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Soviet Journal of Quantum Electronics

Resonance fluorescence and Raman scattering pumped by an adiabatic pulse

Б. В. Крыжановский, A. O. Melikyan

Published Jan 31, 1984• 1 citation
Publisher

Abstract

The approximation of nonoverlapping lines is used to calculate spectra of resonance fluorescence and Raman scattering when two- and three-level atoms are pumped by a smooth pulse of duration comparable with the excited-state lifetime. The difference between the quasienergy terms, that determines the satellite frequency, depends on time and has the same value twice, at the pulse leading and trailing edges, so that interference may occur between the radiation produced in the appropriate parts of the pulse. However, the interference pattern is blurred since radiative broadening destroys the coherence. Relationships are obtained between the parameters for which interference may be observed. An analysis is made of the change to short pulses when allowance can be made for the scattered field using the first order of perturbation theory.

DOI
10.1070/qe1984v014n01abeh004641

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The approximation of nonoverlapping lines is used to calculate spectra of resonance fluorescence and Raman scattering when two- and three-level atoms are pumped by a smooth pulse of duration comparable with the excited-state lifetime. The difference between the quasienergy terms, that determines the satellite frequency, depends on time and has the same value twice, at the pulse leading and trailing edges, so that interference may occur between the radiation produced in the appropriate parts of the pulse. However, the interference pattern is blurred since radiative broadening destroys the coherence. Relationships are obtained between the parameters for which interference may be observed. An analysis is made of the change to short pulses when allowance can be made for the scattered field using the first order of perturbation theory.
The theory of resonance Raman effect, resonantly enhanced two-photon absorption, and resonance fluorescence---valid also for strong fields---is treated in a unified and simplified way. Dressed states, Bloch equations, and perturbation theory are used to calculate line positions, and integrated intensities both for steady state and transient excitation. The case of adiabatic following is solved explicitly; it occurs when an off-resonance incident pulse is turned on and off slowly. It leads to the identification of Raman scattering, two-photon absorption, and Rayleigh scattering with an adiabatic process while fluorescence and consecutive two-photon absorption with nonadiabaticity. Time-dependent spectra are defined in a rigorous way. Our formulas agree in the various limits with those that appear in the literature.
Abstract Double resonance, resonance Raman and resonance fluorescence are discussed in terms of a superposition of adiabatic states. The adiabatic states are the instantaneous eigenstates of a two‐level Hamiltonian which includes the interaction with a near‐resonant coherent pulse and which has been transformed by a unitary transformation so that its only time‐dependence is that of the field envelope of the pulse. Resonance Raman results from spontaneous transitions to a third, lower state from the adiabatic following state which reduces to the initial (lower) state of the two‐level system in the absence of radiation. Resonance fluorescence is produced by spontaneous transition to the lower third state from the upper adiabatic state which reduces to the upper state of the two‐level system in the absence of radiation. Differential equations allowing the calculation of the probability amplitudes of the adiabatic states are given and a method of solving these equations by successive approximation is proposed. Saturation effects such as dynamic Stark shift and splitting (Autler—Townes effect) and optical nutation are interpreted in terms of perturbation of adiabatic energy levels and interference effects between adiabatic states. The possibility of observing optical nutation in a two‐level system by using time‐resolved double resonance experiments is suggested. Decay of the states of the two‐level system is taken into account leading to extended adiabaticity conditions which show that adiabatic following becomes possible even at resonance. For weak fields it is shown that adiabatic following at resonance can produce light scattering narrower than the linewidth as predicted by Heitler. The adiabatic states theory has also been extended to near‐resonance multiphoton interaction for systems that can be described by an effective two‐level Hamiltonian.
The resonant Raman scattering in a three level system produces an optical pumping of molecules from the initial to the final states which are radiatively coupled to the intermediate resonant state. We consider the pumping that is produced by an intense, pulsed, monochromatic radiation field that is near-resonant with the initial resonance frequency. The Heitler–Ma damping theory is solved exactly for the case when the resonance fluorescence is weak compared to the Raman scattering, or any other processes which might cause irreversible decay of the resonant state. In particular, we examine the usefulness of dressed states to describe the intense field limit. The spectral line shape for the Raman scattering is obtained. The transient behavior following the onset of the laser pulse is examined and a careful analysis of the pumping rate and its relationship to both weak and strong field theories is presented.
The resonance fluorescence of a two-level atom interacting with a laser pulse is studied, following the short-pulse approximation. The authors demonstrate that an explicit expression of the energy spectrum in terms of atomic-state amplitudes holds also for an off-resonance excitation. Some analytically solvable cases are studied in detail, showing that the main spectral properties of the fluorescence emitted under adiabatic and non-adiabatic pulsed excitation can be easily described. For the first time the continuous dependence of the fluorescence spectrum on laser detuning is reported for a smooth pulse.
A theoretical investigation is reported of the Raman scattering and fluorescence (doublet) spectra of three-level quantum systems subjected to a strong laser field reducing broadening of the spectral lines caused by adiabatic perturbations (elastic collisions). The dependences of the frequency shifts, widths, and integrated intensities of the spectral components of the doublet on the intensity and frequency of the laser field are derived allowing for the influence of this field on the collision dynamics.
Time dependent description of resonance Raman scattering is performed for a general system, by a density matrix reformulation of damping theory originally used for resonance fluorescence of atom. Radiative damping in the intermediate states can be described in terms of "damping operator" in realistic situations. In large ergodic systems, the scattering reduces to luminescence if the relaxation time within the excited states is much shorter than the radiative lifetime. In a typical case, time resolved emission spectra consist of various stages (i) scattering complex where absorption and emission are inseparable, (ii) dynamical and then (iii) kinetic relaxations giving rise to the hot luminescence, which finally converges to (iv) the ordinary luminescence from relaxed excited states. Hot luminescence does not appear within a motionally narrowed line. The interpretation of spectra depends also on the method of observation.