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Chinese Physics Letters

Oscillation Period of Two-Level Systems Driven by Time-Dependent Fields

Xian-Geng Zhao

Published Dec 1, 1999• 1 citation
Publisher

Abstract

We study the dynamics of two-level systems under the influence of time-dependent external fields. An oscillation period describing the transition between two states is obtained analytically by the use of perturbation theory, from which the results for any special case can be derived. We illustrate two examples to show the advantage of our theory, in which the phenomenon of localization/delocalization can be addressed uniformly by oscillation period.

DOI
10.1088/0256-307x/16/12/021

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We study the dynamics of two-level systems under the influence of time-dependent external fields. An oscillation period describing the transition between two states is obtained analytically by the use of perturbation theory, from which the results for any special case can be derived. We illustrate two examples to show the advantage of our theory, in which the phenomenon of localization/delocalization can be addressed uniformly by oscillation period.
The object of the research are the quantum transitions of a many-level system between its stationary states under the influence of an alternating external electric field. The transition amplitudes and probabilities are calculated by the method of perturbation theory in the approximation of a classical external field. It is illustrated that in the case when the external field frequency is equal to the frequency of any quantum transition, then the probability of this transition fluctuate nearly the average value which is oscillating with Rabi frequency. Probabilities of other quantum transitions are very small and change chaotically with time.
If the perturbation is turned on for a brief period of time and then turned off, the particle ends up in the original potential. But it may have been induced to transition from one eigenstate to another during the perturbation. The calculation of the probability of that transition is the topic of time-dependent perturbation theory (TDPT). Again, formula are presented rather than derived, and two examples are provided: a linear perturbation, and an oscillating perturbation. These examples, respectively, show how selection rules arise, and how light of a given frequency excites energy transitions of the same frequency. This latter phenomenon is called resonance .
A two level system is considered which has no static dipole moment, e.g. molecule H2H_2H2​ in its ground electronic state. If strong enough external field is applied, it will dynamically distort such a system and supply it with time (and field) dependent dipole moment. Although it is impossible to do so in the undistorted system which has no coupling to the dipole component of the external field, having induced in it a dipole moment, the rotational and vibrational dynamics of such system can be manipulated using lasers. In this work, a system is considered in which the external perturbation dynamically induces the transition dipole moment between only two distinct levels. The aim of the work is to show how the driving pulse can be analytically designed, that will produce Rabi-like complete population oscillations between the two levels.
The time-dependent (physical) spectrum of stimulated Raman scattering (SRS) from a two-level system is calculated, proving the influence of the spectral width Γ of the detector on the obtained spectral line shape. In addition, the time evolution of the process leading to the Raman line is investigated. For a partially excited system, the scattered field intensity exhibits oscillations in time, and Γ is found to affect the amplitude of the oscillations in the Raman line intensity. A numerical analysis of the result is performed for the case of monochromatic external fields.