Perturbative results on localization for a driven two-level system
Marco Frasca · Physical review. B, Condensed matter · 2003
Using perturbation theory in the strong coupling regime, that is, the dual Dyson series, and renormalization-group techniques to resum 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 by proving how this correction does not modify at all the localization condition for a strong field as arising from the zeros of the zeroth 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. The strong coupling expansion we obtain proves to be accurate in the regime of high-frequency driving field. This computation gives an explicit analytical form to Floquet eigenstates and quasienergies for this problem, for high-frequency driving fields, supporting recent theoretical and experimental findings for quantum devices expected to give a representation for qubits in quantum computation.