Geometric phase and controllability of quantum systems

K. Berrada, Hichem Eleuch

In the present paper, we study the geometric phase by considering a model that closely describes a realistic experimental scenario. We present an active way to control and quench the variation of the geometric phase using ultra-short strong pulses for a two-level quantum system with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we study the variation of the geometric phase with a few cycles pulse and a smooth phase jump over a finite time intervals. The control of the variation rate of the geometric phase is obtained by acting on the shape of the phase transient and other parameters of the considered system. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.

Sonia G. Schirmer, I. C. H. Pullen, A. I. Solomon

Arno Böhm, Ali Mostafazadeh, Hiroyasu Koizumi +2 more

David Viennot

We describe the geometric (Berry) phases arising when some quantum systems are driven by control classical parameters but also by outer classical stochastic processes (as, for example, classical noises). The total geometric phase is then divided into an usual geometric phase associated with the control parameters and a second geometric phase associated with the stochastic processes. The geometric structure in which these geometric phases take place is a composite bundle (and not an usual principal bundle), which is explicitly built in this paper. We explain why the composite bundle structure is the more natural framework to study this problem. Finally, we treat a very simple example of a two-level atom driven by a phase modulated laser field with a phase instability described by a Gaussian white noise. In particular, we compute the average geometric phase issued from the noise.

А. Г. Бутковский, Yu. I. Samoilenko

D. De Munshi, Manas Mukherjee

Abelian and Non-Abelian evolution of a quantum system manifests differently in the geometric phase acquired by the system under such evolutions. In this work we develop and study, using dressed state techniques, an experimentally realizable spin system which allows us to transit smoothly from non-Abelian to Abelian evolutions by changing externally controllable parameters. The study provides insights into the underlying physical phenomenon governing such a transition allowing us greater control on phase generation in a quantum system. The robustness of geometric phase against fluctuations of the external parameters of the system has also been studied in this work. The noise analysis has direct consequence on the present search for fault tolerant quantum gates using geometric phase.