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

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.

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

“…Different channels of relaxation are described by the Lindblad operators L k . For the limitations of the Lindblad equation, see (Teixeira et al, 2021).…”

Floquet engineering of non-equilibrium superradiance

“…For this purpose we choose a dissipative model. We note that the Lindblad master equation applied to strongly driven two-level systems with weak dissipation has been found to show some deviations from more accurate methods [46]. We understand these deviations to be small enough to not affect the central results of this paper.…”

Many-excitation removal of a transmon qubit using a single-junction quantum-circuit refrigerator and a two-tone microwave drive

“…We attribute this effect to the involved multi-level structure of the system showcasing the nontrivial interplay between driving and thermal environment. In principle, a refinement in the reset theory could be achieved, for example, through more sophisticated models taking into account multi-photon decay channels or suitably optimized to treat time-dependent Hamiltonians and dissipative environments 30 .…”

“…( 5 ) and from different physical phenomena, such as drive-induced and bath-induced shifts, we add the small correction term to the energy levels, . Notably, the incorporation of frequency shifts to the driven system Hamiltonian is important for accurately estimating the stabilization times and the steady state of quantum systems 30 .…”