Quantum—Classical Correspondence for Two-Level Atoms

S. Y. Chen, Yanan Zhang, Jing Yang +2 more

A. O. Bolivar

Li You, J. Cooper

An operational method is presented that can avoid some of the difficulties associated with numerically simulating the Langevin operator equations for a dissipative quantum optical system. The approach is based on a set of quantum-classical correspondence rules that relate atomic operators in the Heisenberg picture to their corresponding double-dimensioned classical atomic variables. With this approach, the Langevin operator equations can be transformed into a doubled set of classical stochastic differential equations (SDE's). The relationship to the quantum regression theory up to the two-time correlation function and similarities to the positive P representation are discussed. As an illustrative example, we show that both the resonance fluorescence spectrum (Mollow spectrum) as well as the absorption spectrum for a two-level atom interacting with a near-resonance field can be simulated from the doubled set of classical SDE's without explicit reference to the quantum regression theorem.

Li You, J. Cooper, P. Zoller

We demonstrate the successful simulation of classical stochastic differential equations obtained from the positive P phase-space technique for two-level atoms pumped by a near-resonant laser. Numerical results for both the resonance fluorescence spectrum and the absorption spectrum are compared with the exact results.

Junqing Li, Liu Fang, Xing Yong-Zhong +1 more