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The Journal of Chemical Physics

Population transfer by multiple stimulated Raman scattering

Y. B. Band, Paul S. Julienne

Published Oct 15, 1991• 48 citations
Publisher

Abstract

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.

DOI
10.1063/1.461642

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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 compare the results of full density matrix calculations with recently reported experimental results describing the population transfer in Na2 using Raman scattering with the fundamental laser beam temporally shifted relative to the Stokes laser beam. Our calculations confirm the conclusion that almost total transfer of the population into the terminal level of the Raman transition can be achieved when the laser frequencies are tuned to resonance and the fundamental laser beam is temporally delayed relative to the Stokes shifted laser beam but still partially overlapping it. We analyze our results when the frequencies of the lasers are tuned off-resonance as a function of the Rabi frequencies and the detuning, and compare with experimental and theoretical results. The alignment of the terminal level as a function of time displacement of the Stokes and pump beams is predicted.
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.
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.
Highly efficient and selective population transfer in NO molecules in the electronic ground state (X2{\mathit{X}}^{2}X2${\mathrm{\ensuremath{\Pi}}}_{1/2}$) from the vibrational level v''=0 to the level v''=6 is demonstrated. It shows, for the first time with pulsed lasers, that a rather generally applicable scheme for complete control over the level population in atoms and molecules is now available. The efficiency relies on a counterintuitive interaction sequence of two lasers with the molecule in a process of stimulated Raman scattering involving adiabatic passage.