Quantum filtering for systems driven by fields in single-photon states or superposition of coherent states

We derive the stochastic master equations, that is to say, quantum filters, and master equations for an arbitrary quantum system probed by a continuous-mode bosonic input field in two types of non-classical states. Specifically, we consider the cases where the state of the input field is a superposition or combination of: (1) a continuous-mode single photon wave packet and vacuum, and (2) any number of continuous-mode coherent states.

[1]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[2]  Samuel L. Braunstein,et al.  Weak-force detection with superposed coherent states , 2002 .

[3]  S. Scheel,et al.  Single-photon sources–an introduction , 2009 .

[4]  K Mølmer,et al.  Generation of a superposition of odd photon number states for quantum information networks. , 2006, Physical review letters.

[5]  M. R. James,et al.  Quantum Feedback Networks: Hamiltonian Formulation , 2008, 0804.3442.

[6]  Shanhui Fan,et al.  Full inversion of a two-level atom with a single-photon pulse in one-dimensional geometries , 2010 .

[7]  Kae Nemoto,et al.  Schrödinger cats and their power for quantum information processing , 2004 .

[8]  Matthew R. James,et al.  The Series Product and Its Application to Quantum Feedforward and Feedback Networks , 2007, IEEE Transactions on Automatic Control.

[9]  Hidenori Kimura,et al.  Transfer function approach to quantum control-part I: Dynamics of quantum feedback systems , 2003, IEEE Trans. Autom. Control..

[10]  I. Stamatescu,et al.  Decoherence and the Appearance of a Classical World in Quantum Theory , 1996 .

[11]  Gardiner,et al.  Driving a quantum system with the output field from another driven quantum system. , 1993, Physical review letters.

[12]  Thomas Pellizzari,et al.  Photon-Wavepackets as Flying Quantum Bits , 1998 .

[13]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[14]  G. Milburn,et al.  Quantum computation with optical coherent states , 2002, QELS 2002.

[15]  J. Cirac,et al.  Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network , 1996, quant-ph/9611017.

[16]  Luc Bouten,et al.  Stochastic Schrödinger equations , 2003 .

[17]  H. Carmichael.  An open systems approach to quantum optics , 1993 .

[18]  J. Fink,et al.  Experimental state tomography of itinerant single microwave photons. , 2011, Physical review letters.

[19]  Carmichael,et al.  Quantum trajectory theory for cascaded open systems. , 1993, Physical review letters.

[20]  A. Lvovsky,et al.  Quantum state reconstruction of the single-photon Fock state. , 2001, Physical Review Letters.

[21]  Andrew G. Glen,et al.  APPL , 2001 .

[22]  Valerio Scarani,et al.  Efficient excitation of a two-level atom by a single photon in a propagating mode , 2010, 1010.4661.

[23]  E. Brändas,et al.  Unstable states in the continuous spectra , 2010 .

[24]  G. Johnson,et al.  Springer Handbook of Lasers and Optics , 2008 .

[25]  G. J. Milburn.  Coherent control of single photon states , 2008 .

[26]  Gary J. Nutt,et al.  Open Systems , 2019 .

[27]  W. Lange,et al.  PREFACE: Final issue of Journal of Optics B: Quantum and Semiclassical Optics , 2005 .

[28]  R. Sillitto.  The Quantum Theory of Light , 1974 .

[29]  Matthew R. James,et al.  An Introduction to Quantum Filtering , 2006, SIAM Journal of Control and Optimization.

[30]  K. Parthasarathy.  An Introduction to Quantum Stochastic Calculus , 1992 .

[31]  Collett,et al.  Nonlocality of a single photon. , 1991, Physical review letters.

[32]  Gilles Brassard,et al.  Quantum Cryptography , 2005, Encyclopedia of Cryptography and Security.

[33]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .

[34]  Hidenori Kimura,et al.  Transfer function approach to quantum Control-Part II: Control concepts and applications , 2003, IEEE Trans. Autom. Control..

[35]  K. Banaszek,et al.  Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity , 2005 .

[36]  K. Mølmer,et al.  Wave-function approach to dissipative processes in quantum optics. , 1992, Physical review letters.

[37]  Philippe Grangier,et al.  Generation of optical ‘Schrödinger cats’ from photon number states , 2007, Nature.

[38]  Gardiner,et al.  Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[39]  Collett,et al.  Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation. , 1985, Physical review. A, General physics.

[40]  M. Orrit,et al.  Single-photon sources , 2005 .

[41]  V. P. Belavkin,et al.  Measurements continuous in time and a posteriori states in quantum mechanics , 1991 .

[42]  H. Heuer.  Critical slowing down in local dynamics simulations , 1992 .

[43]  G. Staszewska,et al.  Nondemolition quantum filtering , 1995 .

[44]  Maira Amezcua,et al.  Quantum Optics , 2012 .

[45]  Julien Laurat,et al.  Generating Optical Schrödinger Kittens for Quantum Information Processing , 2006, Science.

[46]  A. D. Boozer,et al.  Deterministic Generation of Single Photons from One Atom Trapped in a Cavity , 2004, Science.

[47]  T. Ralph,et al.  Optimized generation of heralded Fock states using parametric down-conversion , 2009, 0909.4147.

[48]  Robin L. Hudson,et al.  Quantum Ito's formula and stochastic evolutions , 1984 .

[49]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[50]  G. Milburn,et al.  Quantum Measurement and Control , 2009 .

[51]  R. Gielerak,et al.  Stochastic Methods in Mathematics and Physics: Xxiv Karpacz Winter School on Theoretical Physics, Karpacz, Poland, 13-27 Jan 1988 , 1989 .

[52]  Gerd Leuchs,et al.  Perfect excitation of a matter qubit by a single photon in free space , 2008, 0808.1666.

[53]  Kathy P. Wheeler,et al.  Reviews of Modern Physics , 2013 .

[54]  V. P. Belavkin,et al.  Quantum Diffusion, Measurement and Filtering I , 1994 .

[55]  Hendra Ishwara Nurdin,et al.  Quantum master equation and filter for systems driven by fields in a single photon state , 2011, IEEE Conference on Decision and Control and European Control Conference.

[56]  Michael Pepper,et al.  Electrically Driven Single-Photon Source , 2001, Science.