Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach

TL;DR

This paper extends the Born-Oppenheimer approximation to open quantum systems using the quantum trajectory approach, analyzing its validity and comparing it with previous methods through examples.

Contribution

It introduces a new extension of the BO approximation for open systems within the quantum trajectory framework, highlighting the role of dissipation in fast variables.

Findings

Dissipation in fast variables enhances the BO approximation.

The new extension is complementary to previous effective Hamiltonian methods.

Illustrative examples demonstrate the method's applicability.

Abstract

Based on the quantum trajectory approach, we extend the Born-Oppenheimer (BO) approximation from closed quantum system to open quantum system, where the open quantum system is described by a master equation in Lindblad form. The BO approximation is defined and the validity condition is derived. We find that the dissipation in fast variables benefits the BO approximation that is different from the dissipation in slow variables. A detailed comparison between this extension and our previous approximation (that is based on the effective Hamiltonian approach, see X. L. Huang and X. X. Yi, Phys. Rev. A 80, 032108 (2009)) is presented. Several new features and advantages are analyzed, which show that the two approximations are complementary to each other. Two examples are taken to illustrate our method.