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arXiv:cond-mat/0609390 · Physical Review Letters

Precision Measurements of Collective Oscillations in the BEC-BCS Crossover

A. Altmeyer, S. Riedl, Christoph Kohstall, Matthew J. Wright, R. Geursen, M. Bartenstein, Cheng Chin, Johannes Hecker Denschlag, Rudolf Grimm

Published Jan 22, 2007• 240 citations
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Abstract

We report on precision measurements of the frequency of the radial compression mode in a strongly interacting, optically trapped Fermi gas of (6)Li atoms. Our results allow for a test of theoretical predictions for the equation of state in the BEC-BCS crossover. We confirm recent quantum Monte Carlo results and rule out simple mean-field BCS theory. Our results show the long-sought beyond-mean-field effects in the strongly interacting Bose-Einstein condensation (BEC) regime.

DOI
10.1103/physrevlett.98.040401

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We report on precision measurements of the frequency of the radial compression mode in a strongly interacting, optically trapped Fermi gas of (6)Li atoms. Our results allow for a test of theoretical predictions for the equation of state in the BEC-BCS crossover. We confirm recent quantum Monte Carlo results and rule out simple mean-field BCS theory. Our results show the long-sought beyond-mean-field effects in the strongly interacting Bose-Einstein condensation (BEC) regime.
We study collective excitation modes of a fermionic gas of (6)Li atoms in the BEC-BCS crossover regime. While measurements of the axial compression mode in the cigar-shaped trap close to a Feshbach resonance confirm theoretical expectations, the radial compression mode shows surprising features. In the strongly interacting molecular BEC regime, we observe a negative frequency shift with increasing coupling strength. In the regime of a strongly interacting Fermi gas, an abrupt change in the collective excitation frequency occurs, which may be a signature for a transition from a superfluid to a collisionless phase.
We report on measurements of an elementary surface mode in an ultracold, strongly interacting Fermi gas of 6Li^{6}\mathrm{Li}6Li atoms. The radial quadrupole mode allows us to probe hydrodynamic behavior in the crossover from Bose-Einstein condensation (BEC) to the Bardeen-Cooper-Schrieffer (BCS) regime without being influenced by changes in the equation of state. We examine the frequency and damping of this mode, along with its expansion dynamics. In the unitarity limit and on the BEC side of the resonance, the observed frequencies agree with standard hydrodynamic theory. However, on the BCS side of the crossover, a striking downshift of the oscillation frequency is observed in the hydrodynamic regime as a precursor to an abrupt transition to collisionless behavior; this indicates coupling of the oscillation to fermionic pairs.
A perturbation method is developed for calculating the oscillating frequencies of collective modes of trapped superfluid Fermi gases from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensation (BEC). Based on the complete and orthogonal eigenfunction set obtained recently and a series expansion of the equation of state beyond the mean-field approximation, the corrections of eigenfrequencies and eigenfunctions of all collective modes are given systematically, which are valid for various superfluid regimes in the BCS-BEC crossover beyond the mean-field approximation. Expressions of frequency correction of the collective modes for both spherical and axial symmetric traps excited near the BCS, BEC, and unitarity limits are provided explicitly, and their dependence on interatomic interaction strength and anisotropic trapping parameter is also discussed in detail.
We study two-body correlations in a spin-balanced ultracold harmonically trapped Fermi gas of ^{6}Li atoms in the crossover from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein-Condensate (BEC) regime. For this, we precisely measure Tan's contact using a novel method based on photoexcitation of atomic pairs, which was recently proposed by Wang et al. [Photoexcitation measurement of Tan's contact for a strongly interacting Fermi gas, Phys. Rev. A 104, 063309 (2021).PLRAAN2469-992610.1103/PhysRevA.104.063309]. We map out the contact in the entire phase diagram of the BCS-BEC crossover for various temperatures and interaction strengths, probing regions in phase space that have not been investigated yet. Our measurements reach an uncertainty of ≈2% at the lowest temperatures and thus represent a precise quantitative benchmark. By comparison to our data, we localize the regions in phase space where theoretical predictions and interpolations give valid results. In regions where the contact is already well known we find excellent agreement with our measurements. Thus, our results demonstrate that photoinduced loss is a precise probe to measure quantum correlations in a strongly interacting Fermi gas.
We show that the study of the collective oscillations in a harmonic trap provides a very sensitive test of the equation of state of a Fermi gas near a Feshbach resonance. Using a scaling approach, whose high accuracy is proven by comparison with exact hydrodynamic solutions, the frequencies of the lowest compressional modes are calculated at T=0 in terms of a dimensionless parameter characterizing the equation of state. The predictions for the collective frequencies, obtained from the equations of state of mean-field BCS theory and of recent Monte Carlo calculations, are discussed in detail.
Theoretical predictions for the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of 6Li. The calculations rest on a single theoretical approach that includes pairing fluctuations beyond mean-field. Excellent agreement with experimental results is obtained. Theoretical predictions for the zero-temperature chemical potential and gap at the unitarity limit are also found to compare extremely well with Quantum Monte Carlo simulations and with recent experimental results.