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arXiv:0805.3315

Exploring the order parameter symmetry of p-wave Fermi condensates

Wei Zhang, C. A. R. Sá de Melo

Published May 21, 2008• 0 citations
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Abstract

We discuss the time-of-flight expansion of dilute p-wave Fermi condensates on the BEC side of Feshbach resonances, as a way to extract information about the order parameter symmetry for superfluidity. We show that the cloud profile is in general sensitive to the interaction strength between fermions, the magnitude and direction of external magnetic fields, and to the angular momentum projection of the order parameter. In particular, due to the anisotropic nature of p-wave interactions we show that the time-of-flight expansion of a p-wave superfluid is anisotropic even if the superfluid is confined to a completely isotropic trap, unlike the case of Bose or s-wave Fermi condensates, which under the same circumstances expand isotropically. Furthermore, we demonstrate that expanding p-wave superfluids released from axially symmetric traps experience anisotropy inversions, where the aspect ratio between the axial and radial directions change during expansion, while the axial symmetry can also be lost reflecting the spatial anisotropy of the underlying interaction.

DOI
10.48550/arxiv.0805.3315

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We discuss the time-of-flight expansion of dilute p-wave Fermi condensates on the BEC side of Feshbach resonances, as a way to extract information about the order parameter symmetry for superfluidity. We show that the cloud profile is in general sensitive to the interaction strength between fermions, the magnitude and direction of external magnetic fields, and to the angular momentum projection of the order parameter. In particular, due to the anisotropic nature of p-wave interactions we show that the time-of-flight expansion of a p-wave superfluid is anisotropic even if the superfluid is confined to a completely isotropic trap, unlike the case of Bose or s-wave Fermi condensates, which under the same circumstances expand isotropically. Furthermore, we demonstrate that expanding p-wave superfluids released from axially symmetric traps experience anisotropy inversions, where the aspect ratio between the axial and radial directions change during expansion, while the axial symmetry can also be lost reflecting the spatial anisotropy of the underlying interaction.
We discuss the time evolution and matter-wave interference of Fermi condensates on the Bose-Einstein condensate side of Feshbach resonances for sss- and ppp-wave superfluids, upon release from harmonic traps. In sss-wave systems, where the order parameter is a complex scalar, we find that the interference patterns depend on the relative phase of the order parameters of the condensates. In ppp-wave systems involving the mixture of two hyperfine states, we show that the interference pattern exhibits a polarization effect depending on the relative orientation of the two vector order parameters. Lastly, we also point out that ppp-wave Fermi condensates exhibit an anisotropic expansion, reflecting the spatial anisotropy of the underlying interaction between fermions and the orbital nature of the vector order parameter. Potential applications of our results include systems of ultracold atoms that exhibit ppp-wave Feshbach resonances, such as 6Li^{6}\mathrm{Li}6Li or 40K^{40}\mathrm{K}40K.
We discuss matter wave interference of Fermi condensates in strongly coupled s-wave and p-wave channels and the time evolution of a single cloud upon release from trap. In s-wave systems, where the order parameter is a complex scalar, we find that the interference patterns depend on the relative phase of the order parameters of the condensates. In p-wave systems involving the mixture of two-hyperfine states, we show that the interference pattern exhibits a polarization effect depending on the relative orientation of the two vector order parameters. However, in p-wave systems involving a single hyperfine state, we show that this angular effect reduces to an overall phase difference between the two interfering clouds, similar to s-wave. Lastly, we also point out that p-wave Fermi condensates exhibit an anisotropic expansion, reflecting the spatial anisotropy of the underlying interaction between fermions and the orbital nature of the vector order parameter.
We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.
The anisotropic Fermi superfluid of ultra-cold Fermi atoms under the ppp-wave Feshbach resonance is studied theoretically. The pairing symmetry of the ground state is determined by the strength of the atom-atom magnetic dipole interaction. It is kz{k}_{z}kz​ for a strong dipole interaction; while it becomes ${k}_{z}\ensuremath{-}i\ensuremath{\beta}{k}_{y}$, up to a rotation about $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$, for a weak one. (Here $\ensuremath{\beta}<1$ is a numerical coefficient.) By changing the external magnetic field or the atomic gas density, a phase transition between these two states can be driven. We discuss how the pairing symmetry of the ground state can be determined in the time-of-flight experiments.
Abstract We present a study of static and expansion properties of strongly interacting Fermi superfluids containing a vortex initially trapped by cylindrically symmetric potentials. Based on the order-parameter equation in the framework of the Gross–Pitaevskii equation, a unified expression for the energy of a vortex line in the crossover from a Bardeen–Cooper–Schrieffer superfluid to a molecular Bose–Einstein condensate is analytically presented. Numerical simulations show that the combined effects of interactions and trap configurations lead to an interesting property that the free expansion rate of the vortex core radius is smaller than that of the radius of the superfluid in the radial direction, when the strongly interacting Fermi superfluid containing a vortex is released from a cigar-shaped trap. The effects of the trap anisotropy and vortex on the Efimovian expansions of a unitary Fermi superfluid in real experimental setups are also predicted.
We study the super Efimovian expansions of a superfluid Fermi gas in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC), by using superfluid hydrodynamic equations with the equation of state fitting from the experimental data and a scaling approach. We find that in an isotropic trap, the super Efimovian expansion of the Fermi superfluid in the unitary limit is characterized by the double-log periodicity, while for an axially symmetric trap, the double-log periodicity only emerges in the longer direction for a large anisotropy of the trapping frequencies. Away from unitarity where the scale invariance is broken, the super Efimovian expansions of the superfluid Fermi gases deviate from the double-log oscillations. The oscillations in the BCS regime deviate upward from the double-log oscillations, whereas the oscillations in the BEC regime deviate downward and the deviation in the BEC limit is the most significant. This difference can be used to discriminate different superfluid regimes.