Abstract

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

Particle–wave dichotomy in quantum Monte Carlo: unlocking the quantum correlations

Ivan P. Christov
J. Opt. Soc. Am. B 34(9) 1817-1823 (2017)

Quantum-jump approach to dissipative processes: application to amplification without inversion

Claude Cohen-Tannoudji, Bruno Zambon, and Ennio Arimondo
J. Opt. Soc. Am. B 10(11) 2107-2120 (1993)

Quantum-trajectory pictures of laser cooling

G. Nienhuis, J. de Kloe, and P. van der Straten
J. Opt. Soc. Am. B 12(4) 520-530 (1995)

Analytical solution to the master equation for a quantized cavity mode

A. Mufti, H. A. Schmitt, A. B. Balantekin, and M. Sargent
J. Opt. Soc. Am. B 10(11) 2100-2106 (1993)

Effect of feedback control on the dynamics of quantum discord with and without the rotating-wave approximation

Jun-qing Cheng, Wei Wu, and Jing-bo Xu
J. Opt. Soc. Am. B 34(4) 701-708 (2017)