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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Multilevel atomic dynamics in modulated laser field

Sergey V. Prants

Published May 3, 1994• 1 citation
Publisher

Abstract

We develop the group-theoretical approach for analytically solving the time-dependent Schrodinger equations for multilevel atoms driven by amplitude- and/or frequency-modulated concurrent laser fields. The time evolution of externally driven N-level atoms is calculated in an explicit matrix form. The exact analytical conditions for complete population transfer and its return are simply connected with the parameters of the symmetry. We consider in detail the case of a four-level system driven by concurrent laser pulses of different forms.

DOI
10.1117/12.175134

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We develop the group-theoretical approach for analytically solving the time-dependent Schrodinger equations for multilevel atoms driven by amplitude- and/or frequency-modulated concurrent laser fields. The time evolution of externally driven N-level atoms is calculated in an explicit matrix form. The exact analytical conditions for complete population transfer and its return are simply connected with the parameters of the symmetry. We consider in detail the case of a four-level system driven by concurrent laser pulses of different forms.
Abstract We investigate the dynamics of a two-level quantum system driven by a laser pulse characterized by Lorentzian frequency and sub-Lorentzian amplitude modulations. Complete analytical solutions, expressed via confluent Heun functions, are derived. Our analysis reveals that explicit exact analytical solutions exist under infinite sets of specific parameter conditions. The effects of modulation parameters and initial conditions on the final transition probabilities are examined analytically and numerically. Furthermore, the method is demonstrated to be directly applicable to two closely related models with Lorentzian pulses.
We present an iterative analytic solution for the time dynamics of the 87Rb^{87}\text{R}\text{b}87Rb four-level atoms excited by a train of ultrashort pulses. It enables fast and accurate calculation of the system time evolution circumventing the use of time-consuming numerical procedures. The obtained solution is used to study the complex interaction of atoms with the pulse-train electric field, both in time and frequency domain. We investigate the influence of pulse-train physical parameters, such as the pulse peak power, the repetition frequency and the central laser wavelength on the accumulation of population and coherence in the system characterized by relaxation times larger than the pulse repetition period.
A multilevel system driven strongly by several near-resonant and arbitrary modulated optical fields is considered. The orthonormal basis of the time-dependent quasienergy states is introduced to represent in a matrix form the density operator and the operators describing atom-field interaction and relaxation. The above formalism simplifies the density-matrix equations of motion and provides a uniform treatment of resonance phenomena such as probe wave resonances, parametric resonances, and quantum interference. Special consideration is given to the steady-state and transient-time evolution of two- and three-level systems.
This paper is an extension of Fujii et al (quant--ph/0307066) and in this one we again treat a model of atom with n energy levels interacting with n(n-1)/2 external laser fields, which is a natural extension of usual two level system. Then the rotating wave approximation (RWA) is assumed from the beginning. To solve the Schr{\" o}dinger equation we set the {\bf consistency condition} in our terminology and reduce it to a matrix equation with symmetric matrix QQQ consisting of coupling constants. However, to calculate exp⁡(−itQ)\exp(-itQ)exp(−itQ) {\bfexplicitly} is not easy. In the case of three and four level systems we determine it in a complete manner, so our model in these levels becomes realistic. In last, we make a comment on Cavity QED quantum computation based on three energy levels of atoms as a forthcoming target.