A hybrid state of matter that includes both superfluid and normal fluid should be stable, according to new calculations. The theory predicting the state was controversial.
We predict that a new superfluid phase, the incompressible excitonic superfluid (IESF), in the phase diagram of ultracold Bose atoms in d>1 dimensional optical lattices, which is caused by the spontaneous breaking of the symmetry of translation of the lattice. Within mean field theory, the critical temperature of the phase transition from this IESF to the normal fluid (NF) is calculated and the triple-critical point of the three phases is determined. We also investigate both configuration and gauge field fluctuations and show the IESF state is stable against these fluctuations. We expect this IESF phase can be experimentally observed by loading cold Bose atoms into a two-dimensional lattice where the atom filling fraction deviates slightly from exact commensurations. The signatures distinguishing this IESF from the common atom superfluid (ASF) are that (i) the critical temperature of the IEST/NF transition is independent of interaction, unlike the ASF/NF transition; (ii) the IESF is incompressible while the ASF is compressible.
In a recent paper [cond-mat/0303185], Wu and Yip presented calculations that they interpreted as indicating an instability of the interior gap phase -- a new, hybrid superfluid-normal state of matter that we proposed in [PRL 90, 047002 (2003)]. Here we observe that their interpretation does not apply to the situations of most physical interest. Their instability was derived under the implicit assumption that one should perturb the relevant systems, which typically contain two distinct species, at fixed values of the separate chemical potentials. However it can be, and generally is, appropriate to enforce different constraints, involving fixed values of particle numbers. Then one often finds, as indicated in our original paper, stable states of the kind we claimed.