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.

32 pages, 5 figures, modified version published in New Journal of Physics

References in corpus (14)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Efficient coupling of photons to a single molecule and the observation of its resonance fluorescence
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Measurement of Autler-Townes and Mollow transitions in a strongly driven superconducting qubit
• Simulating spin-boson dynamics with stochastic Liouville-von Neumann equations
• Non-perturbative stochastic method for driven spin-boson model
• Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
• Control of charge migration in molecules by ultrashort laser pulses
• Stückelberg interference in a superconducting qubit under periodic latching modulation
• Coherent control of an effective two-level system in a non-Markovian biomolecular environment
• Observation of Mollow Triplets with Tunable Interactions in Double Lambda Systems of Individual Hole Spins
• Validity of Born-Markov master equations for single and two-qubit systems
• Photon-number-dependent effective Lamb shift
• Dissipative dynamics of a driven qubit: interplay between non-adiabatic dynamics and noise effects from weak to strong coupling regime

Cited by in corpus (6)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Quantum error correction under numerically exact open-quantum-system dynamics
• Many-excitation removal of a transmon qubit using a single-junction quantum-circuit refrigerator and a two-tone microwave drive
• Memory effects in a sequence of measurements of non-commuting observables
• Modeling the dynamics of quantum systems coupled to large dimensional baths using effective energy states
• Floquet Engineering of Non-Equilibrium Superradiance