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arXiv:1112.5277 · Journal of Statistical Mechanics Theory and Experiment

Field theory of low energy excitations of a mixture of two species of pseudospin-\frac {1}{2} Bose gases with interspecies spin exchange

Li Ge, Yu Shi

Published Jun 11, 2012• 0 citations
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Abstract

We develop a low energy effective field theory of a mixture of two species of pseudospin- atoms with interspecies spin exchange, in addition to density–density interaction. This approach is beyond the single-orbital-mode approximation. In a wide parameter regime, it indicates the existence of the four elementary excitations, especially the gapped mode due to interspecies spin exchange. The spectrum of the effective spin Hamiltonian yielded by the single-mode approximation can be obtained by quantizing the homogeneous excitation, which is spin excitation and is the long-wavelength limit of the gapped mode among the elementary excitations. These low energy excitations may be experimentally detected by using Bragg spectroscopy.

DOI
10.1088/1742-5468/2012/06/p06004

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Sine-Gordon model coupled with a free scalar field emergent in the low-energy phase dynamics of a mixture of pseudospin-12\frac{1}{2}21​ Bose gases with interspecies spin exchange
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Number and spin densities in the ground state of a trapped mixture of two pseudospin-12\frac{1}{2}21​ Bose gases with interspecies spin-exchange interaction
We consider the ground state of a mixture of two pseudospin- Bose gases with interspecies spin exchange in a trapping potential. In the mean field approach, the ground state can be described in terms of four wavefunctions governed by a set of coupled Gross–Pitaevskii-like (GP-like) equations, which differ from the usual GP equations in the existence of an interference term due to spin-exchange coupling between the two species. Using these GP-like equations, we calculate such ground state properties as chemical potentials, density profiles and spin density profiles, which are directly observable in experiments. We compare the cases with and without spin exchange. It is demonstrated that the spin exchange between the two species lowers the chemical potentials, tends to equalize the wavefunctions of the two pseudospin components of each species, and, thus, homogenizes the spin density. The novel features of the density and spin density profiles can serve as experimental probes of this novel Bose system.
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A mixture of two species of pseudospin-12\frac{1}{2}21​ Bose gases exhibits interesting interplay between spin and orbital degrees of freedom. Expectation values of various quantities of the collective spins of the two species play crucial roles in the Gross-Pitaevskii-like equations governing the four orbital wave functions in which Bose-Einstein condensation occurs. Consequently, the elementary excitations of these orbital wave functions reflect properties of the collective spins. When the coupling between the two collective spins is isotropic, the energy gap of the gapped orbital excitation peaks. There is a quantum phase transition in the ground state of the effective Hamiltonian of the two collective spins, which have previously been found to be maximally entangled.