It is suggested, on the basis of soluble models, that generalized Bose condensation results from a broken symmetry associated with a nonvanishing pairing amplitude with very large low-momentum components, leading to a nonzero ``pairing density'' pc as well as a nonzero generalized condensate density ρc. For systems of interacting bosons it is proved that (1) nonzero pc implies nonzero ρc, and (2) pc = 0 in one or two dimensions and, more generally, for geometries finite in one dimension and infinite in the other two (films) or finite in two dimensions and infinite in one (pores). It is pointed out that this does not exclude superfluidity in such geometries, but does show the need of a new mechanism to explain it.
We study a ``helical'' superfluid, a nonzero-momentum condensate in a frustrated bosonic model. At mean-field Bogoliubov level, such a novel state exhibits ``smectic'' fluctuation that are qualitatively stronger than that of a conventional superfluid. We develop a phase diagram and compute a variety of its physical properties, including the spectrum, structure factor, condensate depletion, momentum distribution, all of which are qualitatively distinct from that of a conventional superfluid. Interplay of fluctuations, interaction and lattice effects gives rise to the phenomenon of order by disorder, leading to a crossover from the smectic superfluid regime to the anisotropic
XY superfluid phase. We complement the microscopic lattice analysis with a field theoretic description for such a helical superfluid, which we derive from microscopics and justify on general symmetry grounds, reassuringly finding full consistency. Possible experimental realizations are discussed.
We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low-energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground-state
(T=0) superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground-state energy, and low-energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the
s-wave case where the BCS to BEC evolution is just a crossover. Third, we present a Gaussian fluctuation theory near the critical temperature
(T=Tc), and we analyze the number of bound, scattering, and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near
Tc, and compare the Ginzburg-Landau coherence length with the zero-temperature average Cooper pair size.