Sine-Gordon model coupled with a free scalar field emergent in the low-energy phase dynamics of a mixture of pseudospin-1/2 Bose gases with interspecies spin exchange

Abstract

Using the approach of low-energy effective field theory, the phase diagram is studied for a mixture of two species of pseudospin-\(\1/2\) Bose atoms with interspecies spin-exchange. There are four mean-field regimes on the parameter plane of \(g_e\) and \(g_z\), where \(g_e\) is the interspecies spin-exchange interaction strength, while \(g_z\) is the difference between the interaction strength of interspecies scattering without spin-exchange of equal spins and that of unequal spins. Two regimes, with \(|g_z| > |g_e|\), correspond to ground states with the total spins of the two species parallel or antiparallel along \(z\) direction, and the low energy excitations are equivalent to those of two-component spinless Bosons. The other two regimes, with \(|g_e| > |g_z|\), correspond to ground states with the total spins of the two species parallel or antiparallel on \(xy\) plane, and the low energy excitations are described by a sine-Gordon model coupled with a free scalar field, where the effective fields are combinations of the phases of the original four Boson fields. In (1+1)-dimension, they are described by Kosterlitz-Thouless renormalization group (RG) equations, and there are three sectors in the phase plane of a scaling dimension and a dimensionless parameter proportional to the strength of the cosine interaction, both depending on the densities. The gaps of these elementary excitations are experimental probes of the underlying many-body ground states.