Assessment of weak-coupling approximations on a driven two-level system under dissipation

TL;DR

This paper evaluates the accuracy of weak-coupling approximations in driven two-level quantum systems with dissipation, comparing them to non-perturbative methods and proposing experimental validation metrics.

Contribution

It introduces a detailed comparison between Lindblad and stochastic Liouville-von Neumann methods for driven qubits, highlighting the limitations of weak-coupling approximations in certain regimes.

Findings

Weak drive fields show deviations from Lindblad predictions.

Dissipation causes the meltdown of the Mollow triplet.

A proposed metric helps determine the validity of the Lindblad equation.

Abstract

The standard weak-coupling approximations associated to open quantum systems have been extensively used in the description of a two-level quantum system, qubit, subjected to relatively weak dissipation compared with the qubit frequency. However, recent progress in the experimental implementations of controlled quantum systems with increased levels of on-demand engineered dissipation has motivated precision studies in parameter regimes that question the validity of the approximations, especially in the presence of time-dependent drive fields. In this paper, we address the precision of weak-coupling approximations by studying a driven qubit through the numerically exact and non-perturbative method known as the stochastic Liouville-von Neumann equation with dissipation. By considering weak drive fields and a cold Ohmic environment with a high cutoff frequency, we use the Markovian Lindblad master equation as a point of comparison for the SLED method and study the influence of the bath-induced energy shift on the qubit dynamics. We also propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit. In addition, we study signatures of the well-known Mollow triplet and observe its meltdown owing to dissipation in an experimentally feasible parameter regime of circuit electrodynamics. Besides shedding light on the practical limitations of the Lindblad equation, we expect our results to inspire future experimental research on engineered open quantum systems, the accurate modeling of which may benefit from non-perturbative methods.