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The Journal of Chemical Physics

Population transfer by stimulated Raman scattering with delayed pulses using spectrally broad light

Axel Kuhn, George W. Coulston, Guangzhi He, S. Schiemann, Klaas Bergmann, W. S. Warren

Published Mar 15, 1992• 86 citations
Publisher

Abstract

The feasability of selective and complete population transfer between atomic or molecular levels by stimulated Raman scattering with delayed pulses involving spectrally broad light with characteristics typical for pulsed lasers is investigated. In extension of previous work, the effect on the transfer efficiency of phase fluctuations and of the detuning ΔR of the laser frequencies from the two-photon resonance is analyzed. The minimum pulse energy Pmin required to achieve a transfer efficiency of nearly unity is derived analytically, with some restrictions imposed on the type of phase fluctuations. Pmin increases approximately proportional to the square of the bandwidth of the laser radiation and to the square of ΔR. The conclusions are confirmed by the results of extensive numerical calculations. These studies also reveal a high sensitivity of the transfer efficiency to the autocorrelation of the fluctuating light.

DOI
10.1063/1.462840

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The feasability of selective and complete population transfer between atomic or molecular levels by stimulated Raman scattering with delayed pulses involving spectrally broad light with characteristics typical for pulsed lasers is investigated. In extension of previous work, the effect on the transfer efficiency of phase fluctuations and of the detuning ΔR of the laser frequencies from the two-photon resonance is analyzed. The minimum pulse energy Pmin required to achieve a transfer efficiency of nearly unity is derived analytically, with some restrictions imposed on the type of phase fluctuations. Pmin increases approximately proportional to the square of the bandwidth of the laser radiation and to the square of ΔR. The conclusions are confirmed by the results of extensive numerical calculations. These studies also reveal a high sensitivity of the transfer efficiency to the autocorrelation of the fluctuating light.
The characteristics of the stimulated-emission pumping (SEP) method and the technique of stimulated Raman scattering by delayed pulses (STIRAP) are compared, based on numerical results from density matrix calculations. The latter technique requires the use of nearly transform-limited pulses, whereas the former method is successfully implemented with broadband lasers. Damping coefficients γ are introduced to model the consequences of phase fluctuations of the radiation. It is shown that the various techniques can be classified in terms of the delay D of the Stokes laser relative to the pump laser and the damping rate γ. The delay D/ΔτL ≈ −1 and γ = 0 corresponds to the STIRAP mode of operation, whereas the SEP method requires that D/ΔτL ≥ 0 and γΔτL ≫ 1, where ΔτL is the width of the laser pulse.
We present results of density matrix calculations describing population transfer in a four level system via stimulated Raman scattering with three laser pulses whose frequencies are in (or nearly in) resonance with the transitions between the levels. A high degree of transfer to the terminal level is possible via transitions through the two intermediate excited levels, despite the large decay rates of both levels compared with the inverse of the laser pulse durations, provided that the pulse timing sequences are correctly adjusted. Hence multiple stimulated Raman scattering can be an efficient method of moving population into a given molecular level.
Stimulated Raman scattering involving adiabatic passage (STIRAP) is a proven technique for population transfer in three-level systems with strong oscillator strengths. We show that the STIRAP process should also yield high transfer efficiencies when the densities of states near the intermediate and final levels are high, provided certain criteria for the experimentally controllable parameters are met. We also show that high transfer efficiencies may even be possible when the pump and Stokes lasers can access levels outside of the three-level system. The criteria are derived with an approach that emphasizes the adiabatic nature of the transfer process in an eigenvector of the interaction Hamiltonian that resembles a trapped state. The results are compared to density matrix calculations.
We demonstrate that various properties of population transfer by delayed pulses in three-level systems on two-photon resonance can be deduced analytically and for general pulse shapes. We use the fact that the three-level system reduces to effective two-level problems at large intermediate-level detuning \ensuremath{\Delta}, on resonance (\ensuremath{\Delta}=0) and for completely overlapping pulses. Special attention is paid to the effect of the pulse order on the population transfer efficiency. We show that on resonance the transfer efficiency depends substantially on the pulse order, while at large \ensuremath{\Delta} it does not. We also find that under some natural restrictions on the symmetry of the problem, the population of the initial level does not depend on the pulse order at any \ensuremath{\Delta}. Furthermore, we demonstrate that the population transfer in the three-level system can be viewed as a level-crossing problem in an equivalent two-level system not only at large \ensuremath{\Delta} (which is known) but also on resonance, \ensuremath{\Delta}=0. The effective on-resonance two-level problem is interesting by itself as it shows that a level crossing and adiabatic evolution do not necessarily lead to complete population inversion. As examples throughout the paper, we present several analytically solvable models.
The feasibility of a novel technique for efficient and selective population transfer from a thermally populated level 1 via an intermediate state 2 to level 3 is experimentally demonstrated. It is shown for sodium dimers that the process of on- or near-resonance stimulated Raman scattering with only partially overlapping laser beams is, in particular, useful for the selective population of high vibrational levels of particles in a molecular beam. This is achieved when the interaction with the Stokes laser, coupling levels 2 and 3, begins earlier than the interaction with the pump laser. The phenomenon, which is closely related to the formation of ‘‘trapped states,’’ is quantitatively explained using the basis of eigenstates of molecules strongly coupled to the radiation fields. The similarity and difference to related techniques such as rapid adiabatic passage phenomena in two-level systems, off-resonant stimulated Raman scattering, or stimulated emission pumping is briefly discussed.