Low-frequency Landau-Zener-St\"uckelberg interference in dissipative superconducting qubits

TL;DR

This paper investigates low-frequency Landau-Zener-Stückelberg interference in dissipative superconducting qubits, providing analytical models that describe the system's dynamics beyond common approximations and aiding in microwave cooling applications.

Contribution

It develops comprehensive analytical descriptions of LZS interference at low frequencies, including nonresonant effects and decoherence, extending beyond traditional perturbation methods.

Findings

Analytical models match numerical simulations across parameter space.

Identifies minimal frequency for effective microwave cooling.

Describes nonresonant and decoherence effects in qubit dynamics.

Abstract

Landau-Zener-St\"uckelberg (LZS) interference of continuously driven superconducting qubits is studied. Going beyond the second order perturbation expansion, we find a time dependent stationary population evolution as well as unsymmetrical microwave driven Landau-Zener transitions, resulting from the nonresonant terms which are neglected in rotating-wave approximation. For the low-frequency driving, the qubit population at equilibrium is a periodical function of time, owing to the contribution of the nonresonant terms. In order to obtain the average population, it is found that the average approximation based on the perturbation approach can be applied to the low-frequency region. For the extremely low frequency which is much smaller than the decoherence rate, we develop noncoherence approximation by dividing the evolution into discrete time steps during which the coherence is lost totally. These approximations present comprehensive analytical descriptions of LZS interference in most of parameter space of frequency and decoherence rate, agreeing well with those of the numerical simulations and providing a simple but integrated understanding to system dynamics. The application of our models to microwave cooling can obtain the minimal frequency to realize effective microwave cooling.