Dynamics of a qubit-oscillator system with periodically varying coupling

TL;DR

This paper explores the dynamics of a qubit-oscillator system with periodically varying coupling using Floquet theory, providing analytical and numerical insights into nonadiabatic phenomena relevant for quantum control.

Contribution

It introduces a Floquet-based framework for analyzing time-periodic qubit-oscillator interactions, including perturbative methods for aperiodic cases, advancing understanding of nonadiabatic quantum dynamics.

Findings

Analytical and numerical Floquet solutions agree well.

Perturbative approaches are effective for aperiodic time dependence.

The method is promising for studying time-periodic quantum systems.

Abstract

The dynamics of qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the qubit/oscillator coupling. The case of a single qubit coupled to a resonator populated with $n= 0,1$ photons is explicitly treated. The time-dependent Schr\"{o}dinger equation describing the system's dynamics is solved within the Floquet formalism and a perturbative approach in the time- and Laplace-domain. Good quantitative agreement is found between the analytical and numerical calculations within the Floquet approach, making it the most promising candidate for the study of time-periodic problems. Nonetheless, the time- or Laplace-domain perturbative approaches can be used in the presence of aperiodic time-dependent terms in the Hamiltonian.