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Two-dimensional Fermi gases near a ppp-wave resonance

Shao-Jian Jiang, Fei Zhou

Published Apr 25, 2017• 0 citations
OpenAlex

Abstract

We study the stability of $p$-wave superfluidity for two-dimensional Fermi gases near a $p$-wave Feshbach resonance. A systematic analysis is carried out in the limit when the interchannel coupling is strong. We show that a homogeneous $p$-wave pairing is actually unstable due to quantum fluctuations, in contrast to the previously predicted $p+ip$ superfluid in the weak-coupling limit [V. Gurarie et al., Phys. Rev. Lett. 94, 230403 (2005)]. This indicates an onset of instability at certain intermediate interchannel coupling strength. Alternatively, the instability can also be driven by lowering the particle density.

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We study the stability of ppp-wave superfluidity for two-dimensional Fermi gases near a ppp-wave Feshbach resonance. A systematic analysis is carried out in the limit when the interchannel coupling is strong. We show that a homogeneous ppp-wave pairing is actually unstable due to quantum fluctuations, in contrast to the previously predicted p+ipp+ipp+ip superfluid in the weak-coupling limit [V. Gurarie et al., Phys. Rev. Lett. 94, 230403 (2005)]. This indicates an onset of instability at certain intermediate interchannel coupling strength. Alternatively, the instability can also be driven by lowering the particle density.
We study the stability of ppp-wave superfluidity against quantum fluctuations in two-dimensional Fermi gases near a ppp-wave Feshbach resonance. An analysis is carried out in the limit when the interchannel coupling is strong. By investigating the effective potential of the pairing field via the standard loop expansion, we show that a homogeneous ppp-wave pairing state becomes unstable when two-loop quantum fluctuations are taken into account. This is in contrast to the previously predicted p+ipp+ipp+ip superfluid in the weak-coupling limit [V. Gurarie et al., Phys. Rev. Lett. 94, 230403 (2005)]. It implies a possible onset of instability at certain intermediate interchannel coupling strength. Alternatively, the instability can also be driven by lowering the particle density. At the end, we discuss the validity of our analysis.
The induced intraspecies interactions among the majority species, mediated by the minority species, is computed for a population-imbalanced two-component Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is dominant for equal populations, leading to singlet sss-wave pairing, we find that, in the strongly imbalanced regime, the induced intraspecies interaction leads to ppp-wave pairing and superfluidity of the majority species. Thus, we predict that the observed spin-polaron Fermi-liquid state in this regime is unstable to ppp-wave superfluidity, in accordance with the results of Kohn and Luttinger, below a temperature that, near unitarity, we find to be within current experimental capabilities. We present possible experimental signatures of the ppp-wave state using radiofrequency spectroscopy as well as density-density correlations after free expansion.
We investigate single-particle properties of a one-component Fermi gas with a tunable p-wave interaction. Including pairing fluctuations associated with this anisotropic interaction within a TTT-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature TcT_{\rm c}Tc​. Starting from the weak-coupling regime, we show that the so-called pseudogap first develops in these quantities with increasing the interaction strength. However, when the interaction becomes strong to some extent, the pseudogap becomes obscure to eventually disappear in the strong-coupling regime. This non-monotonic interaction dependence is quite different from the case of an s-wave interaction, where the pseudogap simply develops with increasing the interaction strength. The difference between the two cases is shown to originate from the momentum dependence of the p-wave interaction, which vanishes in the low momentum limit. We also identify the pseudogap regime in the phase diagram with respect to the temperature and the p-wave interaction strength. Since the pseudogap is a precursor phenomenon of the superfluid phase transition, our results would be useful for the research toward the realization of p-wave superfluid Fermi gases.
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.
Fermionic superfluidity in atomic Fermi gases across a Feshbach resonance is normally described by the atom-molecule theory, which treats the closed channel as a noninteracting point boson. In this work we present a theoretical description of the resonant superfluidity in analogy to the two-band superconductors. We employ the underlying two-channel scattering model of Feshbach resonance where the closed channel is treated as a composite boson with binding energy ${\ensuremath{\varepsilon}}_{0}$ and the resonance is triggered by the microscopic interchannel coupling U12{U}_{12}U12​. The binding energy ${\ensuremath{\varepsilon}}_{0}$ naturally serves as an energy scale of the system, which has been sent to infinity in the atom-molecule theory. We show that the atom-molecule theory can be viewed as a leading-order low-energy effective theory of the underlying fermionic theory in the limit ${\ensuremath{\varepsilon}}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$ and ${U}_{12}\ensuremath{\rightarrow}0$, while keeping the phenomenological atom-molecule coupling finite. The resulting two-band description of the superfluid state is in analogy to the BCS theory of two-band superconductors. In the dilute limit ${\ensuremath{\varepsilon}}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$, the two-band description recovers precisely the atom-molecule theory. The two-band theory provides a natural approach to study the corrections because of a finite binding energy ${\ensuremath{\varepsilon}}_{0}$ in realistic experimental systems. For broad and moderate resonances, the correction is not important for current experimental densities. However, for extremely narrow resonance, we find that the correction becomes significant. The finite binding energy correction could be important for the stability of homogeneous polarized superfluid against phase separation in imbalanced Fermi gases across a narrow Feshbach resonance.
Using the Gaussian pair fluctuation theory, we investigate quantum fluctuations of a strongly interacting two-dimensional chiral ppp-wave Fermi superfluid at the transition from a Bose-Einstein condensate (BEC) to a topologically nontrivial Bardeen-Cooper-Schrieffer superfluid. Near the topological phase transition at zero chemical potential, $\ensuremath{\mu}=0$, we observe that quantum fluctuations strongly renormalize the zero-temperature equations of state, sound velocity, pair-breaking velocity, and Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the Fermi superfluid, all of which can be nonanalytic functions of the interaction strength. The indication of nonanalyticity is particularly evident in the BKT critical temperature, which also exhibits a pronounced peak near the topological phase transition. Across the transition and towards the BEC limit we find that the system quickly becomes a trivial interacting Bose liquid, whose properties are less dependent on the interparticle interaction. The qualitative behavior of composite bosons in the BEC limit remains to be understood.