the system Hamiltonians are given. Finally, the identification of Hamiltonian is realized by selecting the equilibrium state of the system equal to the desired target state. For two typical categories of noise: Purely dephasing decoherence and amplitude damping decoherence, we check the validity of the proposed estimation scheme.

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43

James, M. R., and J. E. Gough. "Quantum Dissipative Systems and Feedback Control Design by Interconnection." IEEE Transactions on Automatic Control 55, no. 8 (August 2010): 1806–21. http://dx.doi.org/10.1109/tac.2010.2046067.

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44

Xue, Shibei, Rebing Wu, Michael R. Hush, and Tzyh-Jong Tarn. "Non-Markovian coherent feedback control of quantum dot systems." Quantum Science and Technology 2, no. 1 (March 1, 2017): 014002. http://dx.doi.org/10.1088/2058-9565/aa6125.

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45

Geremia, J. "Real-Time Quantum Feedback Control of Atomic Spin-Squeezing." Science 304, no. 5668 (April 9, 2004): 270–73. http://dx.doi.org/10.1126/science.1095374.

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46

Zong, Xiao-Lan, Wei Song, Ming Yang, and Zhuo-Liang Cao. "Influence of Quantum Feedback Control on Excitation Energy Transfer*." Chinese Physics Letters 37, no. 6 (June 2020): 060501. http://dx.doi.org/10.1088/0256-307x/37/6/060501.

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47

Doherty, A. C., and K. Jacobs. "Feedback control of quantum systems using continuous state estimation." Physical Review A 60, no. 4 (October 1, 1999): 2700–2711. http://dx.doi.org/10.1103/physreva.60.2700.

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48

IMAE, Joe, Yui TAKENAKA, and Tomoaki KOBAYASHI. "716 Quantum Optimal Control of Purification via Measurement Feedback." Proceedings of Conference of Kansai Branch 2013.88 (2013): _7–16_. http://dx.doi.org/10.1299/jsmekansai.2013.88._7-16_.

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49

Handel, Ramon van, John K. Stockton, and Hideo Mabuchi. "Modelling and feedback control design for quantum state preparation." Journal of Optics B: Quantum and Semiclassical Optics 7, no. 10 (September 14, 2005): S179—S197. http://dx.doi.org/10.1088/1464-4266/7/10/001.

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50

Gough, J., V. P. Belavkin, and O. G. Smolyanov. "Hamilton–Jacobi–Bellman equations for quantum optimal feedback control." Journal of Optics B: Quantum and Semiclassical Optics 7, no. 10 (September 14, 2005): S237—S244. http://dx.doi.org/10.1088/1464-4266/7/10/006.

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