Effect of anisotropic exchange interactions and short-range phenomena on superfluidity in a homogeneous dipolar Fermi gas

Abstract

We develop a simple numerical method that allows us to calculate the Bardeen-Cooper-Schriefer (BCS) superfluid transition temperature (Tc) precisely for any interaction potential. We apply it to a polarised, ultracold Fermi gas with long-range, anisotropic, dipolar interactions and include the effects of anisotropic exchange interactions. We pay particular attention to the short-range behaviour of dipolar gasses and re-examine current renormalisation methods. In particular, we find that dimerisation of both atoms and molecules significantly hampers the formation of a superfluid. The end result is that at high density/interaction strengths, we find Tc is orders of magnitude lower than previous calculations.PACS numbers: 03.75. Ss, 67.85.Lm A great deal of interest in dipolar Fermi gasses has been generated due to their long range interactions, which lead to many novel effects such as p-wave superfluidity [1][2][3][4], topological superfluidity in 2D systems [5,6], anisotropic and many body effects on the Fermi liquid properties [7,8], the tailoring of novel interaction potentials [9,10], and superfluidity in bilayers [11,12].This rich selection of interesting phenomena has lead to a large effort from many groups to trap and cool a dipolar gas to degeneracy. Many highly successful experiments have resulted from this effort, which have concentrated on both molecular [13][14][15][16][17][18][19] and atomic, highly-magnetic dipolar gasses [20][21][22][23][24][25][26][27]. These experiments investigated features such as the precise control of ultracold chemical reactions [14][15][16], quantum chaos in dipolar collisions [22,23], anisotropic interaction effects in the Fermi surface [25], and dipolar collisions [24]. As yet, however, a dipolar Fermi superfluid has not been observed.Predictions for the superfluid transition temperature of a dipolar Fermi gas (T c ) have been calculated in a number of works under various conditions [1, 4-6, 11, 12, 28-30]. These works consider a dipolar Fermi gas within an idealised condensed matter paradigm, which is usually applicable for thermodynamically stable systems. However, an ultra-cold dilute gas is not stable. We investigate the complications that this introduces and produce our own predictions for Tc that differ significantly from these previous works at high densities or interaction strengths. After deriving our results, we compare our methodology with previous works in Section V. This paper will be set out as follows. In Section I we review some important theoretical and experimental background involving the stability of p-wave gasses, particularly the collapse into p-wave dimers. We will then investigate how adding long-range interactions affects these pwave dimers and produces dipolar-interaction-dominated bound states. In Section II we see that these dipolar bound states can have a large effect on the stability of the gas and therefore also on T c . A key result of this paper is that we will show that in attempting to renormalise out the short range behavior of a dipo...

Leggett mode in a two-component Fermi gas with dipolar interactions

“…To deal with the short-range divergence of the dipolar interaction, the most common method of using the two-body T -matrix as a way to renormalize the interaction [28] is not tractable in the manybody calculations, since the dipolar interaction couples different partial wave channels [29][30][31]. A useful strategy for renormalization is to take the Born approximation [32][33][34], which unfortunately is appropriate in the weakly interacting regime only [35][36][37]. In this work, we consider an effective separable interaction potential that couples different angular momentum channels (i.e., |l−l | ≤ 2) in the strongly interacting regime, as was used in Ref.…”

Fermi surface deformations and pairing in mixtures of dipolar and non-dipolar fermions

“…Also in dipolar Fermi gases exotic states of matter are expected. For instance, the attractive part of the dipolar interaction can lead to a p-wave superfluid, which was not yet realized experimentally, but has been studied extensively in the literature [16][17][18][19][20][21][22][23]. For strong dipolar interactions the Fermi gas collapses, while the dipolar gas is in a metastable state for small interactions due to the Fermi pressure [19,[24][25][26].…”