work [@multipartsupconfew; @commupair] provides an interesting challenge for experiments to observe the communal state in physical systems. In real space the superconducting order parameter will exhibit a beat pattern due to the interference between similar $q$-vectors, which could allow the identification of the particular $q$-vectors in the superconductor. The order parameter and its spread in momentum could be determined in an ultracold atomic gas experiment through density-density correlations measured from time-of-flight experiments [@Altman04]. In contrast, FFLO and crystalline FFLO theories predict sharp peaks in the condensate fraction, as in spin-balanced BCS theory, at fixed magnitude of the pairing momenta.

Additionally, as the communal number pair $({N_\uparrow},{N_\downarrow})$ is a function of the spin imbalance, multiple phase transitions through several superconducting phases should be observed as the imbalance is increased. Each transition is expected to be second order, and so the communal superconducting phase would be characterized by a series of singularities in the heat capacity and the compressibility, which should be directly observable in ultracold atomic gases [@Ku12] as the spin-imbalance is changed. No such phase transitions are expected for the FFLO phase at fixed temperature.

An orthogonal line of questioning that may be of concern in real experiments is on 