Abstract
We study the stability of the paired fermionic $p$-wave superfluid made out of identical atoms all in the same hyperfine state close to a $p$-wave Feshbach resonance. First we reproduce known results concerning the lifetime of a three-dimensional superfluid, in particular, we show that it decays at the same rate as its interaction energy, which may preclude its equilibration before it decays. Then we proceed to study its stability in the case when the superfluid is confined to two dimension (2D) by means of an optical harmonic potential. We find that the relative stability is improved in 2D in the BCS regime, such that the decay rate is now parametrically slower than the appropriate interaction energy scale, leading to the possibility of an equilibrated $p$-wave superfluid in 2D.
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