Spinor Bose gas in an elongated trap

We examine a spinor Bose gas confined by an elongated trap. Since a spin-independent energy is much higher than a spin-dependent energy in alkali species, the system exhibits different properties by changing a radial confinement. We show that if a spin-dependent coupling is positive, a spin-liquid condensate, which breaks the charge U(1) symmetry but preserves the spin rotational symmetry, can be realized in an intermediate confinement regime. Properties of the spin-liquid condensate are visible if a temperature is lower than a spin gap to characterize the spin-disorder property. If a temperature is higher than the gap but lower than a spin-dependent coupling energy, on the other hand, a regime in which a spin sector is described by a semiclassical wave emerges. A characterization in each regime by means of correlation functions and topological solitons is also discussed.