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Journal of Chemical Theory and Computation

Theory for Quantum Interference Signal from an Inhomogeneously Broadened Two-Level System Excited by an Optically Phase-Controlled Laser-Pulse Pair

Shin‐ichiro Sato

Published Apr 18, 2007• 9 citations
Publisher

Abstract

A useful expression for the quantum interference (QI) signal was derived for an inhomogeneously broadened two-level system when it was excited by an optically phase-controlled laser-pulse pair. It was shown that the QI signal oscillates as a function of a relative optical phase, with the reduced angular frequency given by the relation ωa = (Γ(2)ω0 + γg(2)Ω)/(γg(2) + Γ(2)), where γg and Γ are standard deviations of the system's absorption and the laser spectra both having a Gaussian line shape, respectively, and ω0 and Ω are the center angular frequency of the system absorption and the carrier angular frequency of the laser, respectively.

DOI
10.1021/ct7000073

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A useful expression for the quantum interference (QI) signal was derived for an inhomogeneously broadened two-level system when it was excited by an optically phase-controlled laser-pulse pair. It was shown that the QI signal oscillates as a function of a relative optical phase, with the reduced angular frequency given by the relation ωa = (Γ(2)ω0 + γg(2)Ω)/(γg(2) + Γ(2)), where γg and Γ are standard deviations of the system's absorption and the laser spectra both having a Gaussian line shape, respectively, and ω0 and Ω are the center angular frequency of the system absorption and the carrier angular frequency of the laser, respectively.
We have considered the interference spectra arising from the competition between a spontaneous process and one induced by a laser field in a two-level atom. Expressions for the spectral functions have been derived describing the spectra of the excited and ground states of the atom in the low- and high-intensity limit of the laser field. For the excited-state spectra in the low-intensity limit, the frequency profiles of the two peaks, which arise from the spontaneous and the induced processes, cancel each other out completely near the center of the line, while for the ground state the induced process dominates. For finite values of the detuning, the spectra of the excited state consist of two peaks, which have positive and negative frequency profiles, respectively. The computed spectra have been graphically presented and discussed. In the high-intensity limit, the dynamic Stark effect dominates the spectra of the excited and ground states of the atom. Expressions for the correlation functions have been derived that describe the emission or the absorption of a laser photon at two different times. The derived expressions for the corresponding delay functions in the low- and high-intensity limits have been found to be identical to those recently proposed in the literature. The laser field has been treated as a classical as well as a quantized entity.
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 $(\ensuremath{\phi}=\ensuremath{\pi})$.
Frequency-modulated spectra of coherently driven quantum systems are calculated using the density-matrix formulation. The modulated spectra are shown to be related to the two-time correlation functions of the polarization operators of the system. In the limit of modulation frequencies small compared to the width of the spectral features under study, the in-phase signal (quadrature signal) is shown to be related to the derivative of absorption (second derivative of dispersion) in the absence of any modulation. Modulation spectra in strong fields are calculated explicitly for two-level systems; such spectra are shown to yield useful information concerning light shifts and Rabi splittings. The influence of laser temporal fluctuations on such modulation spectra is also discussed.
A study is made of the distance dependence of carrier phase and average frequency of an electromagnetic pulse propagating through a quantum two-level system. Phenomenological differential equations are introduced to describe the distance rate of change of first- and second-moment deviations of the pulse carrier frequency from its original input frequency. In equilibrium the equations predict characteristics of pulse propagation in steady state. For both absorber and amplifier cases, computer plots are presented of the distance dependence of pulse shape, carrier phase, Fourier amplitude, and pulse energy for selected types of homogeneous and inhomogeneous line broadening and for specific input-pulse conditions. Off-resonance formation of a single $2\ensuremath{\pi}$ hyperbolic secant pulse of self-induced transparency may evolve from input-pulse areas less than $\ensuremath{\pi}$, as well as slightly greater than $\ensuremath{\pi}$, accompanied by frequency modulation and pulse breakup. The amplification of pulsed carrier radiation is accompanied by frequency pulling toward resonance. With and without phase modulation, stability conditions for stable pulse propagation are obtained. Either frequency pulling toward or frequency pushing away from resonance is dominant for an absorber, according to the dominance, respectively, of homogeneous or inhomogeneous line broadening. In the slowly-varying-pulse-envelope approximation, a steady-state solution is found for a symmetrically-phase-modulated pulse propagating in an amplifier with scattering losses. The mean carrier frequency for the pulse is displaced off resonance by one linewidth above the resonance transition frequency of a homogeneously broadened system.