Quantum anomaly and 2D-3D crossover in strongly interacting Fermi gases

Abstract

We present an experimental investigation of collective oscillations in harmonically trapped Fermi gases through the crossover from two to three dimensions. Specifically, we measure the frequency of the radial monopole or breathing mode as a function of dimensionality in Fermi gases with tunable interactions. The frequency of this mode is set by the adiabatic compressibility and probes the thermodynamic equation of state. In 2D, a dynamical scaling symmetry for atoms interacting via a δ-potential predicts the breathing mode to occur at exactly twice the harmonic confinement frequency. However, a renormalized quantum treatment introduces a new length scale which breaks this classical scale invariance resulting in a so-called quantum anomaly. Our measurements deep in the 2D regime lie above the scale-invariant prediction for a range of interaction strengths indicating the breakdown of a δ-potential model for atomic interactions. As the dimensionality is tuned from 2D to 3D we see the breathing oscillation frequency evolve smoothly towards the 3D limit.

5 pages, 3 figures

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• Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one
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• Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry
• Pseudogap regime of a strongly interacting two-dimensional Fermi gas with and without confinement-induced effect range of interactions
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• Residual bulk viscosity of a disordered 2D electron gas
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• Scale Invariance in the Lowest Landau Level
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• The inverse-square interaction phase diagram: unitarity in the bosonic ground state