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Physical Review A

Spontaneous emission in stimulated Raman adiabatic passage

Peter A. Ivanov, Nikolay V. Vitanov, Klaas Bergmann

Published Nov 18, 2005• 43 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.72.053412

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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 \ensuremathΩ02∕\ensuremathΓ{\ensuremath{\Omega}}_{0}^{2}∕\ensuremath{\Gamma}\ensuremathΩ02​∕\ensuremathΓ, where \ensuremathΓ\ensuremath{\Gamma}\ensuremathΓ is the spontaneous emission rate and \ensuremathΩ0{\ensuremath{\Omega}}_{0}\ensuremathΩ0​ 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.
This work explores the effect of phase relaxation on the population transfer efficiency in stimulated Raman adiabatic passage (STIRAP). The study is based on the Liouville equation, which is solved analytically in the adiabatic limit. The transfer efficiency of STIRAP is found to decrease exponentially with the dephasing rate; this effect is stronger for shorter pulse delays and weaker for larger delays, since the transition time is found to be inversely proportional to the pulse delay. Moreover, it is found that the transfer efficiency of STIRAP in the presence of dephasing does not depend on the peak Rabi frequencies at all, as long as they are sufficiently large to enforce adiabatic evolution; hence increasing the field intensity cannot reduce the dephasing losses. It is shown also that for any dephasing rate, the final populations of the initial state and the intermediate state are equal. For strong dephasing all three populations tend to 13\frac{1}{3}31​.
Abstract We investigate theoretically the population transfer process in a Λ-type three-level quantum system (QS) near a metallic nanosphere using the stimulated Raman adiabatic passage (STIRAP) technique. We combine density matrix quantum dynamical calculations with first-principle electromagnetic calculations, which quantify the influence of the plasmonic nanoparticle on the electric field of the pump and Stokes pulses in STIRAP as well as on the spontaneous emission rates within the Λ-type system. We study the population transfer process by varying the free-space spontaneous emission rate, the distance of the QS from the nanosphere, the polarization direction with respect to the nanoparticle surface and the relative strength of the pump and Stokes pulses used in STIRAP. We find that when the pump and Stokes fields have tangential and radial polarizations with respect to the nanosphere surface, the transfer efficiency is improved due to the increase of the decay rate of the excited state to the target state relatively to the decay to the initial state. The optimal population transfer is achieved for small interparticle distances, moderate free space spontaneous decay rate, large values of the pump Rabi frequency and small values of the Stokes Rabi frequency. When we exchange the polarization directions of the pump and Stokes fields we can still find a range of parameters where the population transfer remains efficient, but larger Stokes Rabi frequencies are necessary to overcome the increased decay rate from the excited state back to the initial state.
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.
We discuss the detrimental effect of small rapid random fluctuations of laser-field amplitude and phase upon the efficiency of stimulated Raman adiabatic passage (STIRAP). Such fluctuations typically accompany the laser stabilization procedures that produce nearly monochromatic light on top of a much broader bandwidth Lorentz-profile pedestal which may carry only a few percent or less of the total power. As we will show, their effects differ qualitatively from the fluctuations that have hitherto been considered (for example, phase diffusion). We present analytic expressions for the population transfer efficiency of STIRAP when limited by stochastic fluctuations of this type. These expressions show, in contrast to situations discussed in the past in which population transfer improves with increasing peak Rabi frequencies, that for the weak broadband noise that accompanies a strong narrow-spectral component, there is an optimum value for the peak Rabi frequency and that the effect of fluctuations, although small, cannot be entirely eliminated in practice. The mission of the current work is to point out that, under the given circumstances, efforts in experiments trying to overcome the detrimental consequences of fluctuations by increasing the intensity, which is the intuitively proper approach, will not be successful.
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.