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arXiv:cond-mat/0512134 · Physical Review Letters

Acoustic Attenuation Probe for Fermion Superfluidity in Ultracold-Atom Gases

S. Gaudio, Bogdan Mihaila, Krastan B. Blagoev, Kevin S. Bedell, Eddy Timmermans

Published Mar 15, 2007• 3 citations
arXivHTMLPDF

Abstract

Dilute gas Bose-Einstein condensates (BEC's), currently used to cool fermionic atoms in atom traps, can also probe the superfluidity of these fermions. The damping rate of BEC-acoustic excitations (phonon modes), measured in the middle of the trap as a function of the phonon momentum, yields an unambiguous signature of BCS-like superfluidity, provides a measurement of the superfluid gap parameter, and gives an estimate of the size of the Cooper pairs in the BEC-BCS crossover regime. We also predict kinks in the momentum dependence of the damping rate which can reveal detailed information about the fermion quasiparticle dispersion relation.

DOI
10.1103/physrevlett.98.110407

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Dilute gas Bose-Einstein condensates (BEC's), currently used to cool fermionic atoms in atom traps, can also probe the superfluidity of these fermions. The damping rate of BEC-acoustic excitations (phonon modes), measured in the middle of the trap as a function of the phonon momentum, yields an unambiguous signature of BCS-like superfluidity, provides a measurement of the superfluid gap parameter, and gives an estimate of the size of the Cooper pairs in the BEC-BCS crossover regime. We also predict kinks in the momentum dependence of the damping rate which can reveal detailed information about the fermion quasiparticle dispersion relation.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
The low-energy modes of a superfluid atomic Fermi gas at zero temperature are investigated. The Bose-Einstein-condensate (BEC) side of the superfluid phase is studied in detail. The atoms are assumed to be in only one internal state, so that for a sufficiently diluted gas the pairing of fermions can be considered effective in the l=1 channel only. In agreement with previous works on p-wave superfluidity in Fermi systems, it is found that the px+ipyp_x+ip_ypx​+ipy​ phase represents the lowest energy state in both the Bardeen-Cooper-Schrieffer (BCS) and BEC sides. Our calculations show that at low energy three branches of collective modes can emerge, with different species of dispersion relations: a phonon-like mode, a single-particle-like mode and a gapped mode. A comparison with the Bogoliubov excitations of the corresponding spinor Bose condensate is made. They reproduce the dispersion relations of the excitation modes of the p-wave superfluid Fermi gas to a high accuracy.
We calculate the sound velocity and the damping rate of the collective excitations of a 2D fermionic superfluid in a non-perturbative manner. Specifically, we focus on the Anderson–Bogoliubov excitations in the BEC-BCS crossover regime, as these modes have a sound-like dispersion at low momenta. The calculation is performed within the path-integral formalism and the Gaussian pair fluctuation approximation. From the action functional, we obtain the propagator of the collective excitations and determine their dispersion relation by locating the poles of this propagator. We find that there is only one kind of collective excitation, which is stable at T = 0 and has a sound velocity of v F / 2 for all binding energies, i.e., throughout the BEC-BCS crossover. As the temperature is raised, the sound velocity decreases and the damping rate shows a non-monotonous behavior: after an initial increase, close to the critical temperature T C the damping rate decreases again. In general, higher binding energies provide higher damping rates. Finally, we calculate the response functions and propose that they can be used as another way to determine the sound velocity.
We study the acoustic attenuation rate in the Fermi-Bose model describing mixtures of bosonic and fermionic atom gases. We demonstrate the dramatic change of the acoustic attenuation rate as the fermionic component is evolved through the BEC to BCS crossover, in the context of a mean-field model applied to a finite-range fermion-fermion interaction at zero temperature, such as discussed previously by Parish et al. [Phys. Rev. B 71, 064513 (2005)] and Mihaila et al. [Phys. Rev. Lett. 95, 090402 (2005)]. The shape of the acoustic attenuation rate as a function of the boson energy represents a signature for superfluidity in the fermionic component.
This thesis presents experiments probing physics in the crossover between Bose-Einstein condensation (BEC) and BCS superconductivity using an ultracold gas of atomic fermions. Scattering resonances in these ultracold gases (known as Feshbach resonances) provide the unique ability to tune the fermion-fermion interactions. The work presented here pioneered the use of fermionic Feshbach resonances as a highly controllable and tunable system ideal for studying the cusp of the BCS-BEC crossover problem. Here pairs of fermionic atoms have some properties of diatomic molecules and some properties of Cooper pairs. I present studies of a normal Fermi gas at a Feshbach resonance and the work required to cool the gas to temperatures where superfluidity in the crossover is predicted. These studies culminated in our observation of a phase transition at the cusp of the BCS-BEC crossover through condensation of fermionic atom pairs. I also discuss subsequent work that confirmed the crossover nature of the pairs in these condensates.
Fermionic many-body systems provide an unrivaled arena to investigate how interactions drive the emergence of collective quantum behavior, such as macroscopic coherence and superfluidity. Central to these phenomena is the formation of Cooper pairs, correlated states of two fermions that behave as composite bosons and condense below a critical temperature. However, unlike elementary bosons, these pairs retain their internal structure set by underlying fermionic correlations, essential for understanding superfluid properties throughout the so-called Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover -- a cornerstone of strongly correlated fermionic matter. Here, we harness a sonic analog of the optical Sagnac effect to disclose the composite nature of fermionic condensates across the BEC-BCS crossover. We realize an in-situ loop interferometer by coherently exciting two counter-propagating long-wavelength phonons of an annular fermionic superfluid with tuneable interparticle interactions. The frequency degeneracy between clock- and anticlock-wise sound modes is lifted upon controllably injecting a quantized supercurrent in the superfluid ring, resulting in a measurable Doppler shift that enables us to probe the elementary quantum of circulation and the angular momentum carried by each particle in the fermionic fluid. Our observations directly reveal that the superflow circulation is quantized in terms of h/2mh/2mh/2m, where mmm is the mass of the constituents, in striking contrast to bosonic condensates where h/mh/mh/m is the relevant circulation quantum. Further, by operating our interferometer at tunable temperature, we measure the thermal depletion of the superfluid in the unitary Fermi gas, demonstrating phonon interferometry as a powerful technique for probing fundamental properties of strongly-correlated quantum systems.