Time dependence of a two-level system in a sinusoidal field

Namita Gupta

N. E. Nevesskiǐ

Sunsheng Yang, Yang Ya-Ping, Chen Hong

We propose an inverse idea of controlling the evolution of the population inversion by a time-dependent coupling between the cavity field and a two-level system described through the Jaynes–Cummings model. We demonstrate the detailed procedure by obtaining the population evolution taking the non-sinusoidal form, which is different from the previous sinusoidal Rabi oscillation as the cavity field frequency and coupling parameters are constant during the interaction time.

J.V. Moloney, William J. Meath

A previous exact formal and practical solution for the time-dependent Schrödinger equation for a two-level non-degenerate system in an arbitrarily strong sinusoidal field is transformed for an N-level system to a Floquet form. Using the Floquet form of the solution computationally convenient expressions are obtained for the phase and the phase-long time-averaged induced transition probabilities. The method exploits the time periodicity of the Schrödinger equation and the solution over the initial period of the hamiltonian provides all the information needed to obtain both the unaveraged and the averaged transition probabilities for the system. The method is illustrated by specific examples which are used to discuss some of the temporal features of the multi-photon spectra of two-level systems.

Gerald F. Thomas, William J. Meath

An efficient computational algorithm for evaluating the evolution operator, and related induced transition probabilities, for a multilevel system interacting with an amplitude-modulated sinusoidal field of arbitrary strength, modulating envelope, frequency and phase, is developed. The algorithm is based on the Riemann product integral representation of the evolution operator in conjunction with Frazer's method of mean coefficients and avoids the introduction of commonly used perturbative or rotating wave approximations. Model calculations for the interaction of a two-level system with a Gaussian pulse are presented and used to discuss the dependence of time-resolved and steady-state frequency sweep spectra on some of the pulse characteristics.