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arXiv:0705.4460 · Physical Review Letters

Strongly Resonant p -Wave Superfluids

Jesper Levinsen, Nigel R. Cooper, Victor Gurarie

Published Nov 19, 2007• 73 citations
arXivHTMLPDF

Abstract

We study theoretically a dilute gas of identical fermions interacting via a p-wave resonance. We show that, depending on the microscopic physics, there are two distinct regimes of p-wave resonant superfluids, which we term "weak" and "strong." Although expected naively to form a paired superfluid, a strongly resonant p-wave superfluid is in fact unstable toward the formation of a gas of fermionic trimers. We examine this instability and estimate the lifetime of the p-wave molecules due to the collisional relaxation into trimers. We discuss consequences for the experimental achievement of p-wave superfluids in both weakly and strongly resonant regimes.

DOI
10.1103/physrevlett.99.210402

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We study theoretically a dilute gas of identical fermions interacting via a p-wave resonance. We show that, depending on the microscopic physics, there are two distinct regimes of p-wave resonant superfluids, which we term "weak" and "strong." Although expected naively to form a paired superfluid, a strongly resonant p-wave superfluid is in fact unstable toward the formation of a gas of fermionic trimers. We examine this instability and estimate the lifetime of the p-wave molecules due to the collisional relaxation into trimers. We discuss consequences for the experimental achievement of p-wave superfluids in both weakly and strongly resonant regimes.
This thesis presents theoretical work in s- and p-wave resonantly paired Fermi gases at zero temperature. In the BEC regime of the wide-resonance s-wave BCS-BEC crossover, the chemical potential, speed of sound, condensate depletion, and ground state energy are computed. The quantities are calculated in a low density approximation. The bosonic scattering length is computed diagrammatically to be approximately 0.60a with a the fermionic scattering length, confirming a well-known result. The perturbative approach breaks down in the intermediate BCS-BEC crossover regime which is not investigated. Quantum corrections are computed in the low density expansion, and the mass-imbalanced two-species Fermi gas is investigated. For identical fermions, it is discussed how p-wave Feshbach resonances naturally fall into two classes of "weak" and "strong", depending on the short-distance physics. It is shown how bound fermionic trimers appear in the strongly-resonant superfluid. The appearance of the trimer under the strengthening of the resonance is investigated, and the lifetime of p-wave diatomic molecules due to collisional relaxation into trimers is estimated.
We investigate a two-component mixture of resonantly interacting Fermi gases as a function of the ratio $\ensuremath{\kappa}$ of the heavy to the light mass of the two species. The diffusion Monte Carlo method is used to calculate the ground-state energy and the pair correlation function starting from two different guiding wave functions, which describe, respectively, the superfluid and the normal state of the gas. Results show that the mixture is stable and superfluid for mass ratios smaller than the critical value ${\ensuremath{\kappa}}_{c}=13\ifmmode\pm\else\textpm\fi{}1$. For larger values of $\ensuremath{\kappa}$ simulations utilizing the wave function of the normal state are unstable towards cluster formation. The relevant cluster states driving the instability appear to be formed by one light particle and two or more heavy particles within distances on the order of the range of the interatomic potential. The small overlap between the wave function of the trimer bound state and the guiding wave function used to describe the superfluid state produces the unphysical stability of the superfluid gas above ${\ensuremath{\kappa}}_{c}$.
We theoretically study a possible pairing mechanism for a two-dimensional population imbalanced Fermi gas with short-range repulsive interactions, which can be realized on the upper branch of a Feshbach resonance. We use a well-controlled renormalization-group approach, which allows an unbiased study of the instabilities of imbalanced Fermi liquid without assumption of a broken symmetry and gives a numerical calculation of the transition temperature from microscopic parameters. Our results show a leading superfluid instability in the ppp-wave channel for the majority species. The corresponding mechanism is that there are effective attractive interactions for the majority species, induced by the particle-hole susceptibility of the minority species, where the mismatch of the Fermi surfaces of the two species plays an important role. We also propose an experimental protocol for detecting the ppp-wave superfluidity and discuss the corresponding experimental signatures.
We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium ((40)K), and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about 0.5T(F). Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly coupled fermions to the Bose-Einstein condensation of strongly bound composite bosons.
We investigate theoretically fermionic superfluidity induced by Feshbach resonance in the orbital p-wave channel and determine the general phase diagram. In contrast with superfluid (3)He, due to the dipole interaction, the pairing is extremely anisotropic. When this dipole interaction is relatively strong, the pairing has symmetry k(z). When it is relatively weak, it is of symmetry k(z) + ibetak(y) (up to a rotation about z;, here beta < 1). A phase transition between these two states can occur under a change in the magnetic field or the density of the gas.
One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological p p ix y+ superfluid for identical fermions in two dimensions (2D).The expectations of reaching the critical temperature T c through p-wave Feshbach resonance in spin-polarized fermionic gases have soon faded away because on approaching the resonance, the system becomes unstable due to inelastic-collision processes.Here, we consider an alternative scenario in which a single-component degenerate gas of fermions in 2D is paired via phonon-mediated interactions provided by a 3D BEC background.Within the weak-coupling regime, we calculate the critical temperature T c for the fermionic pair formation using the Bethe-Salpeter formalism, and show that it is significantly boosted by higher-order diagrammatic terms, such as phonon dressing and vertex corrections.We describe in detail an experimental scheme to implement our proposal, and show that the long-sought p-wave superfluid is at reach with state-of-the-art experiments.