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Modern Physics Letters B

Ground states of a mixture of pseudospin-1 2 Bose gases with interspecies spin exchange

Rukuan Wu, Yu Shi

Published Feb 1, 2016• 0 citations
Publisher

Abstract

In this paper, we analytically find the ground states of a mixture of two species of pseudospin-[Formula: see text] Bose gases with interspecies spin exchange in quite generic parameter regimes. In the most interesting phase, the ground state is strongly entangled between the two species in a very wide parameter regime, and is an entangled Bose-Einstein condensate. The phase diagram and elementary excitations are studied.

DOI
10.1142/s0217984916501311

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In this paper, we analytically find the ground states of a mixture of two species of pseudospin-[Formula: see text] Bose gases with interspecies spin exchange in quite generic parameter regimes. In the most interesting phase, the ground state is strongly entangled between the two species in a very wide parameter regime, and is an entangled Bose-Einstein condensate. The phase diagram and elementary excitations are studied.
We consider a mixture of two distinct species of atoms of pseudospin 12\frac{1}{2}21​ with both intraspecies and interspecies spin-exchange interactions and find all the ground states in a general case of the parameters in the effective Hamiltonian. In general, corresponding to the two-species and two-pseudospin states, there are four orbital wave functions into which the atoms condense. We find that in certain parameter regimes, the ground state is the so-called polarized entangled Bose-Einstein condensation; that is, in addition to condensation of interspecies singlet pairs, there are unpaired atoms with spins polarized in the same direction. The interspecies entanglement and polarization significantly affect the generalized Gross-Pitaevskii equations governing the four orbital wave functions into which the atoms condense, as an interesting interplay between spin and orbital degrees of freedom.
We consider a mixture of two species of spin-1 atoms with interspecies spin exchange, which may cooperate or compete with intraspecies spin exchanges and thus dramatically affect the ground state. It represents a new class of bosonic gases differing from single-species spinor gases. We determine the exact ground states in several parameter regimes and study the composite structures using the generating function method generalized here to be applicable to a mixture of two species of spinor gases. The most interesting phase is the so-called entangled Bose-Einstein condensation (BEC), which is fragmented BEC with quantum entanglement between the two species and with both interspecies and intraspecies singlet pairs. For comparison, we also apply the generating function method to a mixture of two species of pseudospin-12\frac{1}{2}21​ atoms, for which the total spin quantum number of each species is fixed as half of the atom number, in contrast with the case of spin 111, for which it is a variable determined by energetics. Consequently, singlet pairs in entangled BEC of a pseudospin-12\frac{1}{2}21​ mixture are all interspecies. Interspecies spin exchange leads to novel features beyond those of spinor BEC of a single species of atoms as well as mixtures without interspecies spin exchange.
We consider the effective spin Hamiltonian describing a mixture of two species of pseudo-spin-12\frac{1}{2}21​ Bose gases with interspecies spin exchange. First we analyze the stability of the fixed points of the corresponding classical dynamics, of which the signature is found in quantum dynamics with a disentangled initial state. Focusing on the case without an external potential, we find all the ground states by taking into account quantum fluctuations around the classical ground state in each parameter regime. The nature of entanglement and its relation with classical bifurcation is investigated. When the total spins of the two species are unequal, the maximal entanglement at the parameter point of classical bifurcation is possessed by the excited state corresponding to the classical fixed point which bifurcates, rather than by the ground state.
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.
We study the condensate dynamics of the so-called entangled Bose-Einstein condensation (EBEC), which is the ground state of a mixture of two species of pseudospin-12\frac{1}{2}21​ atoms with interspecies spin-exchange scattering in certain parameter regimes. EBEC leads to four interdependent superfluid components, each corresponding to the orbital wave function associated with a spin component of a species. The four superflows have various counter-relations, and altogether lead to a conserved total supercurrent and a conserved total spin supercurrent. In the homogeneous case, we also obtain the elementary excitations due to variations of the single-particle orbital wave functions, by exactly solving the generalized time-dependent Bogoliubov equations. There are three gapless Bogoliubov modes and one Klein-Gordon-like gapped mode. The origin of these excitations are also discussed from the perspective of spontaneous breaking of the symmetries possessed by the system.
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.