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Chinese Physics B

Linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules

Shao-Ying Meng, Xihao Chen, Wei Wu, Libin Fu

Published Apr 1, 2012• 3 citations
Publisher

Abstract

In the present paper, we investigate the linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules through the stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions for the appearance of linear instability. Moreover, taking 40 K and 6 Li atom—molecule conversion systems as examples, we give the unstable regions numerically. We also attempt to obtain the adiabatic criterion for this nonlinear system with classical adiabatic dynamics and study the adibaticity of the dark state with the adiabatic condition.

DOI
10.1088/1674-1056/21/4/040308

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In the present paper, we investigate the linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules through the stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions for the appearance of linear instability. Moreover, taking 40 K and 6 Li atom—molecule conversion systems as examples, we give the unstable regions numerically. We also attempt to obtain the adiabatic criterion for this nonlinear system with classical adiabatic dynamics and study the adibaticity of the dark state with the adiabatic condition.
In this paper, we investigate the dynamical instability of the dark state in the conversion of Bose-Fermi mixtures into stable molecules through a stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions where the dynamical instability appears and find that such instability in the Bose-Fermi mixture system is caused not only by bosonic interparticle interactions but also by Pauli blocking terms, which is different from the scenario of a pure bosonic system where instability is induced by nonlinear interparticle collisions. Taking a 40 K- 87 Rb mixture as an example, we give the unstable regions numerically.
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.
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 dynamical stability of a dark state of the atom-heteronuclear-trimer conversion system in a stimulated Raman adiabatic passage process. By casting the quantum Hamiltonian into an effective classical one and analyzing the eigenvalues of the Hamiltonian-Jacobi matrix obtained by linearizing the equations of motion around the fixed point corresponding to the dark state, we analytically obtain the condition for the occurrence of the dynamical instability of the atom-trimer dark state. Taking heteronuclear atoms of 87Rb and 41K as an example, we numerically give the unstable region. We find that the dynamical instability is induced by the interparticle interactions. Moreover，the occurrence of the dynamical instability depends on not only the emergence of the real or complex eigenvalues of the Hamiltonian-Jacobi matrix but also the scanning rate of the external fields.
The efficiency of converting two-species fermionic atoms into bosonic molecules is investigated in terms of mean-field Lagrangian density. We find that the stimulated Raman adiabatic passage technique aided by Feshbach resonance is more effective than the bare Feshbach resonance for 6Li^{6}\text{L}\text{i}6Li atoms rather than 40K^{40}\text{K}40K atoms. We also generally consider the symmetry and its relevant conservation law, which enables us to introduce a natural definition of adiabatic fidelity for a coherent population trapping state. The calculated values of the fidelity are presented and then we provide an explanation of why the conversion efficiencies for 40K^{40}\text{K}40K and 6Li^{6}\text{L}\text{i}6Li are distinctly different.
We give a brief description of theoretical studies on multi-component systems and detailed discussions on systems with atom-to-molecule conversion. The conversion of two species of atoms into stable molecules through the Feshbach resonance assisted by stimulated Raman adiabatic passage in photoassociation is studied with the help of mean-field Langrange density. The conversion efficiency is large for the fully bosonic system as well as the boson-fermion mixture as long as the general two-photon resonance condition is satisfied.