A Monte Carlo wave function method in quantum optics

We present a wave-function approach to the study of the evolution of a small system when it is coupled to a large reservoir. Fluctuations and dissipation originate in this approach from quantum jumps that occur randomly during the time evolution of the system. This approach can be applied to a wide class of relaxation operators in the Markovian regime, and it is equivalent to the standard master-equation approach. For systems with a number of states N much larger than unity this Monte Carlo wave-function approach can be less expensive in terms of calculation time than the master-equation treatment. Indeed, a wave function involves only N components, whereas a density matrix is described by N2 terms. We evaluate the gain in computing time that may be expected from such a formalism, and we discuss its applicability to several examples, with particular emphasis on a quantum description of laser cooling.

[1]  Zoller,et al.  Monte Carlo simulation of the atomic master equation for spontaneous emission. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[2]  P. Meystre,et al.  Transition from diffraction to diffusion in the near-resonant Kapitza-Dirac effect: a numerical approach , 1991 .

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

[4]  E. Sudarshan,et al.  Zeno's paradox in quantum theory , 1976 .

[5]  T. Hänsch,et al.  Cooling of gases by laser radiation , 1975 .

[6]  C. cohen-tannoudji,et al.  Single-Atom Laser Spectroscopy. Looking for Dark Periods in Fluorescence Light , 1986 .

[7]  N. Gisin.  Quantum measurements and stochastic processes , 1984 .

[8]  S. Putterman,et al.  Wave-function collapse due to null measurements: The origin of intermittent atomic fluorescence. , 1987, Physical review. A, General physics.

[9]  B. R. Mollow.  Pure-state analysis of resonant light scattering: Radiative damping, saturation, and multiphoton effects , 1975 .

[10]  J. Dalibard,et al.  Limit of Doppler cooling , 1989 .

[11]  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.

[12]  Walls,et al.  Quantum jumps in atomic systems. , 1988, Physical review. A, General physics.

[13]  C. cohen-tannoudji,et al.  Deflection of an atomic beam by a laser wave: transition between diffractive and diffusive regimes , 1984 .

[14]  M. D. Srinivas,et al.  Photon Counting Probabilities in Quantum Optics , 1981 .

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

[16]  Siegmund Brandt,et al.  Statistical and Computational Methods in Data Analysis , 1971 .

[17]  K. Mølmer,et al.  Momentum diffusion of atoms moving in laser fields , 1992 .

[18]  Singh,et al.  Photoelectron waiting times and atomic state reduction in resonance fluorescence. , 1989, Physical review. A, General physics.

[19]  W. Louisell.  Quantum Statistical Properties of Radiation , 1973 .

[20]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[21]  V. Belavkin,et al.  Nondemolition observation of a free quantum particle. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[22]  G. Orriols,et al.  Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping , 1976 .

[23]  P. Kelley,et al.  Theory of Electromagnetic Field Measurement and Photoelectron Counting , 1964 .

[24]  Melvin Lax,et al.  Quantum Noise. XI. Multitime Correspondence between Quantum and Classical Stochastic Processes , 1968 .

[25]  R. Dicke,et al.  Interaction‐free quantum measurements: A paradox? , 1981 .

[26]  M. Scully,et al.  The Quantum Theory of Light , 1974 .

[27]  S. Stenholm,et al.  Broad band resonant light pressure , 1980 .