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

Spin dynamics and domain formation of a spinor Bose-Einstein condensate in an optical cavity

Lu Zhou, Han Pu, Hong Yuan Ling +2 more

We consider a ferromagnetic spin-1 Bose-Einstein condensate (BEC) dispersively coupled to a unidirectional ring cavity. We show that the ability of the cavity to modify, in a highly nonlinear fashion, matter-wave phase shifts adds an additional dimension to the study of spinor condensates. In addition to demonstrating strong matter-wave bistability as in our earlier publication [L. Zhou et al., Phys. Rev. Lett. 103, 160403 (2009)], we show that the interplay between atomic and cavity fields can greatly enrich both the physics of critical slowing down in spin-mixing dynamics and the physics of spin-domain formation in spinor condensates.We consider a ferromagnetic spin-1 Bose-Einstein condensate (BEC) dispersively coupled to a unidirectional ring cavity. We show that the ability of the cavity to modify, in a highly nonlinear fashion, matter-wave phase shifts adds an additional dimension to the study of spinor condensates. In addition to demonstrating strong matter-wave bistability as in our earlier publication [L. Zhou et al., Phys. Rev. Lett. 103, 160403 (2009)], we show that the interplay between atomic and cavity fields can greatly enrich both the physics of critical slowing down in spin-mixing dynamics and the physics of spin-domain formation in spinor condensates.

arXiv:1005.4121Physical Review AJun 30, 201033 citations

Information entropy for a two-dimensional rotating Bose–Einstein Condensate

Arnaldo Gammal

Jan 1, 20190 citations

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.