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arXiv:1001.5335 · Physical Review A

Quantum states of a binary mixture of spinor Bose-Einstein condensates

Zhi-Fang Xu, Jie Zhang, Yunbo Zhang, Li You

Published Mar 9, 2010• 19 citations
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Abstract

We study the structure of quantum states for a binary mixture of spin-1 atomic Bose-Einstein condensates. In contrast to collision between identical bosons, the $s$-wave scattering channel between interspecies does not conform to a fixed symmetry. The spin-dependent Hamiltonian thus contains noncommuting terms, making the exact eigenstates more challenging to obtain because they now depend more generally on both the intra- and interspecies interactions. We discuss two limiting cases, where the spin-dependent Hamiltonian reduces respectively to sums of commuting operators. All eigenstates can then be directly constructed, and they are independent of the detailed interaction parameters.

DOI
10.1103/physreva.81.033603

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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.
We study the ground state and classify its phase diagram for a mixture of two spin-1 condensates in the absence of an external magnetic (B)(B)(B) field according to atomic parameters for intra- and interspecies spin-exchange coupling and singlet-pairing interaction. Ignoring the interspecies singlet-pairing interaction, the ground-state phases are found analytically. A numerical approach of simulated annealing is adopted when the singlet-pairing interaction is present. Our results on the phase diagram and the boundaries between phases allow for easy identifications of quantum phase transitions, which can be induced through the tuning of optical traps and atom numbers. They provide insight and guidance for several ongoing experiments on mixtures of spinor condensates.
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 analyze theoretically Josephson oscillations in a mixture of two Zeeman states of a spinor Bose-Einstein condensate in a double-well potential. We find that in the strongly polarized case, the less populated component exhibits a complex dynamics with an anti-Josephson behavior, i.e., oscillates in phase with the more populated one. In the balanced population case, the Josephson oscillations unveil a dependence with the different spin collision channels. This effect could be used to experimentally measure the distinct scattering lengths entering in the description of a spinor condensate. Our numerical results are in close agreement with an analytical description of the binary mixture using a two-mode model.
We study the ground-state phases for a mixture of two atomic spin-1 Bose-Einstein condensates in the presence of a weak magnetic (BBB) field. The ground state is found to contain a broken-axisymmetry (BA) phase due to competitions among intraspecies and interspecies spin-exchange interactions and the linear Zeeman shifts. This is in contrast to the case of a single-species spin-1 condensate, where the axisymmetry breaking results from competitions among the linear and quadratic Zeeman shifts and the intraspecies ferromagnetic interaction. All other remaining ground-state phases for the mixture are found to preserve axisymmetry. We further elaborate on the ground-state phase diagram and calculate the Bogoliubov excitation spectra of the phases. For the BA phase, there exist three Goldstone modes that attempt to restore the broken U(1) and SO(2) symmetries.
We study the ground-state properties of a mixture formed by two spin-1 condensates in the absence of an external magnetic field. As the collisional symmetry between interspecies bosonic atoms is broken, the interspecies coupling interaction ($\ensuremath{\beta}$) and interspecies singlet-pairing interaction ($\ensuremath{\gamma}$) arise. The ground state can be calculated using the angular momentum theory analytically for $\ensuremath{\gamma}=0$. The full quantum approach of exact diagonalization is adopted numerically to consider the more general case as $\ensuremath{\gamma}\ensuremath{\ne}0$. We illustrate the competition between the two interspecies interactions and find that as singlet-pairing interaction dominates (or the total spin vanishes), there are still different types of singlet formations which are well determined by $\ensuremath{\beta}$.