Quantum noise, scaling, and domain formation in a spinor Bose-Einstein condensate

In this paper we discuss Bose-Einstein spinor condensates for F=1 atoms in the context of ⁸⁷Rb, 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 su(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,−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=−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.