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arXiv:1103.1023 · Physical Review A

Three-dimensional quantum phase diagram of the exact ground states of a mixture of two species of spin- 1 Bose gases with interspecies spin exchange

Yu Shi, Li Ge

Published Jan 24, 2011• 18 citations
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Abstract

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.

DOI
10.1103/physreva.83.013616

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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 consider a mixture of two species of spin-1 atoms with both interspecies and intraspecies spin exchanges in a weak magnetic field. Under the usual single mode approximation, it can be reduced to a model of coupled giant spins. We find most of its ground states. This is a complicated problem of energy minimization, with three quantum variables under constraints, i.e., the total spin of each species and the total spin of the whole mixture, as well as four parameters, including intraspecies and interspecies spin coupling strengths and the magnetic field. The quantum phase diagram is very rich. Compared with the case without a magnetic field, the ground states are modified by a magnetic field, which also modifies the ground state boundaries or introduces new crossover regimes on the phase diagram. Without interspecies spin coupling, the quantum phase transitions existing in absence of a magnetic field disappear when a magnetic field is applied, which leads to crossover regimes in the phase diagram. Under ferromagnetic interspecies spin coupling, the ground states remain disentangled no matter whether there is a magnetic field. For antiferromagnetic interspecies spin coupling, a magnetic field entangles the ground states in some parameter regimes. When the intraspecies spin couplings are both ferromagnetic, the quantum phase transition between antiferromagnetic and zero interspecies spin couplings survives the magnetic field. When the intraspecies spin couplings are both antiferromagnetic, a magnetic field induces new quantum phase transitions between antiferromagnetic and zero interspecies spin couplings.
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 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.
Ground-state phase diagram of two-component Bose gases with Rashba spin-orbit coupling is determined via a variational approach. A phase in which the fully polarized condensate occupies zero momentum is identified. This zero-momentum phase competes with the spin density wave phase when interspecies interaction is stronger than intraspecies interaction, and the former one is always the ground state for weak spin-orbit coupling. When the energies of these two phases are close, there is a phase separation between them. At finite temperature, such a zero-momentum condensation can be induced by a ferromagnetic phase transition in normal state. The spontaneous spin polarization removes the degeneracy of quasiparticles' energy minima, and consequently the modified density of state accommodates a Bose condensation to appear below a critical temperature.
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.