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Physical Review A

Adiabatic population transfer in the D1 transition of K39

J. J. Fernández-Soler, J. L. Font, Ramon A. Vilaseca

Published Jun 22, 2018• 1 citation
Publisher

Abstract

Four-photon stimulated Raman adiabatic passage--like (STIRAP-like) processes in the frame of the ${D}_{1}$ optical transition line of atomic $^{39}\mathrm{K}$ 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 $F=1$ and another with $F=2$, 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.

DOI
10.1103/physreva.97.063848

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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⟩|F=2,M=+2\ensuremath{\rangle}∣F=2,M=+2\ensuremath⟩ to the final ground state ∣F=1,M=0\ensuremath⟩|F=1,M=0\ensuremath{\rangle}∣F=1,M=0\ensuremath⟩, 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.
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).
We have considered a coherent population transfer to a higher excited singlet state ( S2 ) of molecules with anomalous fluorescence in molecular assemblies (e.g., a dense medium). A direct excitation to S2 requires light in the UV region. Because of this, the transition is conveniently realized by a two-step (two-photon) process: S0→S1→S2 , where transitions S0→S1 and S1→S2 correspond to the optical region. We have shown that efficient stimulated Raman adiabatic passage (STIRAP) in the ladder configuration can be realized in this case, using suitably chirped pulses, to compensate a change of the two-photon transition frequency in time, induced by the pulses themselves, due to near dipole-dipole interactions. We have provided a reduced state formulation of the optical control process. Chirping the “pump” pulse that excites transition S0→S1 is nonequivalent to chirping the “Stokes” pulse that excites transition S1→S2 , with respect to the population of the intermediate state ( S1 ) in the pulse nonadiabatic regime. We have also shown that with suitably chirped pulses, efficient STIRAP still persists even for a rather large decay of the intermediate state.
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.
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.
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.
Multistate stimulated Raman adiabatic passage (STIRAP) is a process which allows for adiabatic population transfer between the two ends of a chainwise-connected quantum system. The process requires large temporal areas of the driving pulsed fields (pump and Stokes) in order to suppress the nonadiabatic couplings and thereby to make adiabatic evolution possible. To this end, in the present paper a variation of multistate STIRAP, which accelerates and improves the population transfer, is presented. In addition to the usual pump and Stokes fields it uses shortcut fields applied between the states, which form the dark state of the system. The shortcuts cancel the couplings between the dark state and the other adiabatic states thereby resulting (in the ideal case) in a unit transition probability between the two end states of the chain. Specific examples of five-state systems formed of the magnetic sublevels of the transitions between two degenerate levels with angular momenta Jg=2{J}_{g}=2Jg​=2 (of ground or lower level) and Je=1{J}_{e}=1Je​=1 or Je=2{J}_{e}=2Je​=2 (of excited or upper level) are considered in detail, for which the shortcut fields are derived analytically. The proposed method is simpler than the usual ``shortcuts to adiabaticity'' recipe, which prescribes shortcut fields between all states of the system, while the present proposal uses shortcut fields between the sublevels forming the dark state only. The results are of potential interest in applications where high-fidelity quantum control is essential, e.g., quantum information, atom optics, formation of ultracold molecules, cavity QED, etc.