Mediated interactions in mixtures of ultracold atoms

TL;DR

The paper reviews mediated interactions in ultracold Bose-Fermi mixtures, detailing how fermionic particle-hole excitations generate impurity-impurity forces and how BEC phonons mediate interactions among fermions. It couples theoretical mechanisms—Efimov physics, RKKY oscillations, Yukawa screening, and long-range van der Waals contributions—to experimental observations in the $^{133}$Cs-$^{6}$Li mixture, spanning both weak- and strong-coupling regimes. Key findings include observable fermion-mediated attractions among bosons, suppression and revival of sound modes, and a novel fermion-mediated boson-boson pairing resonance, illustrating how mediated interactions can drive nontrivial many-body states. The work points toward engineering long-range interactions in optical lattices and exploring Bose-Fermi droplets and mediated pairing in BCS–BEC crossover contexts, broadening the landscape of quantum simulation with ultracold atoms.

Abstract

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.

Figures (9)

• Figure 1: Mediated interaction $V(R)$ between bosons in a Fermi gas for different Bose-Fermi coupling $a_\text{BF}$; the interaction is normalized by the Fermi energy $E_\text{F}$. The contribution from scattering states (RKKY; dotted) combines with the bound-state contribution (dashed) to the full interaction (solid lines). For repulsive $a_\text{BF}>0$ the bound-state contribution reaches positive values because it is measured from the single-particle energy, Eq. \ref{['eq:pot']}.
• Figure 2: Induced scattering length $a_\text{ind}(a_\text{BF})$ between two heavy impurities in a Fermi sea. The full solution of the Schrödinger equation Eq. \ref{['eq:varphase']} [blue solid] supports resonant scattering between the impurities [arrows]. It is compared to the Born approximation Eq. \ref{['eq:born']} [red dashed] and perturbation theory Eq. \ref{['eq:aind']} [gray dotted], which show no induced resonance.
• Figure 3: Induced interaction between two heavy impurities in a BEC (red dots): crossover from Efimov scaling Eq. \ref{['eq:becefimov']} at short impurity distances $R$ from scattering off a single boson (blue dot) to Yukawa scaling Eq. \ref{['eq:yukawa']} at intermediate distances from exchanging a single phonon (wavy line) and to van der Waals scaling Eq. \ref{['eq:vdw']} at large distances from exchange of two phonons.
• Figure 4: Calculated scattering lengths as a function of magnetic field in the region of interest. The red line shows the narrow Feshbach resonance in the Li$_\text{a}$–Cs spin channel near 893 G, and the blue line indicates a broad resonance in the Li$_\text{b}$–Cs channel near 889 G. The Cs–Cs scattering length is plotted in black. Source: Li-Cs scattering lengths extracted from Ref. johansen2017 and Cs-Cs scattering lengths extracted from Ref. berninger2013.
• Figure 5: Three-body recombination rate $K_3$ plotted as a function of inverse boson-fermion scattering length $1/a$, demonstrating Efimov resonances near two Li-Cs Feshbach resonances. (a) shows the behavior near the broad Li$_\text{b}$-Cs resonance at 889 G, while (b) focuses on the narrow Li$_\text{a}$-Cs resonance near 893 G. $K_3$ is normalized to the off-resonant value $K_3^{(0)}$. Vertical arrows indicate observed Efimov resonance positions. The dashed arrow in (b) points to a suppression feature in $K_3$ at positive scattering length. Magenta dotted lines show predictions from universal Efimov theory; black curves are guides to the eye consisting of the sum of Gaussians. Insets show data far from the resonance. Error bars represent 1-$\sigma$ statistical uncertainty. Source: adapted from Ref. johansen2017.