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Physical Review A

Stimulated hyper-Raman adiabatic passage. I. The basic problem and examples

Леонід Петрович Яценко, S. Guérin, Thomas Halfmann, K. Böhmer, Bruce W. Shore, Klaas Bergmann

Published Dec 1, 1998• 42 citations
Publisher

Abstract

We discuss various theoretical issues that arise when one extends the conventional stimulated Raman adiabatic passage, involving a pump pulse preceded by a Stokes pulse, to situations in which the pump interaction involves a two-photon transition. As in the simpler cases, it is possible to obtain complete population transfer between an initial state and a targeted final state, if certain general conditions on the pulses are met. We point out important considerations, associated with dynamic Stark shifts and multiphoton ionization, which make successful population transfer more difficult in the multiphoton extension. We illustrate these problems and requirements by considering specific examples of excitation in metastable helium.

DOI
10.1103/physreva.58.4683

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When one extends the conventional stimulated Raman adiabatic passage method of population transfer; involving a pump pulse preceded by a Stokes pulse, to situations in which the pump (or pump and Stokes) interaction involves a two-photon transition, there occur unavoidable dynamic Stark shifts which prevent maintenance of the relevant resonance conditions. Such shifts can prevent the desired population transfer. We show, through numerical modeling and analytic considerations, that the detrimental effects of dynamic shifts can be compensated by a suitable choice of (static) detunings of the carrier frequencies of the two pulses, so that population transfer can be achieved. We present simple analytic expressions for bounding the range of detunings for which population transfer can occur, and we present numerical results supporting the simple picture of the two-step linewidth. We illustrate these remarks by considering specific examples.

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Stimulated Raman adiabatic passage with unequal couplings: Beyond two-photon resonance

Iavor I. Boradjiev, Nikolay V. Vitanov

The technique of stimulated Raman adiabatic passage (STIRAP) is a highly efficient tool for coherent population transfer in a chainwise-connected three-state quantum system. It is widely accepted that the two-photon resonance between the two end states of the chain is a crucial condition for STIRAP. This assumption is indeed correct when the two driving fields, pump and Stokes, produce nearly equal couplings for their respective transitions. We show analytically, supported by numeric examples, that when the pump and Stokes couplings differ significantly, the two-photon population transfer profile is distorted and its center is shifted away from the two-photon resonance; hence, the optimal operation of STIRAP demands a two-photon detuning. We derive simple analytic estimates for the center and the width of the two-photon profile. The results are of potential importance in situations when the pump and Stokes fields are of different physical natures (e.g., laser and cavity fields) or when two-photon resonance is unwanted (e.g., in the presence of residual light).

