Perturbative results on localization for a driven two-level system

TL;DR

This paper develops a perturbative approach using the dual Dyson series and renormalization group techniques to analyze localization in a driven two-level quantum system, providing explicit analytical expressions for Floquet states and energies.

Contribution

It introduces a second-order perturbation series for a driven two-level system in the strong coupling regime, including third-order energy corrections, and compares it with weak coupling results.

Findings

Third-order energy correction does not affect localization conditions.

Explicit analytical Floquet eigenstates and quasi-energies are derived.

Results support experimental findings relevant for quantum computing qubits.

Abstract

Using perturbation theory in the strong coupling regime, that is, the dual Dyson series, and renormalization group techniques to re-sum secular terms, we obtain the perturbation series of the two-level system driven by a sinusoidal field till second order. The third order correction to the energy levels is obtained proving how this correction does not modify at all the localization condition for a strong field as arising from the zeros of the zero-th Bessel function of integer order. A comparison with weak coupling perturbation theory is done showing how the latter is contained in the strong coupling expansion in the proper limits. This computation gives an explicit analytical form to Floquet eigenstates and quasi-energies for this problem, supporting recent theoretical and experimental findings for quantum devices expected to give a representation for qubits in quantum computation.