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arXiv:cond-mat/0603754 · Physical Review Letters

Bose-Einstein Condensation with an Entangled Order Parameter

Yu Shi, Qian Niu

Published Apr 11, 2006• 33 citations
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Abstract

We propose a practically accessible non-mean-field ground state of Bose-Einstein condensation, which occurs in an interspecies two-particle entangled state, and is thus described by an entangled order parameter. A suitably defined entanglement entropy is used as the characterization of the non-mean-field nature, and is found to persist in a wide parameter regime. The interspecies entanglement leads to novel interference terms in the dynamical equations governing the single-particle orbital wave function. Experimental feasibility and several methods of probe are discussed. We urge the study of multichannel scattering between different species of atoms.

DOI
10.1103/physrevlett.96.140401

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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.
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We revisit in detail the non-mean-field ground-state phase diagram for a binary mixture of spin-1 Bose-Einstein condensates including quantum fluctuations. The noncommuting terms in the spin-dependent Hamiltonian under the single-spatial-mode approximation make it difficult to obtain exact eigenstates. Utilizing spin-z-component conservation and total spin angular momentum conservation, we numerically derive information on the building blocks and evaluate the von Neumann entropy to quantify the ground states. The mean-field phase boundaries are found to remain largely intact, yet the ground states show fragmented and entangled behaviors within large parameter spaces of interspecies spin-exchange and singlet-pairing interactions.
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.