We theoretically examine the rotation of an atomic Bose-Einstein condensate in an elliptical trap, both in the absence and presence of a quantized vortex. Two methods of introducing the rotating potential are considered -adiabatically increasing the rotation frequency at fixed ellipticity, and adiabatically increasing the trap ellipticity at fixed rotation frequency. Extensive simulations of the Gross-Pitaevskii equation are employed to map out the points where the condensate becomes unstable and ultimately forms a vortex lattice. We highlight the key features of having a quantized vortex in the initial condensate. In particular, we find that the presence of the vortex causes the instabilities to shift to lower or higher rotation frequencies, depending on the direction of the vortex relative to the trap rotation.

The dynamics of two-component Bose-Einstein condensates in rotating traps is investigated. In the Thomas-Fermi limit, equations of motion are derived showing multiple static solutions for a vortex free condensate. Dynamic stability analysis of these solutions and comparison with Truncated Wigner simulations enables us to identify the regimes for which vortex states will occur. In addition, our analysis predicts centre-of-mass oscillations that are induced by interspecies interactions and affect each component separately. For attractive interspecies interactions, these oscillations lead to a stable symmetry broken state.Comment: v4: more material added. 9 pages, 6 figures v5: figures fixed v6:some rewording v7:fixed figure

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...