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arXiv:0901.1505 · Physical Review A

Binary mixture of spinor atomic Bose-Einstein condensates

Zhi-Fang Xu, Yunbo Zhang, Li You

Published Feb 10, 2009• 31 citations
arXivHTMLPDF

Abstract

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 $(B)$ 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.

DOI
10.1103/physreva.79.023613

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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 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 $\ensuremath{\beta}$.
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 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 find nearly all the exact ground states of a mixture of two species of spin-1 atoms with both interspecies and intraspecies spin exchanges in the absence of a magnetic field. The quantum phase diagram in the three-dimensional parameter space and its two-dimensional cross sections are described. The boundaries where the ground states are either continuous or discontinuous are determined, with the latter identified as where quantum phase transitions take place. The two species are always disentangled if the interspecies spin coupling is ferromagnetic or zero. Quantum phase transitions occur when the interspecies spin coupling varies between antiferromagnetic and zero or ferromagnetic while the two intraspecies spin couplings both remain ferromagnetic. On the other hand, by tuning the interspecies spin coupling from zero to antiferromagnetic and then back to zero, one can circumvent the quantum phase transition due to sign change of the intraspecies spin coupling of a single species, which is spin decoupled with the other species with ferromagnetic intraspecies spin coupling. Generally speaking, interplay among interspecies and two intraspecies spin exchanges significantly enriches quantum phases of spinor atomic gases.
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 quantum spin mixing in a mixture of two spin-1 condensates including coherent interspecies mixing processes, using condensates of 87{}^{87}87Rb and 23{}^{23}23Na atoms in the ground lower hyperfine F=1F=1F=1 manifold as prototype examples. Adopting the single spatial mode approximation for each of the two spinor condensates, we find the mixing dynamics reduce to that of three coupled nonrigid pendulums with clear physical interpretation. With suitably prepared initial states, the spin mixing dynamics allow for the determination of interspecies singlet-pairing as well as spin-exchange interaction parameters.