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.
© 1993 Optical Society of America
Original Manuscript: April 7, 1992
Revised Manuscript: July 8, 1992
Published: March 1, 1993
Klaus Mølmer, Yvan Castin, and Jean Dalibard, "Monte Carlo wave-function method in quantum optics," J. Opt. Soc. Am. B 10, 524-538 (1993)