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Laser Physics

Phase control of the excitation of a two-level system with short laser pulses

M. G. Arustamyan, Valery Alexandrovich Astapenko

Published Jun 1, 2008• 15 citations
Publisher

Abstract

The possibility of the phase control for the excitation of a quantum system in the discrete spectrum under the action of a short high-intensity laser pulse with a controlled phase is theoretically analyzed. The analysis is performed using the example of the simplest two-level system (TLS) employing a numerical solution to equations for the optical Bloch vector. It is demonstrated that the excitation probability and the mean dipole moment of the quantum system, which determine the normal luminescence and the superradiance in the TLS ensemble, respectively, substantially depend on the phase of the laser pulse for relatively short and powerful laser pulses.

DOI
10.1134/s1054660x08060121

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The possibility of the phase control for the excitation of a quantum system in the discrete spectrum under the action of a short high-intensity laser pulse with a controlled phase is theoretically analyzed. The analysis is performed using the example of the simplest two-level system (TLS) employing a numerical solution to equations for the optical Bloch vector. It is demonstrated that the excitation probability and the mean dipole moment of the quantum system, which determine the normal luminescence and the superradiance in the TLS ensemble, respectively, substantially depend on the phase of the laser pulse for relatively short and powerful laser pulses.
The excitation of a two-level system by a chirped laser pulse is analyzed using an analytical approach (in the perturbation-theory limit) that involves the modified rotating-wave approximation and the numerical solution to the Bloch equation. The dependence of the population of the upper energy level on the chirp is studied for various radiation intensities and pulse durations. An exact solution is compared with the result obtained using the modified rotating-wave approximation and the perturbation theory. It is demonstrated that, for a certain range of parameters, the excitation probability of a two-level system can be effectively controlled via a variation in the chirp.
The saturation effect during the excitation of a two-level system by laser pulses is investigated in the framework of two approaches: excitation probability based on Karplus–Schwinger spectral profile and exact solution of Bloch equations. Simple analytical expression for the excitation probability by exponential pulse is derived. The excitation spectra obtained using this expression were compared with the result of solving the Bloch equations for various values of the pulse duration and the Rabi frequency, which describes the strength of the electromagnetic interaction. It is shown that in the case of long pulses, there is a satisfactory correspondence between the two approaches, but in short-pulse limit and strong saturation, the probability description based on Karplus–Schwinger spectral profile and perturbation theory does not provide satisfactory results.
A theoretical investigation on the coherent control of optical transient four-wave mixing interactions in two-level systems with two intense few-cycle propagating laser pulses of central angular frequencies $\ensuremath{\omega}$ and $3\ensuremath{\omega}$ is reported. By numerically solving the full Maxwell-Bloch equations beyond the slowly varying envelope and rotating-wave approximations in the time domain, the nonlinear coupling to the optical field at frequency $5\ensuremath{\omega}$ is found to depend critically on the initial relative phase $\ensuremath{\phi}$ of the propagating pulses: the coupling is enhanced when the pulses interfere constructively in the center $(\ensuremath{\phi}=0)$, while it is nearly suppressed when they are out of phase $(\ensuremath{\phi}=\ensuremath{\pi})$.
The presentation is devoted to the theoretical investigation of nonlinear scattering of ultrashort electromagnetic pulses (USP) on two-level quantum system. We consider the scattering of several types of USP, namely, so called corrected Gaussian pulse (CGP) and cosine wavelet pulse. Such pulses have no constant component in their spectrum in contrast with traditional Gaussian pulse. It should be noted that the presence of constant component in the limit of ultrashort pulse durations leads to unphysical results. The main purpose of the present work is the investigation of the change of pulse temporal shape after scattering as a function of initial phase at different distances from the target. Numerical calculations are based on the solution of Bloch equations and expression for scattering field strength via dipole moment of two-level system exposed by the action of incident USP. In our calculation we also account for the influence of refracting index of the air on electric field strength in the pulse after scattering.
The ability to modify the character of fluorescent emission by a laser-controlled, optically nonlinear process has recently been shown theoretically feasible, and several possible applications have already been identified. In operation, a pulse of off-resonant probe laser beam, of sufficient intensity, is applied to a system exhibiting fluorescence, during the interval of excited-state decay following the initial excitation. The result is a rate of decay that can be controllably modified, the associated changes in fluorescence behavior affording new, chemically specific information. In this paper, a two-level emission model is employed in the further analysis of this all-optical process; the results should prove especially relevant to the analysis and imaging of physical systems employing fluorescent markers, these ranging from quantum dots to green fluorescence protein. Expressions are presented for the laser-controlled fluorescence anisotropy exhibited by samples in which the fluorophores are randomly oriented. It is also shown that, in systems with suitably configured electronic levels and symmetry properties, fluorescence emission can be produced from energy levels that would normally decay nonradiatively.
Coherent manipulations of atoms using laser light The internal structure of a particle - an atom or other quantum system in which the excitation energies are discrete - undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes - the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laser-pulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a three-dimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping "dark" states.