arXiv:1201.5711 · Physical Review A

Quantum spin mixing in a binary mixture of spin-1 atomic condensates

Zhi-Fang Xu, Dajun Wang, Li You

Published Jul 20, 2012• 10 citations

Abstract

We study quantum spin mixing in a mixture of two spin-1 condensates including coherent interspecies mixing processes, using condensates of ${}^{87}$Rb and ${}^{23}$Na atoms in the ground lower hyperfine $F=1$ 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.

DOI: 10.1103/physreva.86.013632

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arXiv:1201.5711 · Physical Review A

Quantum spin mixing in a binary mixture of spin-1 atomic condensates

Zhi-Fang Xu, Dajun Wang, Li You

Published Jul 20, 2012• 10 citations

arXiv HTML PDF

Abstract

We study quantum spin mixing in a mixture of two spin-1 condensates including coherent interspecies mixing processes, using condensates of

{}^{87}

Rb and

{}^{23}

Na atoms in the ground lower hyperfine

F=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.

DOI: 10.1103/physreva.86.013632

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We study quantum spin mixing in a mixture of two spin-1 condensates including coherent interspecies mixing processes, using condensates of

{}^{87}

Rb and

{}^{23}

Na atoms in the ground lower hyperfine

F=1

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.

We provide further details on atom number fluctuation during spin-mixing dynamics inside an

F=1

spinor condensate, based on the effective quantization approach we reported earlier [L. Chang et al., Phys. Rev. Lett. 99, 080402 (2007)] for the semiclassical nonrigid pendulum model in terms of the relative phase and the atomic population in the magnetic $(B\text{\ensuremath{-}})$field insensitive hyperfine state

|{F}_{z}=0⟩

. Many features of the classical nonrigid pendulum model are reproduced. In addition, features typically associated with full quantum simulations specific to our model system, such as atom number fluctuations both in stationary states and during the dynamics of spin mixing, are faithfully revealed with our effective quantization approach. We check the validity of the effective quantization theory by performing extensive numerical comparisons with the results from full quantum many-body simulations. We study the effect of quantum coherence in our system and provide a solid theoretical basis to resolve the resolution limit in counting atoms that is needed to clearly detect quantum correlation effects in spin mixing.

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.