[Paper Review] Sound propagation in a Fermi gas near a Feshbach resonance

James Joseph, Bason Clancy+4 more|arXiv (Cornell University)|Dec 21, 2006

Cold Atom Physics and Bose-Einstein Condensates1 references3 citations

TL;DR

This study measures sound velocity in a strongly interacting ultracold Fermi gas near a Feshbach resonance, using laser-induced density perturbations in an optically trapped 6Li gas. The results confirm the universal equation of state across the BEC-BCS crossover, with sound velocity matching quantum Monte Carlo predictions and revealing a universal constant β = -0.570(0.015) at unitarity.

ABSTRACT

Sound waves are observed and studied in an optically trapped degenerate Fermi gas of spin-up and spin-down atoms with magnetically tunable interactions. Measurements are made throughout the crossover region, from a weakly-interacting Fermi gas through the resonant Fermi superfluid regime to a Bose condensate of dimer molecules. The measured sound velocities test the equation of state and confirm the universal hypothesis.

Motivation & Objective

• To probe the equation of state of a strongly interacting Fermi gas across the BEC-BCS crossover using sound velocity measurements.
• To test the universal hypothesis in strongly correlated quantum systems by measuring sound speed at unitarity.
• To determine the location of the Feshbach resonance and validate theoretical models of the equation of state.
• To investigate hydrodynamic behavior and potential coupling between first and second sound in a degenerate Fermi gas.
• To measure the universal constant β connecting interaction energy and Fermi energy in the unitary limit.

Proposed method

• Excited sound waves via a blue-detuned 532 nm laser knife, creating a localized density depression in a cigar-shaped optical trap.
• Imaged the propagating density features after variable in-trap propagation times, using time-of-flight absorption imaging to avoid saturation.
• Measured sound velocity by tracking the axial propagation of density valleys and peaks, using both right- and left-traveling features to cancel cloud motion.
• Calibrated trap frequencies and Fermi energy for each measurement to determine the local Fermi velocity vF and dimensionless interaction parameter 1/kFa.
• Used the hydrodynamic relation c₀/vF = (μ_loc / ε_F)^(1/4) / √5 to extract the equation of state from measured sound velocity.
• Compared results with theoretical models including mean-field theory (Leggett), quantum Monte Carlo, and molecular BEC theories with a_mol = 0.6a.

Experimental results

Research questions

• RQ1 How does sound velocity vary across the BEC-BCS crossover in a unitary Fermi gas near a Feshbach resonance?
• RQ2 Does the sound velocity at unitarity remain independent of density, confirming the universal hypothesis?
• RQ3 What is the value of the universal constant β that relates interaction energy to Fermi energy in the unitary regime?
• RQ4 Why is the measured sound velocity systematically lower than mean-field predictions in the molecular BEC regime?
• RQ5 Could coupling between first and second sound or soliton-like excitations explain the observed deviation from theory?

Key findings

• At unitarity (B = 834(2) G), the normalized sound velocity c₀/vF remains constant across a 12 μK to 410 nK range of trap depths, confirming the universal hypothesis.
• The measured universal constant β = -0.570(0.015) is consistent with the theoretical prediction β = -0.57, validating the universal equation of state.
• In the molecular BEC regime (1/kFa > 1), the measured sound velocity is systematically lower than mean-field theory (Leggett) predictions, but agrees well with quantum Monte Carlo calculations.
• The sound velocity in the BEC regime is well described by a molecular BEC model with a_mol = 0.6a, yielding a prediction close to the measured values.
• At 1/kFa < -1.3 (weakly interacting Fermi gas), sound propagation is not observed; instead, the density depression fills without wave propagation, indicating non-hydrodynamic behavior.
• The Feshbach resonance location is determined to be closer to 834 G than to 822 G, based on the density independence of c₀/vF at resonance.