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Journal of the Optical Society of America B

Population transfer by stimulated Raman scattering with delayed pulses and by the stimulated-emission pumping method: a comparative study

Guo‐Zhong He, Axel Kuhn, S. Schiemann, Klaas Bergmann

Published Sep 1, 1990• 60 citations
Publisher

Abstract

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.

DOI
10.1364/josab.7.001960

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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.
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.
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.
This work explores the effect of spontaneous emission on the population transfer efficiency in stimulated Raman adiabatic passage (STIRAP). The approach uses adiabatic elimination of weakly coupled density matrix elements in the Liouville equation, from which a very accurate analytic approximation is derived. The loss of population transfer efficiency is found to decrease exponentially with the factor ${\ensuremath{\Omega}}_{0}^{2}∕\ensuremath{\Gamma}$, where $\ensuremath{\Gamma}$ is the spontaneous emission rate and ${\ensuremath{\Omega}}_{0}$ is the peak Rabi frequency. The transfer efficiency increases with the pulse delay and reaches a steady value. For large pulse delay and large spontaneous emission rate STIRAP degenerates into optical pumping.
The technique of stimulated Raman adiabatic passage (STIRAP) is an efficient and robust technique for population transfer in three-state chain-wise connected quantum systems, 1-2-3. Here we analyze the transition time in STIRAP, that is the time it takes for the population to be transferred from state 1 to state 3. We derive a very simple formula for this transition time, which shows that it is inversely proportional to the nonadiabatic coupling $\mathrm{\ensuremath{\vartheta}\ifmmode \dot{}\else \.{}\fi{}}({t}_{c})$, estimated at the time tc{t}_{c}tc​ when the pump and Stokes couplings have the same value. Explicit formulas for several pulse shapes of the pump and Stokes fields are derived. Contrary to the naive expectation that the transition time might be proportional to the delay between the pump and Stokes pulses, or to the width of their overlap region, we find that the transition time is inversely proportional to the delay, i.e., larger delays produce faster transitions. We also calculate the transition time in two important variations of the STIRAP technique---bright-STIRAP and STIRAP in multistate systems---where similar features are found.
It introduced several methods to transfer population,including two-level system and three-level system, and gave some comparisons on transfer efficiency and transfer velocity of them in theory. It is shown that population transfer by coherent pulse sequence is better than incoherence one. Numerical simulation results showed that when using Stimulated Raman Adiabatic Rapid Passage (STIRAP), in which the pump laser pulse fully overlaps the Stokes pulse with the Stokes preceding the pump, population can be transferred completely and rapidly. Robust control of population transfer among Zeeman sublevels in the ground states of three-level system is investigated using adiabatic rapid passage in theory. The laser pulse widths are supposed to be short compared to the lifetime of the excited level, which means adiabatic. We demonstrated that techniques of STIRAP can be found to optimize population transfer in the ground states of three-level Λ system.
Abstract The population transfer of a NaH molecule from the ground state X 1 Σ + to the target state A 1 Σ + via stimulated Raman adiabatic passage (STIRAP) is investigated. The results show that the intensity, delay time and detuning have a significant effect on population transfer. A large population transfer is observed with increased pump and Stokes intensity, especially when the pump and Stokes intensity match. Population transfer also depends on the delay time between the pump laser pulse and the Stokes laser pulse. The detuning of the two pulses influences the population transfer. Efficient population transfer can be realized under the resonant or two-photon resonant condition.