Quantum dynamics of a two-level system under extrenal field

Abstract

We present exact analytic solutions for non-linear quantum dynamics of twolevel system (TLS) subject to periodic-in-time external field. >n constructing the exactly solvable models, we use approach where the form of external perturbation is chosen to preserve n integrability constraint, which yields single non-linear differential equation for the ac-field. solution to this equation is expressed in terms of Jacobi elliptic functions with three independent parameters that allows n to choose the frequency, average value, and amplitude of the time-dependent field at will. This form of the ac-drive is especially relevant to the problem of dynamics of TLS charge defects that cause dielectric losses ?n superconducting qubits.