Few-body perspective of a quantum anomaly in two-dimensional Fermi gases

Abstract

Quantum anomaly manifests itself in the deviation of breathing mode frequency from the scale invariant value of $2\omega$ in two-dimensional harmonically trapped Fermi gases, where $\omega$ is the trapping frequency. Its recent experimental observation with cold-atoms reveals an unexpected role played by the effective range of interactions, which requires quantitative theoretical understanding. Here we provide accurate, benchmark results on quantum anomaly from a few-body perspective. We consider the breathing mode of a few trapped interacting fermions in two dimensions up to six particles and present the mode frequency as a function of scattering length for a wide range of effective range. We show that the maximum quantum anomaly gradually reduces as effective range increases while the maximum position shifts towards the weak-coupling limit. We extrapolate our few-body results to the many-body limit and find a good agreement with the experimental measurements. Our results may also be directly applicable to a few-fermion system prepared in microtraps and optical tweezers.

arXiv comment6+5 pages, 4+4 figures

References in corpus (34)

• Theory of Bose-Einstein condensation in trapped gases
• Deterministic Preparation of a Tunable Few-Fermion System
• Interatomic collisions in a tightly confined Bose gas
• Collective oscillations of a 1D trapped Bose gas
• Breathing Modes and Hidden Symmetry of Trapped Atoms in 2D
• Cooling a single atom in an optical tweezer to its quantum ground state
• The unitary gas in an isotropic harmonic trap: symmetry properties and applications
• Building one molecule from a reservoir of two atoms
• Few-body physics with ultracold atomic and molecular systems in traps
• Virial expansion for a strongly correlated Fermi gas
• Scale invariance and viscosity of a two-dimensional Fermi gas
• Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases
• An Example of Quantum Anomaly in the Physics of Ultra-Cold Gases
• Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas
• Exact Numerical Results on the Ground State of Strongly Interacting Fermi Gases in Two Dimensions
• Pressure, compressibility, and contact of the two-dimensional attractive Fermi gas
• Anomalous breaking of scale invariance in a two-dimensional Fermi gas
• Exact few-body results for strongly correlated quantum gases in two dimensions
• Apparent low-energy scale invariance in two-dimensional Fermi gases
• Quantum anomaly and 2D-3D crossover in strongly interacting Fermi gases
• First and second sound in a strongly interacting Fermi gas
• Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
• Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas
• Reduced quantum anomaly in a quasi-2D Fermi superfluid: The significance of the confinement-induced effective range of interactions
• Illustration of universal relations for trapped four-fermion system with arbitrary s-wave scattering length
• Few-body precursor of the Higgs mode in a superfluid Fermi gas
• Fermi-to-Bose crossover in a trapped quasi-2D gas of fermionic atoms
• Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction
• Universality of the unitary Fermi gas: A few-body perspective
• Collective modes of a one-dimensional trapped atomic Bose gas at finite temperatures
• Trapped unitary two-component Fermi gases with up to ten particles
• Effective-range dependence of two-dimensional Fermi gases
• Collective modes of a two-dimensional Fermi gas at finite temperature
• Effective theory for ultracold strongly interacting fermionic atoms in two dimensions

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• Nonuniversal Equation of State of a Quasi-2D Bose Gas in Dimensional Crossover
• Universal Properties of Anisotropic Dipolar Bosons in Two Dimensions
• Hierarchical dimensional crossover of an optically-trapped quantum gas with disorder
• Scale and conformal invariance in rotating interacting few-fermion systems
• When does a Fermi puddle become a Fermi sea? Emergence of pairing in two-dimensional trapped mesoscopic Fermi gases