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 Rb-87, as studied experimentally by the Stamper-Kurn group [L. E. Sadler , 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.