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Physical Review A

Linear instability and adiabatic fidelity for the dark state in a nonlinear atom-trimer conversion system

Shao-Ying Meng, Libin Fu, Jing Chen, Jie Liu

Published Jun 30, 2009• 17 citations
Publisher

Abstract

We investigate the linear instability and the adiabatic fidelity of a dark state in a nonlinear atom-trimer conversion that is implemented by a stimulated Raman adiabatic passage (STIRAP). We find that the interparticle interactions could induce the instability of the atom-trimer dark state in some parameter regimes. We also discuss the adiabatic evolution of the dark state in terms of a newly defined adiabatic fidelity. Based on our theoretical analysis, we propose a feasible two-photon STIRAP scheme that has high adiabatic fidelity, less instability, and therefore could yield high atom-trimer conversion efficiency.

DOI
10.1103/physreva.79.063415

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We investigate the linear instability and the adiabatic fidelity of a dark state in a nonlinear atom-trimer conversion that is implemented by a stimulated Raman adiabatic passage (STIRAP). We find that the interparticle interactions could induce the instability of the atom-trimer dark state in some parameter regimes. We also discuss the adiabatic evolution of the dark state in terms of a newly defined adiabatic fidelity. Based on our theoretical analysis, we propose a feasible two-photon STIRAP scheme that has high adiabatic fidelity, less instability, and therefore could yield high atom-trimer conversion efficiency.
We investigate the adiabaticity of the dark state in a nonlinear atom-trimer conversion system in a stimulated Raman adiabatic passage (STIRAP). We find that, in the absence of the nonlinear collisions, the adiabatic condition for this nonlinear system only depends on the Rabi-frequency of the dimer-trimer coupling optical field, which is different from traditional STIRAP processes. In the presence of the nonlinear collisions, the adiabatic condition also relies on the atom-dimer coupling Rabi frequency. However, its influence is really small. Moreover, we propose a more feasible two-photon STIRAP scheme that has better adiabaticity and hence could yield higher atom-trimer conversion efficiency.
This paper investigates the dynamical instability and adiabatic evolution of the atom–homonuclear–trimer dark state of a condensate system in a stimulated Raman adiabatic passage aided by Feshbach resonance. It obtains analytically the regions for the appearance of dynamical instability caused by the interparticle interactions. Moreover, the adiabatic property of the dark state is also studied in terms of a newly defined adiabatic fidelity. It shows that the nonlinear collisions have a negative effect on the adiabaticity of the dark state and hence reduce the conversion efficiency.
From the non-U（1） invariance of the atom-dimer conversion system, we generalized the definition of fidelity to this nonlinear system. By making use of the adiabatic fidelity, we investigated the dynamics and adiabaticity of the atom-dimer conversion system in a stimulated Raman adiabatic passage （STIRAP）. We found that the adiabatic fidelity for the coherent population trapping state or dark state, as the function of the adiabatic parameter, approaches to unity following a power law. The power exponent, however, is much smaller than that predicted by the linear adiabatic theorem. We further discuss how to achieve higher adiabatic fidelity for the dark state through optimizing the external parameters of STIRAP and hence to optimize the adiabaticity of the system and obtain high conversion efficiency.
The adiabaticity of the stimulated Raman adiabatic passage (STIRAP) for the 87Rb atom–molecule conversion in a condensate system is investigated in terms of a newly defined adiabatic fidelity. The evolution of the dark state in the STIRAP is simulated numerically by considering the interparticle interactions and spontaneous emissions of the excited molecular state. We find that these terms will reduce the adiabatic fidelity; however, one can still achieve higher adiabatic fidelity through optimizing the external parameters of the STIRAP. Our discussions are helpful in obtaining higher conversion efficiency from an atomic Bose–Einstein condensate to its molecular counterpart in experiment.
In the present paper, we investigate the instability, adiabaticity, and controlling effects of external fields for a dark state in a homonuclear atom–tetramer conversion that is implemented by a generalized stimulated Raman adiabatic passage. We analytically obtain the regions for the appearance of dynamical instability and study the adiabatic evolution by a newly defined adiabatic fidelity. Moreover, the effects of the external field parameters and the spontaneous emissions on the conversion efficiency are also investigated.
By generalizing the definition of fidelity for the nonlinear system, we investigate the dynamics and adiabaticity of the population transfer for atom-molecule three-level $\ensuremath{\Lambda}$ system on a stimulated Raman adiabatic passage (STIRAP). We find that the adiabatic fidelity for the coherent population trapping state or dark state, as the function of the adiabatic parameter, approaches to unit in a power law. The power exponent, however, is much less than the prediction of the linear adiabatic theorem. We further discuss how to achieve higher adiabatic fidelity for the dark state through optimizing the external parameters of the STIRAP.