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arXiv:1502.00402 · Physical Review A

Induced interactions in a superfluid Bose-Fermi mixture

J. J. Kinnunen, Georg M. Bruun

Published Apr 30, 2015• 42 citations
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Abstract

We analyze a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC crossover. Using a quasiparticle random-phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC, respectively, we show that the single-particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, we can use these prominent effects to systematically probe the strongly interacting Fermi gas.

DOI
10.1103/physreva.91.041605

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We analyze a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC crossover. Using a quasiparticle random-phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC, respectively, we show that the single-particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, we can use these prominent effects to systematically probe the strongly interacting Fermi gas.
We propose that the evolution of superfluidity from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime can be realized using ultracold Fermi gas coupled to a single-mode cavity. By the functional integral formalism, we derive an effective atom-only action, which mimics the two-component Fermi gas with tunable two-body interaction. First, we address the features of the cavity-mediated interaction. We find that the matter-light coupling creates an effective sss-wave scattering whose sign and amplitude are controlled by parameters of the cavity. Second, we discuss the fermionic superfluidity on the mean-field level, including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, and dissociation temperature. It is shown that by varying the atom-cavity detuning, a BCS to BEC crossover occurs. In addition, the influences of the atomic collaborative effect and external pumping field on the pairing correlation are also studied.
In this Letter, we study the effect of quasiparticle interactions in a Bose-Fermi superfluid mixture. We consider the lifetime of a quasiparticle of the Bose superfluid due to its interaction with quasiparticles in the Fermi superfluid. We find that this damping rate, i.e., the inverse of the lifetime, has quite a different threshold behavior at the BCS and the BEC side of the Fermi superfluid. The damping rate is a constant near the threshold momentum in the BCS side, while it increases rapidly in the BEC side. This is because, in the BCS side, the decay process is restricted by the constraint that the fermion quasiparticle is located near the Fermi surface, while such a restriction does not exist in the BEC side where the damping process is dominated by bosonic quasiparticles of the Fermi superfluid. Our results are related to the collective mode experiment in the recently realized Bose-Fermi superfluid mixture.
We present a study for the collective dipole oscillations of a mixture of Bose and Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in the ENS experimental setup (Ferrier-Barbut et al 2014 Science 345 1035). The dynamics of the double superfluidity is described by coupled time-dependent order-parameter equations, which are Gross–Pitaevskii equations for the Bose superfluid, coupled to the order-parameter equation including the equation of state fitting from the experimental data for the Fermi superfluid in the BCS–BEC crossover. The numerical simulations show that due to the boson–fermion interaction, the frequencies of the dipole oscillations of the Bose and Fermi superfluids are both downshifted and the frequency shifts increase monotonically from the BCS side to BEC side, which are in agreement with the experiment. We further study the dependencies of the frequency shifts on the oscillation amplitudes and the nonlinear effects, in which the Bose and Fermi superfliuds show different features. The frequency shifts of the Bose superfluid increase linearly as the oscillation amplitudes increase, while the frequency shifts of the Fermi superfluid show a quadratical increase. It is found that the intrinsic dipole oscillations of the Bose (Fermi) superfluid can be triggered by only boosting the Fermi (Bose) superfluid.
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.
Abstract In this work, we present a theoretical study for the collective oscillation modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in harmonic trapping potentials with cylindrical symmetry of experimental interest. To this end, we start from the coupled superfluid hydrodynamic equations for the dynamics of Bose–Fermi superfluid mixtures and use the scaling theory that has been developed for a coupled system. The collective oscillation modes of Bose–Fermi superfluid mixtures are found to crucially depend on the overlap integrals of the spatial derivations of density profiles of the Bose and Fermi superfluids at equilibrium. We not only present the explicit expressions for the overlap density integrals, as well as the frequencies of the collective modes provided that the effective Bose–Fermi coupling is weak, but also test the valid regimes of the analytical approximations by numerical calculations in realistic experimental conditions. In the presence of a repulsive Bose–Fermi interaction, we find that the frequencies of the three collective modes of the Bose and Fermi superfluids are all upshifted, and the change speeds of the frequency shifts in the BCS–BEC crossover can characterize the different groundstate phases of the Bose–Fermi superfluid mixtures for different trap geometries.
Bose–Einstein condensation represents a quintessential manifestation of quantum mechanics at macroscopic scales, where a dilute gas of bosonic atoms undergoes a phase transition to form a coherent matter wave. This study presents a comprehensive theoretical investigation of collective excitations and critical phenomena in interacting Bose–Einstein condensates (BECs). Beginning with the Gross–Pitaevskii equation , we develop the Bogoliubov theory of excitations yielding the spectrum , where is the free-particle energy and characterizes contact interactions. The spectrum reveals phonon behavior at low momenta with sound velocity , transitioning to free-particle dispersion at momenta exceeding the inverse healing length . Collective modes in harmonically trapped condensates are analyzed in the Thomas–Fermi regime, yielding breathing mode frequency and quadrupole frequency . Damping mechanisms including Landau damping ( ) and Beliaev damping ( ) are characterized. The Lee–Huang–Yang correction extends the equation of state beyond mean field. Critical phenomena near are analyzed within the 3D XY universality class, with critical exponents , , and the interaction-induced shift with . All predictions show excellent agreement with experimental measurements on ultracold atomic gases.