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Physical Review A

Theory of quantum beats in optical transmission-correlation and pump-probe experiments for a general Raman configuration

Ian A. Walmsley, Masaharu Mitsunaga, Carson L. Tang

Published Nov 1, 1988• 95 citations
Publisher

Abstract

A perturbative density-matrix theory of quantum beats developed previously has been extended to include the case of a three-level system with ground-state splitting. It is shown that quantum beats should be observable in a transmission-correlation experiment when the optical pulses are resonant or nonresonant with the excited state. The beats may be of magnitude comparable to those from a split excited state, and are insensitive to the amount of homogeneous or inhomogeneous broadening of the optical transitions.

DOI
10.1103/physreva.38.4681

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A perturbative density-matrix theory of quantum beats developed previously has been extended to include the case of a three-level system with ground-state splitting. It is shown that quantum beats should be observable in a transmission-correlation experiment when the optical pulses are resonant or nonresonant with the excited state. The beats may be of magnitude comparable to those from a split excited state, and are insensitive to the amount of homogeneous or inhomogeneous broadening of the optical transitions.
A full density-matrix theory for quantum beats in optical transmission-correlation or pump-probe type of experiments is developed. The model used is a three-level system with split excited-state levels. It is demonstrated on the basis of perturbation theory that quantum beats should be observable in such experiments. Theoretical and numerical results are compared with the complex details, including damped sinusoidal decays, observed in recent femtosecond relaxation studies of large organic dye molecules. It is also shown that there is no separately identifiable decay component corresponding to any homogeneous or inhomogeneous optical dephasing time in such experiments. Similar beating should also be observable in ultrafast spectroscopy using incoherent light and in Raman-type energy-level configurations where the ground state contains split levels.
Recent femtosecond transmission-correlation measurements1 of large organic dye molecules revealed surprising details concerning the ultrafast relaxation dynamics of such dyes. Superposed on simple exponential decays, the observation of damped sinusoidal oscillations with a period of ~ 150 fs has been puzzling. We theoretically and numerically demonstrate that such oscillatory behavior could be due to quantum beats of closely spaced two levels, whose coherent superposition state is optically prepared and monitored by a pair of femtosecond pulses. Although studies of quantum beats have been developed in both fluorescence-type2 and nonfluorescence-type measurements, such as those based on photon echoes3 or polarization spectroscopy,4 this simple method gives a new approach to femtosecond time domain spectroscopy. The generalized perturbation theory5 of optical coherent transients is extended to the case of optical transmission-correlation or pump-probe-type experiments. The model used is a three-level system which has split levels in either the ground or optically excited states. Especially, if the ground state has sublevels, the system becomes quite similar to the case of coherent Raman beats. Both cases are shown to give quantum beats when the excitation pulses are short compared with the inverse sublevel splitting. The period and decay time of the damped sinusoid represent the separation energy and the dephasing time between the sublevels, respectively. Using third-order perturbation theory, the transmission-correlation signal STC(τ) as a function of the first-to-second pulse delay time Is derived for arbitrary-shaped excitation pulses and is given in the form of fourfold integrals with many terms.
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Quantum beats can be observed when an atomic system is prepared in a coherent superposition of eigenstates. It manifests the most basic concept of quantum mechanics: coherence, and has been studied extensively. The common configuration for studying quantum beats is that a three-level system interacts with a pulse excitation, where either upper or lower level can be a closely- spaced doublet [1], We report here a new type of quantum beats, dressed-state quantum beats, observed in a three-level pump-probe configuration (Fig. 1). The three-level system and experimental detail can be found elsewhere [2].
A theory of quantum beats in a Stokes signal observed in pump-probe experiments upon excitation of four-level atoms with two close upper lying levels by femtosecond laser pulses is developed. Quantum beats arise in the intensity of the Stokes field due to the interference of two atomic wave packets generated by ultrashort pump and probe pulses. An analytical solution of the non-steady-state Maxwell-Bloch equations is obtained, and the dependence of the Stokes radiation intensity on the delay time between two laser pulses is investigated. The theoretical results describe qualitatively well the observed features of quantum beats.
The complex polarization behavior of quantum beating between heavy- and light-hole excitons in nonlinear pump-and-probe spectroscopy is experimentally investigated. The strain-split free excitons in thin high-quality ZnSe layers embedded in ternary ZnSx{\mathrm{ZnS}}_{\mathit{x}}ZnSx​${\mathrm{Se}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$ barriers served as the three-level system involved. Spectrally integrated pump-and-probe experiments confirm the theoretically predicted dependence of the quantum-beat phase on the relative polarization of the exciting fields. These observations are discussed in comparison with results from four-wave mixing obtained when using the same experimental setup. Beyond that, spectrally resolved transients measured on the light-hole resonance exhibit pronounced, weakly damped beating phenomena even at negative delay, i.e., with the probe pulses preceding the pump pulses. Additionally, for cross-polarized beams the quantum-beat phase is strongly dependent on the energy of detection. It turns out that the phase observed in the spectrally integrated mode is determined by the off-resonant contributions. \textcopyright{} 1996 The American Physical Society.