arXiv:0704.1995 · Physical Review Letters

Coherent Dynamics of Domain Formation in the Bose Ferromagnet

Qiang Gu, Haibo Qiu

Published May 15, 2007• 24 citations

Abstract

We present a theory to describe domain formation observed very recently in a quenched 87Rb gas, a typical ferromagnetic spinor Bose system. An overlap factor is introduced to characterize the symmetry breaking of MF=+/-1 components for the F=1 ferromagnetic condensate. We demonstrate that the domain formation is a coeffect of the quantum coherence and the thermal relaxation. A thermally enhanced quantum oscillation is observed during the dynamical process of the domain formation. And the spatial separation of domains leads to significant decay of the MF=0 component fraction in an initial MF=0 condensate.

DOI: 10.1103/physrevlett.98.200401

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arXiv:0704.1995 · Physical Review Letters

Coherent Dynamics of Domain Formation in the Bose Ferromagnet

Qiang Gu, Haibo Qiu

Published May 15, 2007• 24 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.98.200401

Related papers

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In this paper we discuss Bose-Einstein spinor condensates for $F=1$ atoms in the context of $^{87}\text{R}\text{b}$ , as studied experimentally by the Stamper-Kurn group [L. E. Sadler et al., Nature (London) 443, 312 (2006)]. The dynamical quantum fluctuations of a sample that starts as a condensate of $N$ atoms in a pure $F=1$ , ${m}_{F}=0$ state are described in analogy to the two-mode squeezing of quantum optics in terms of an $\mathfrak{s}\mathfrak{u}(1,1)$ algebra. In this system the initial ${m}_{F}=0$ condensate acts as a source (pump) for the creation pairs of ${m}_{F}=1,\ensuremath{-}1$ atoms. We show that even though the system as a whole is described by a pure state with zero entropy, the reduced density matrix for the ${m}_{F}=+1$ degree of freedom, obtained by tracing out the ${m}_{F}=\ensuremath{-}1,0$ degrees of freedom, corresponds to a thermal state. Furthermore, these quantum fluctuations of the initial dynamics of the system provide the seeds for the formation of domains of ferromagnetically aligned spins.In this paper we discuss Bose-Einstein spinor condensates for $F=1$ atoms in the context of $^{87}\text{R}\text{b}$, as studied experimentally by the Stamper-Kurn group [L. E. Sadler et al., Nature (London) 443, 312 (2006)]. The dynamical quantum fluctuations of a sample that starts as a condensate of $N$ atoms in a pure $F=1$, ${m}_{F}=0$ state are described in analogy to the two-mode squeezing of quantum optics in terms of an $\mathfrak{s}\mathfrak{u}(1,1)$ algebra. In this system the initial ${m}_{F}=0$ condensate acts as a source (pump) for the creation pairs of ${m}_{F}=1,\ensuremath{-}1$ atoms. We show that even though the system as a whole is described by a pure state with zero entropy, the reduced density matrix for the ${m}_{F}=+1$ degree of freedom, obtained by tracing out the ${m}_{F}=\ensuremath{-}1,0$ degrees of freedom, corresponds to a thermal state. Furthermore, these quantum fluctuations of the initial dynamics of the system provide the seeds for the formation of domains of ferromagnetically aligned spins.

arXiv:0710.3547Physical Review AFeb 14, 200844 citations

Recent experimental studies of

^{87}

Rb spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition taking into account the effects of the trap, non-linearities, finite temperature and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system and estimate the contribution of quantum zero-point fluctuations to the domain formation. Finally, using the strong anisotropy of the trap, we propose ways to observe directly the effects of dipole-dipole interactions on the spinor condensate dynamics.

Recent experimental studies of

^{87}\text{R}\text{b}

spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition within the framework of the semiclassical truncated Wigner approximation. In the process we present a systematic study of the effects of the trap, nonlinearities, finite temperature, and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system by combining results presented here with those presented previously [S. Leslie, J. Guzman, M. Vengalattore, J. D. Sau, M. L. Cohen, and D. M. Stamper-Kurn, Phys. Rev. A 79, 043631 (2009)]. In the process we estimate the contribution of quantum zero-point fluctuations to the domain formation with quantitative accuracy and find discrepancies between the calculations and experiments at the quantitative level, despite the qualitative agreement between theory and experiment. We discuss the possible origins of these discrepancies. Finally, using the strong anisotropy of the trap, we propose ways to observe directly the effects of dipole-dipole interactions on the spinor condensate dynamics.

In this paper we discuss Bose-Einstein spinor condensates for

F=1

atoms in the context of

^{87}\text{R}\text{b}

, as studied experimentally by the Stamper-Kurn group [L. E. Sadler et al., Nature (London) 443, 312 (2006)]. The dynamical quantum fluctuations of a sample that starts as a condensate of

N

atoms in a pure

F=1

{m}_{F}=0

state are described in analogy to the two-mode squeezing of quantum optics in terms of an

\mathfrak{s}\mathfrak{u}(1,1)

algebra. In this system the initial

{m}_{F}=0

condensate acts as a source (pump) for the creation pairs of ${m}_{F}=1,\ensuremath{-}1$ atoms. We show that even though the system as a whole is described by a pure state with zero entropy, the reduced density matrix for the

{m}_{F}=+1

degree of freedom, obtained by tracing out the ${m}_{F}=\ensuremath{-}1,0$ degrees of freedom, corresponds to a thermal state. Furthermore, these quantum fluctuations of the initial dynamics of the system provide the seeds for the formation of domains of ferromagnetically aligned spins.