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arXiv:2012.00986 · Physical Review Research

Ultracold Bose mixtures with spin-dependent fermion-mediated interactions

Renyuan Liao

Published Nov 12, 2020• 9 citations
arXivHTMLPDF

Abstract

We develop a functional integral formulation for binary Bose-Einstein condensates coupled to polarized fermions.We find that spin-dependent fermion-mediated interactions have dramatic effects on the properties of the binary condensates.The quasiparticle spectrum features two branches.The upper branch, which is of density nature, gets modified by the induced interactions, while the lower branch, which is of spin nature, is left intact.The ground-state phase diagram consists of stable region of miscible phases and unstable region toward phase separation.In the stable region, it is further classified by the damping of excitations of the upper branch.We show that it is possible to find region of well-defined, long-lived quasiparticle excitations by tuning relevant parameters, such as boson-fermion mass ratio, boson-fermion number density ratio, and interspecies interactions between bosons as well.We explore the effects of quantum fluctuation due to the effective potential on the binary condensates.It turns out that both the density structure factor and spin density structure factor fulfill the Feynman relation, except that the latter is immune to the fermion-mediated interactions.

DOI
10.1103/physrevresearch.2.043218

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We develop a functional integral formulation for binary Bose-Einstein condensates coupled to polarized fermions.We find that spin-dependent fermion-mediated interactions have dramatic effects on the properties of the binary condensates.The quasiparticle spectrum features two branches.The upper branch, which is of density nature, gets modified by the induced interactions, while the lower branch, which is of spin nature, is left intact.The ground-state phase diagram consists of stable region of miscible phases and unstable region toward phase separation.In the stable region, it is further classified by the damping of excitations of the upper branch.We show that it is possible to find region of well-defined, long-lived quasiparticle excitations by tuning relevant parameters, such as boson-fermion mass ratio, boson-fermion number density ratio, and interspecies interactions between bosons as well.We explore the effects of quantum fluctuation due to the effective potential on the binary condensates.It turns out that both the density structure factor and spin density structure factor fulfill the Feynman relation, except that the latter is immune to the fermion-mediated interactions.
We investigate the homogeneous superfluid mixtures of a Bardeen-Cooper-Schrieffer (BCS) superfluid originating from pairing two-species fermionic atoms and superfluidity stemming from condensation of bosonic atoms. By integrating out the freedoms associated with the BCS superfluid, we derive the fermion-mediated interactions between bosons, which is attractive and can be tuned from long range in the BCS region to short range in the region of Bose-Einstein condensation of molecular dimers. By analyzing the Bogoliubov spectrum and the damping rate of bosonic superfluid, we map out the phase diagram spanned by the boson-fermion mass ratio and the boson-fermion coupling strength, which consists of a phase separation region and two phase-mixing regions with and without Landau damping. The three different phases can coexist at a tricritical point, which moves toward a low boson-fermion mass ratio and a high boson-fermion scattering length as the fermion-fermion interaction strength is tuned up on the BCS side.
We consider a homogeneous mixture of bosons and polarized fermions. We find that long-range and attractive fermion-mediated interactions between bosons have dramatic effects on the properties of the bosons. We construct the phase diagram spanned by boson-fermion mass ratio and boson-fermion scattering parameter. It consists of a stable region of mixing and unstable region toward phase separation. In the stable mixing phase, the collective long-wavelength excitations can either be well behaved with infinite lifetime or be finite in lifetime suffered from the Landau damping. We examine the effects of the induced interaction on the properties of weakly interacting bosons. It turns out that the induced interaction not only enhances the repulsion between the bosons against collapse but also enhances the stability of the superfluid state by suppressing quantum depletion.
We investigate the collective excitations of a low-temperature dilute gas mixture that consists of a Bose-Einstein condensate (BEC) and a Fermi gas that is a normal (i.e., nonsuperfluid) Fermi liquid. We find that the BEC-mediated fermion-fermion interactions, as a consequence of retardation, can become repulsive and support a zero-sound mode that is essentially undamped. In addition, we find a damped zero-sound mode that can be described as a BEC sound mode modified by fermion-mediated boson-boson interactions, and we derive its decay rate caused by Landau damping. We study the mode structure of these excitations and find avoided-crossing behavior as well as a termination point. The collective-mode dynamics also reveals that phase separation sets in when the fermion-mediated boson-boson interaction destroys the stability of the homogeneous BEC. We estimate the time and length scales of the onset of the phase separation, and we discuss the feasibility of experimentally probing these consequences of mediated interactions.
Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a ^{87}Rb BEC to measure the interaction mediated by a ^{40}K DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of η=1.45±0.05^{stat}±0.13^{syst} in the presence of the DFG, providing clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a_{bf_{2}}-a_{bf_{1}}=-5.36±0.44^{stat}±1.43^{syst}a_{0} between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Côté, A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance. Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.
We describe recent theoretical and experimental developments on mediated interactions in mixtures of bosonic and fermionic atoms. We discuss how particle-hole excitations of a Fermi sea can induce long-range interactions between heavy impurities or atoms in a Bose-Einstein condensate. Conversely, phonon excitations of a Bose-Einstein condensate induce interactions between fermionic atoms. These mediated interactions exhibit different short-range and long-range scaling regimes with distance and, if strong enough, can induce fermion superfluidity. We discuss the prospects for observing new phenomena that could arise from mediated interactions. Experimentally, we outline recent studies of the 133Cs-6Li Bose-Fermi mixture, a platform well-suited for investigating fermion-mediated interactions. A Cs Bose-Einstein condensate immersed in a degenerate Li Fermi gas is prepared with tunable interspecies interactions. In the weak-coupling regime, precision measurements of condensate properties reveal fermion-mediated attractions between bosons, matching theoretical predictions. In the strong-coupling regime, we observe suppression and revival of sound modes and novel many-body resonances. Altogether, we aim to highlight both instances where experiment and theory agree well, and promising prospects to engineer long-range interactions in atomic quantum gases.
In the strong-coupling Bose-Einstein condensation (BEC) region where a Feshbach resonance gives rise to tightly bound dimer molecules, we show that a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions. Using a many-body functional integral formalism, the Gaussian fluctuations give rise to an induced dimer-dimer interaction mediated by the unpaired fermions, with the dimer-fermion vertex being given by the (mean-field) Born approximation. Treating the pairing fluctuations to quartic order, we show how the action for a spin-polarized Fermi superfluid reduces to one for a Bose-Fermi mixture. This Bose-Fermi action includes an expression for the effective dimer-unpaired fermion interaction in a spin-polarized Fermi superfluid beyond the Born approximation, in the BEC limit. In the low-density limit, we show how this dimer-fermion interaction gives the sss-wave scattering length aBF=1.18aF{a}_{\mathit{BF}}=1.18{a}_{F}aBF​=1.18aF​ (aF{a}_{F}aF​ is the sss-wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.