Physical Review A•May 20, 2010•21 citations
We discuss various theoretical issues that arise when one extends the conventional stimulated Raman adiabatic passage, involving a pump pulse preceded by a Stokes pulse, to situations in which the pump interaction involves a two-photon transition. As in the simpler cases, it is possible to obtain complete population transfer between an initial state and a targeted final state, if certain general conditions on the pulses are met. We point out important considerations, associated with dynamic Stark shifts and multiphoton ionization, which make successful population transfer more difficult in the multiphoton extension. We illustrate these problems and requirements by considering specific examples of excitation in metastable helium.
When one extends the conventional stimulated Raman adiabatic passage method of population transfer; involving a pump pulse preceded by a Stokes pulse, to situations in which the pump (or pump and Stokes) interaction involves a two-photon transition, there occur unavoidable dynamic Stark shifts which prevent maintenance of the relevant resonance conditions. Such shifts can prevent the desired population transfer. We show, through numerical modeling and analytic considerations, that the detrimental effects of dynamic shifts can be compensated by a suitable choice of (static) detunings of the carrier frequencies of the two pulses, so that population transfer can be achieved. We present simple analytic expressions for bounding the range of detunings for which population transfer can occur, and we present numerical results supporting the simple picture of the two-step linewidth. We illustrate these remarks by considering specific examples.
We report the experimental realization of coherent population transfer from the 23S2{}^{3}S23S state to 23P2{}^{3}P23P fine-structure levels of helium, using the technique of hyper-Raman adiabatic passage, in which the pump-laser coupling involves a two-photon transition. We discuss the dependence of population transfer upon pump and Stokes detunings, and show that by suitably setting the detunings one can transfer population efficiently as either a two-step process to final states or as a single-step two-photon transition to an intermediate state. We use an adiabatic-state picture to interpret these experimental results. Since the optimum detuning depends on the pump laser intensity the transfer efficiency is compromised by the variation of the intensity across the spatial profile of the laser beam. Our experimental data agree well with numerical simulation based on density-matrix equations, including all 15 magnetic sublevels.
This paper discusses a generalization of stimulated Raman adiabatic passage (STIRAP) in which the single intermediate state is replaced by N intermediate states. Each of these states is connected to the initial state ${\ensuremath{\psi}}_{i}$ with a coupling proportional to the pump pulse and to the final state ${\ensuremath{\psi}}_{f}$ with a coupling proportional to the Stokes pulse, thus forming a parallel multi-\ensuremath{\Lambda} system. It is shown that the dark (trapped) state exists only when the ratio between each pump coupling and the respective Stokes coupling is the same for all intermediate states. We derive the conditions for existence of a more general adiabatic-transfer state that includes transient contributions from the intermediate states but still transfers the population from state ${\ensuremath{\psi}}_{i}$ to state ${\ensuremath{\psi}}_{f}$ in the adiabatic limit. We present various numerical examples for success and failure of multi-\ensuremath{\Lambda} STIRAP, which illustrate the analytic predictions. Our results suggest that in the general case of arbitrary couplings, it is most appropriate to tune the pump and Stokes lasers either just below or just above all intermediate states.
Four-photon stimulated Raman adiabatic passage--like (STIRAP-like) processes in the frame of the D1{D}_{1}D1​ optical transition line of atomic 39K^{39}\mathrm{K}39K are investigated theoretically by means of a rigorous model that takes into account all the atomic states involved in the interaction with the pump and Stokes light fields and is valid for any field intensities. The same sequential up-down-up-down transition involving two pump (up) and two Stokes (down) photons, going from the initial ground state $|F=2,M=+2\ensuremath{\rangle}$ to the final ground state $|F=1,M=0\ensuremath{\rangle}$, which was proven in the past to be very convenient for two-photon amplification and lasing, is considered here. The fact that two atomic states, one with F=1F=1F=1 and another with F=2F=2F=2, participate at each intermediate step of the multiphoton process makes the existence of an ideal unique adiabatic transfer state impossible, and at exact four-photon resonance the population-transfer efficiency to the final atomic state is low (below 60% in general, 80% in the best conditions). Nevertheless, it is shown that by choosing appropriate static detunings for the pump and Stokes fields with respect to the atomic transitions the system follows, sequentially, two adiabatic states, connected by an efficient diabatic passage, so that population-transfer efficiency asymptotically approaching 100% for increasing field amplitudes can be reached. These results are quite robust and suggest the possibility of using STIRAP (or STIRAP-like) pumping to, among other applications, increase the (presently very low) efficiency of two-photon amplification and lasing, a so far unfulfilled goal in quantum and nonlinear optics.
Coherent interactions between light fields and simple quantum systems, such as $\ensuremath{\pi}$-pulses and adiabatic passage through frequency chirps and stimulated Raman interactions, generally use one- or two-photon processes. This limits the use of such interactions to energy scales close to the photon energy of the control field. However, recent calculations have shown that a 3-level system, generic to ionized diatomic molecules, shows such a strong multiphoton coupling that $\ensuremath{\pi}$-pulses are possible on at least 12-photon transitions. In this paper, we show that adiabatic transfer of population is also possible on such high-order multiphoton transitions. Full one-dimensional quantum mechanical two-electron calculations confirm this effect even in a system with many excited states and an ionization continuum.
The technique of stimulated Raman adiabatic passage (STIRAP) is a highly efficient tool for coherent population transfer in a chainwise-connected three-state quantum system. It is widely accepted that the two-photon resonance between the two end states of the chain is a crucial condition for STIRAP. This assumption is indeed correct when the two driving fields, pump and Stokes, produce nearly equal couplings for their respective transitions. We show analytically, supported by numeric examples, that when the pump and Stokes couplings differ significantly, the two-photon population transfer profile is distorted and its center is shifted away from the two-photon resonance; hence, the optimal operation of STIRAP demands a two-photon detuning. We derive simple analytic estimates for the center and the width of the two-photon profile. The results are of potential importance in situations when the pump and Stokes fields are of different physical natures (e.g., laser and cavity fields) or when two-photon resonance is unwanted (e.g., in the presence of residual light).