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In ultracold Fermi gases, the effect of spin-imbalance on superfluidity hasbeen the subject of intense study. One of the reasons for this is thatspin-imbalance frustrates the Bardeen-Cooper-Schrieffer (BCS) superfluidpairing mechanism, in which fermions in different spin states combine intoCooper pairs with zero momentum. In 1964, it was proposed that an exoticsuperfluid state called the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, inwhich the Cooper pairs have nonzero momentum, could exist in a spin-imbalancedFermi gas. At the saddle-point (mean field) level, it has been shown that theFFLO state only occupies a very small sliver in the ground state phase diagramof a 3D Fermi gas. However, a question that remains to be investigated is: whatis the influence of phase fluctuations around the saddle point on the FFLOstate? In this work we show that phase fluctuations only lead to relativelysmall quantitative corrections to the presence of the FFLO state in thesaddle-point phase diagram of a 3D spin-imbalanced Fermi gas. Starting from thepartition function of the system, we calculate the effective action within thepath-integral adiabatic approximation. The action is then expanded up to secondorder in the fluctuation field around the saddle point, leading to thefluctuation free energy. Using this free energy, we calculate corrections dueto phase fluctuations to the BCS-FFLO transition in the saddle-point phasediagram. At temperatures at which the FFLO state exists, we find only smallcorrections to the size of the FFLO area. Our results suggest that fluctuationsof the phase of the FFLO order parameter, which can be interpreted as anoscillation of its momentum vector, do not cause an instability of the FFLOstate with respect to the BCS state.

Do phase fluctuations influence the Fulde-Ferrell-Larkin-Ovchinnikov state in a 3D Fermi gas?