Field theory of low energy excitations of a mixture of two species of pseudospin-1/2 Bose gases with interspecies spin-exchange

We develop a low energy effective field theory of a mixture of two species of pseudospin-1/2 atoms with interspecies spin-exchange, in addition to density-density interaction. This approach is beyond the single orbital-mode approximation. In a wide parameter regime, it indicates the existence of the four elementary excitations, especially a gapped mode due to interspecies spin-exchange. On the other hand, the spectrum of the effective spin Hamiltonian yielded by the single mode approximation can be obtained by quantizing the homogeneous excitation, which is spin excitation and is the long-wavelength limit of the gapped mode of elementary excitations. These low energy excitations can be experimentally measured by using Bragg spectroscopy.