[Paper Review] Sound propagation in a Bose-Fermi mixture: from weak to strong interactions

Krutik Patel, Geyue Cai+2 more|PubMed|May 28, 2022

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This study investigates sound propagation in a quantum degenerate Bose-Fermi mixture using ultracold cesium and lithium atoms, tuning interspecies interactions via a Feshbach resonance. It reveals sound mode softening under moderate attraction, followed by unexpected re-emergence of stable sound waves at resonant, strong attractive interactions—challenging perturbative predictions and opening pathways to study novel quantum phases in strongly correlated Bose-Fermi systems.

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_{BF} 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.

Motivation & Objective

• To explore the behavior of phonons in a Bose-Einstein condensate (BEC) coupled to a degenerate Fermi gas across weak to strong interaction regimes.
• To investigate how fermion-mediated interactions affect sound velocity and stability in a quantum degenerate mixture.
• To test theoretical predictions of phonon softening and instability in the presence of attractive interspecies interactions.
• To identify conditions under which stable sound propagation persists despite strong correlations, enabling new quantum simulation opportunities.

Proposed method

• Optically excite density waves in a cigar-shaped cesium-133 BEC by creating a local density depletion with a laser beam.
• Measure the propagation velocity and damping rate of these density waves using in situ imaging of the BEC at varying hold times.
• Tune the interspecies scattering length $ a_{ ext{BF}} $ via a Feshbach resonance to control interaction strength from weak to strong attraction.
• Use a mean-field Hamiltonian including phonon-fermion coupling $ g_k $, with $ g_k ightarrow g_{ ext{BF}} $, to model the system’s effective dynamics.
• Apply a modified hydrodynamic model incorporating fermionic screening and density-dependent corrections to predict sound speed.
• Fit experimental data near the instability threshold to $ v = eta imes ext{sign}(a_{ ext{BF}} - a_c) imes ext{sign}(a_{ ext{BF}}) imes ext{sign}(a_{ ext{BF}} - a_c)^{1/2} $ to extract the critical scattering length $ a_c $.

Experimental results

Research questions

• RQ1 How does the sound velocity of phonons in a BEC change when coupled to a degenerate Fermi gas across varying interaction strengths?
• RQ2 Does phonon softening occur under moderate attractive interspecies interactions, as predicted by perturbation theory?
• RQ3 Can stable sound propagation persist in the strongly interacting regime, particularly at Feshbach resonance?
• RQ4 What is the critical scattering length $ a_c $ at which sound propagation becomes unstable due to strong attractive interactions?
• RQ5 How do mean-field and perturbative models compare with experimental observations in the strong interaction regime?

Key findings

• Sound velocity decreases under moderate attractive interactions, consistent with phonon softening and perturbative predictions.
• Despite strong attraction, stable sound wave propagation re-emerges at resonant interspecies scattering lengths, defying naive expectations of instability.
• The critical scattering length for instability is measured as $ a_c = -790(10) ext{ }a_0 $, with a systematic uncertainty of $ 30 ext{ }a_0 $.
• The sound wave velocity near the instability follows a $ v ightarrow ext{const} imes ext{sign}(a_{ ext{BF}} - a_c) imes ext{sign}(a_{ ext{BF}} - a_c)^{1/2} $ dependence, well-fit by $ v = eta imes ext{sign}(a_{ ext{BF}} - a_c)^{1/2} $.
• The fit yields a velocity scale $ eta = 32(1) ext{ } ext{m} ext{ } ext{m}/ ext{s} imes a_0^{-1/2} $, indicating a non-perturbative recovery of collective modes.
• Theoretical modeling using a mean-field Hamiltonian with effective coupling $ g_k $ and modified compressibility accurately captures the experimental data, including the non-monotonic behavior near $ a_c $.