Quantum Jump Approach to Driven-Dissipative Atom Dynamics

Abstract

Spontaneous photon emission by atoms is a fundamental quantum process with significant implications for quantum technologies. We study the dynamics of N laser-driven two-level atoms interacting with the electromagnetic vacuum and spontaneously emitting photons. Although the framework of master equations for the density matrix provides a rigorous description of this process, its computational cost scales exponentially as ∼ 22N. As an alternative, we implement the quantum jump method, a stochastic approach based on averaging over quantum trajectories. We begin with the case of a single atom and then extend the analysis to a chain of closely spaced atoms, focusing on the error scaling in the stochastic method. By comparing computational performance, we find that the quantum jump approach becomes increasingly advantageous for larger systems. These results establish quantum trajectories as a reliable and efficient tool for simulating collective spontaneous emission in complex quantum systems