Induced interactions in a superfluid Bose-Fermi mixture

Abstract

We analyse a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC cross-over. 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, these prominent effects can be used to systematically probe the strongly interacting Fermi gas.The interplay between induced interactions and superfluidity plays an important role in low temperature physics. In metals, the phonon mediated interaction between electrons leads to the formation of Cooper pairs [1], and induced electron-hole excitations significantly suppress the critical temperature of a BCS superconductor [2,3]. A prominent theory for high temperature superconductivity is that it is caused by spin fluctuations leading to an attractive interaction [4], and induced interactions are important for understanding the properties of liquid helium mixtures [5]. The systems where induced interactions are significant often consist of fermionic and bosonic degrees of freedom. In cold atom gases, BoseFermi mixtures have been realised experimentally for sympathetic cooling [6][7][8], molecule formation [9][10][11][12], and for studying few-body physics [13]. The theoretical studies have focused on mixtures where the Fermi gas is in the normal state [14][15][16][17][18][19][20][21][22][23]. Recently, an experimental breakthrough was reported with the realisation of a mixture of superfluid 7 Li and 6 Li gases [24]. This opens up the exciting possibility to experimentally study for the first time the role of induced interactions in a Bose-Fermi mixture, where both components are superfluid.Here, we study a BEC mixed with a two-component superfluid Fermi gas in the whole BCS-BEC crossover at zero temperature. Using a quasiparticle random-phase approximation (QRPA) to describe the excitations in the Fermi gas, combined with Beliaev theory for the bosons, we show how the fermions give rise to an induced frequency/momentum dependent Bose-Bose interaction, which diverges at the sound mode of the Fermi gas. This results in two qualitatively new effects. First, the dispersion relation of the bosons in the BEC is significantly changed at frequencies/momenta close to the sound mode of the Fermi gas. Second, bosonic excitations are damped due to dissipation, as they can excite quasiparticles in the superfluid Fermi gas [25]. These effects can be used to systematically probe the single particle and collective properties of ...

Two-Element Mixture of Bose and Fermi Superfluids

“…Finally, we can write the governing equation (10) in terms of the tilt angle using Eqn. (14), and recover Eqn. (2) of the main text.…”

“…While the goal of simultaneous superfluidity in mixtures of 4 He- 3 He still remains elusive due to strong inter-isotope interactions [5,6], Bose-Fermi superfluidity in an atomic gas isotopic mixture of 7 Li- 6 Li has recently been realized [7]. The original interest [8,9] in such dual superfluid systems is now strongly intensified [10][11][12][13][14][15][16].…”

“…While the goal of simultaneous superfluidity in mixtures of 4 He-3 He still remains elusive due to strong inter-isotope interactions [5,6], Bose-Fermi superfluidity in an atomic gas isotopic mixture of 7 Li-6 Li has recently been realized [7]. The original interest [8,9] in such dual superfluid systems is now strongly intensified [10][11][12][13][14][15][16].The extension of Bose-Fermi superfluidity to mixtures of different elements is experimentally challenging, but holds the potential to open a larger arena of scientific studies. A large mass ratio between the components is predicted to alter the interaction energy between the superfluids [12] as well as the character of excitations across the Bose-Einstein condensate to Bardeen-CooperSchreiffer (BEC-BCS) crossover for the fermion pairs [15].…”

Critical Velocity and Dissipation of an Ultracold Bose-Fermi Counterflow

“…This critical velocity has been measured both in superfluid helium [10] and ultracold atoms [1,[4][5][6]11]. However the recent production of a Bose-Fermi double superfluid [12] raised new questions on Bose-Fermi mixtures [13][14][15][16] and interrogations on the validity of Landau's argument in the case of superfluid counterflow [17][18][19][20][21][22].In this letter, we study the dynamics of a Bose-Fermi superfluid counterflow in the BEC-BCS crossover and at finite temperature. We show how friction arises when the relative velocity of the Bose and Fermi clouds increases and we confirm that damping occurs only above a certain critical relative velocity v c .…”

Tan's contact and the phase distribution of repulsive Fermi gases: Insights from quantum chromodynamics noise analyses

“…Although we have considered the case of two-body contact interactions exclusively, we expect our results to generalize to more general interactions and to mixed BoseFermi ensembles, a subject of growing relevance [51][52][53][54][55]. We leave such investigation for future study.…”