Sound Propagation in a Bose-Fermi Mixture: From Weak to Strong Interactions

Krutik Patel, Geyue Cai, Henry Ando, and Cheng Chin

Phys. Rev. Lett. 131, 083003 – Published 23 August 2023

Abstract

Particlelike excitations, or quasiparticles, emerging from interacting fermionic and bosonic quantum fields underlie many intriguing quantum phenomena in high energy and condensed matter systems. Computation of the properties of these excitations is frequently intractable in the strong interaction regime. Quantum degenerate Bose-Fermi mixtures offer promising prospects to elucidate the physics of such quasiparticles. In this work, we investigate phonon propagation in an atomic Bose-Einstein condensate immersed in a degenerate Fermi gas with interspecies scattering length $a_{B F}$ tuned by a Feshbach resonance. We observe sound mode softening with moderate attractive interactions. For even greater attraction, surprisingly, stable sound propagation reemerges and persists across the resonance. The stability of phonons with resonant interactions opens up opportunities to investigate novel Bose-Fermi liquids and fermionic pairing in the strong interaction regime.

Received 28 November 2022
Revised 5 May 2023
Accepted 20 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.083003

Physics Subject Headings (PhySH)

Bose-Einstein condensates Bose-Fermi mixtures Fermi gases Quasiparticles & collective excitations

Atomic, Molecular & Optical

Authors & Affiliations

Krutik Patel , Geyue Cai, Henry Ando , and Cheng Chin

The James Franck Institute, Enrico Fermi Institute, and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA

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Issue

Vol. 131, Iss. 8 — 25 August 2023

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Images

Figure 1
Bosonic quasiparticles (phonons) coupled to a fermionic quantum field. (a) Diagrammatic representation of phonons (blue) coupled to excitations of a fermionic field (red). The lowest order diagram contains a single loop and is second order in the phonon-fermion coupling $g_{k}$ . Higher order corrections are indicated by the hatched area. (b) In our experiment, a cigar-shaped Bose-Einstein condensate (BEC) of cesium-133 is immersed in a much larger degenerate Fermi gas of lithium-6. (c) As a phonon with momentum $k$ (black dashed ellipse) propagates, the coupling results in the density modulation of both species and the modification of the sound speed $c$ .
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Figure 2
Excitation and in situ imaging of density waves. (a) A local density depletion $ε$ is created in the center of the cesium BEC by a projected laser beam (bottom panel, red shaded area). The optical potential is abruptly switched off at $t = 0$ and the density dip splits into density waves propagating in opposite directions (top panel, black arrows). Average column densities are shown for three values of the hold time $t = 0$ , 2, 4 ms along with sample normalized one-dimensional (1D) densities $n_{1}^{'}$ for $t = 0 ms$ and $t = 4 ms$ . Data are shown for the Cs-Li Bose-Fermi mixture with interspecies scattering length $a_{B F} = - 335 a_{0}$ . (b) Normalized 1D densities $n_{1}^{'}$ show density wave dynamics for mixtures prepared at various interspecies scattering lengths. Red dashed lines are guides to the eye.
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Figure 3
Sound speeds and damping rates at different interspecies scattering lengths and boson densities. (a) Orange data points indicate samples prepared on the attractive side of the Feshbach resonance $a_{B F} < 0$ . Red data points are prepared on the repulsive side with $a_{B F} > 0$ . Measurement for a bare BEC without femions is shown as the blue square. The crosses indicate samples with no stable sound propagation. The inset shows the ratio of density wave velocities for samples prepared with and without the fermions. The ratios are obtained from the separation of density waves after 8 ms hold time. Calculations from perturbation (black line) and mean-field (magenta line) theory are shown for comparison. The green shaded area represents the phase separation region. The gray area indicates the region where no stable sound propagation is observed. (b) Damping rates of the density waves are compared with the perturbative prediction (black line) evaluated for momentum $k = 2 π / (4 μ m)$ [20]. Cartoons illustrate the Cs (blue) and Li (red) density profiles in different regimes. (c) Density wave velocities for BECs prepared without the Fermi gas (black squares) and with the Fermi gas at $a_{B F} = - 350 a_{0}$ (red circles) and $a_{B F} = - 580 a_{0}$ (blue circles). Lines are fits of the data to a model with both two- and three-body effective interactions between bosons (see text). (d) Colored circles are the effective scattering lengths and hypervolumes extracted from panel (c). The magenta lines are the mean-field predictions and the black line is a cubic fit to the data. The vertical error bars on the data in (a)–(c) are standard errors calculated from fits to averaged experimental density profiles. The horizontal error bars on the data in panels (a), (b), and (d) represent the $1 − σ$ uncertainty of the scattering length [20]. The shaded regions around the theory calculations in panels (a) and (b) indicate the ranges of the predictions [20]. The error bars in panel (d) are standard errors calculated from fits to the data in panel (c).
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Figure 4
Sound propagation across the Feshbach resonance. (a) Normalized 1D densities illustrating the revival of sound propagation at strong interactions based on the same experimental procedure as in Figs. 2 and 3. The arrows on each data set indicate whether the system is ramped toward the resonance starting from the attractive side (orange arrow) or repulsive side (red arrow). Red dashed lines are guides to the eye. (b) Density wave velocity of the Li-Cs mixture across the Feshbach resonance. Data taken from samples prepared on the attractive (repulsive) side are orange (red) in color. The arrows indicate the direction of the scattering length ramp. The blue and green regions indicate the resonant and phase separation regimes, respectively. (c) Damping from the same data set. The black and magenta lines are the same perturbation and mean field predictions as shown in Fig. 3. The vertical error bars in panels (b) and (c) are standard errors from fits to averaged density profiles. The shaded regions around the theory curves in panels (b) and (c) indicate the ranges of the predictions [20]. The vertical dashed line shows the position of the Feshbach resonance. The vertical dotted line shows the position of the Efimov resonance reported in Ref. [28].
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