Time Evolution of Two-Level Systems Driven by Periodic Fields

Abstract

In this paper we study the time evolution of a class of two-level systems driven by periodic fields in terms of new convergent perturbative expansions for the associated propagator U(t). The main virtue of these expansions is that they do not contain secular terms, leading to a very convenient method for quantitatively studying the long-time behaviour of that systems. We present a complete description of an algorithm to numerically compute the perturbative expansions. In particular, we applied the algorithm to study the case of an ac-dc field (monochromatic interaction), exploring various situations and showing results on (time-dependent) observable quantities, like transition probabilities. For a simple ac field, we analised particular situations where an approximate effect of dynamical localisation is exhibited by the driven system. The accuracy of our calculations was tested measuring the unitarity of the propagator U(t), resulting in very small deviations, even for very long times compared to the cycle of the driving field.

1 table, 5 figures. Version 2 contains minor corrections

References in corpus (1)

• Aspects of Two-Level Systems under External Time Dependent Fields

Cited by in corpus (7)

• Dynamical invariants for quantum control of four-level systems
• Spin equation and its solutions
• Darboux transformation for two-level systems
• Two interacting spins in external fields. Four-level systems
• Perturbative Analysis of Dynamical Localisation
• Two and four-level systems in magnetic fields restricted in time
• Effect of a high-frequency magnetic field on the resonant behavior displayed by a spin-$1/2$ particle under the influence of a rotating magnetic field