Acta Physico-Chimica Sinica

Dynamical localization of two-level systems

Yuhui Li, Yun‐An Yan, Jiushu Shao

Published Aug 15, 2004• 0 citations

Abstract

This paper reviews our work on dynamical localization of the two-level system (TLS). By mapping the quantum dynamics of a driven TLS to the classical one of a particle experiencing a two-dimensional harmonic force as well as a periodic magnetic field, deep insights into the mechanism of localization have been gained. Using this scheme we are able to obtain the condition for localization of a TLS subject to the linearly polarized field. The localization induced by delta-function pulses and circularly polarized fields has been analytically investigated. It is found that the circularly-polarized-field induced localization can be fully described by the geometry of an ellipse within a unit circle on a complex plane.

DOI: 10.3866/pku.whxb200408zk22

Related papers

Localization of two-level systems

Lei Wang, Jiushu Shao

The quantum dynamics of the two-level system under a periodic external potential is mapped to the classical one of a charged particle moving in the harmonic-oscillator potential plus a magnetic field in a plane. The behavior of tunneling and localization is fully described by the radial trajectory of the particle. It is shown that localization may happen only if the radial trajectory is periodic. The possible period is an integral multiple of that of the external force. Three models are studied.

Physical Review AFeb 1, 199425 citations

Localization of two-level systems subject to external fields

Moshe Gitterman

The necessary conditions for the localization of a quantum particle in a two-level system subject to periodic oscillations of the height (energy splitting) and the width (tunnelling matrix) of a potential barrier were found. The former field is supposed to have a simple cosine form while the latter has the form of asymmetric pulses or a train of delta-functions.

Journal of Physics A Mathematical and GeneralNov 21, 20015 citations

Controlling quantum coherence by circularly polarized fields

Jiushu Shao, Peter Hänggi A

In terms of analytical results, we demonstrate that, within most parts in parameter space for a two-level magnetic system, suppression of quantum coherence can be induced by the circularly polarized fields. Low-frequency driving yields a dynamical localization opposite to the case of intermediate-to-high-frequency driving. The intrinsic relation between coherent suppression and the dressed-state level-crossing resonance is revealed.

Physical Review ADec 1, 199737 citations

Dynamical model of coherent circularly polarized optical pulse interactions with two-level quantum systems

Gabriela M. Slavcheva, Ortwin G. Hess

We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.

Physical Review ANov 3, 200519 citations

Dynamical localization for two-level systems periodically driven

Daniele Lodi, Marco Maioli, Andrea Sacchetti

Here, we consider a two-level system driven by an external periodic field. We show that the coherent destruction of tunnelling, as proved by Grossmann and co-workers (1991 Phys. Rev. Lett. 67 516; 1992 Europhys. Lett. 18 571) in the case of a monochromatic field, also appears for any periodic driving field given by an even regular function with zero mean value and satisfying a technical condition on the zeros of this function.

Journal of Physics A Mathematical and GeneralDec 16, 20042 citations

Dynamic of the system in a periodic potential, submitted to an electromagnetic wave: Path integral approach

Nsangou Issofa, Christian Platini Fogang Kuetche, M.E. Ateuafack +1 more

Abstract We introduced the formalism of path integrals to describe the dynamics of a system consisting of two particles. One is located in a periodic potential well (first subsystem), while the other particle is outside the well and subjected to a circular electromagnetic field (second subsystem). Thanks to this formalism, we are able to describe the dynamics of our system by a propagator which is the product of two subsystems of propagators. The propagator of the first subsystem is put in the standard form exp[Action] as a result of the coherent spin states. This form of propagator is possible by replacing the spin with a unit vector aligned along the polar and azimuthal directions. The second subsystem propagator come with the use of the Feynman-Vernon functional on the subsystem. Thanks to its two propagators, we have succeeded in explicitly and analytically evaluating the dynamics of our dissipative quantum system by a single propagator. Using this fundamental result, we evaluated the special case where the second subsystem bathed in a super-ohmic environment.

Physica ScriptaFeb 11, 20211 citation