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.Two-dimensional (2D) materials exhibit many novel physical properties [1-4], but strong correlations and imperfections mean these are often difficult to understand theoretically. Quantum gases of neutral atoms may help address such fundamental challenges [5,6], as well as new phenomena, not readily accessible in other systems. One scenario, generally encountered in quantum field theories, is anomalous symmetry breaking. Specifically, a quantum anomaly occurs when a symmetry, present in a classical theory, is broken in the corresponding (renormalized) quantum theory. A paradigmatic example relevant to atomic collisions in ultracold alkali gases is the 2D δ-potential [7,8], where an additional length scale associated with the interactions is required to remove divergences in the elementary theory.Anomalous symmetry breaking has been considered in the context of 2D harmonically confined Bose [9] and Fermi gases [10][11][12] where interactions can be enhanced near a Feshbach resonance. In both cases, the anomaly leads to an increase in the frequency of the radial monopole mode, or breathing oscillation, above the value set by the scaling symmetry of the classical theory [13]. Previous experiments have studied the radial breathing mode in 2D Bose [14,15] and Fermi gases [16], although the anomalous upshift has not yet been observed. More broadly, the breathing mode is a sensitive probe of the adiabatic compressibility and hence the thermodynamic equation of state [17,18] of the gas being studied.In this Letter, we present measurements of the radial breathing mode frequency ω B for highly oblate Fermi gases as a function of the interaction strength and dimensionality. The dimensionality of a harmonically trapped gas can be tuned by varying the chemical potential µ relative to the confinement energies ω i , (i = x, y, z) in each dimension. When ω z µ, k B T ω x,y , where k B is Boltzmann's constant and T is the temperature, motion in the transverse (z) dimension can be frozen...

Few-Body Perspective of a Quantum Anomaly in Two-Dimensional Fermi Gases

“…Many results in the many-body limit can be successfully deduced from few-body studies [20][21][22][23]. In this work, we find that our few-body results reveal two important features observed in the experiments in the presence of a nonzero effective range [10,11]: the maximum quantum anomaly reduces gradually with increasing effective range while the peak position shifts to the weakly-interacting regime. Finally, it is worth emphasizing that the fewfermion system under consideration can nowadays be routinely prepared by using microtraps [24] or optical tweezer [25,26].…”

Resonantly interacting p -wave Fermi superfluid in two dimensions: Tan's contact and the breathing mode

“…At this point, it is interesting to compare the frequency shift exhibited by a resonantly interacting p-wave Fermi superfluid and by a strongly interacting s-wave Fermi superfluid, both in two dimensions. In the latter case, the theoretically predicted maximum quantum anomaly of 10% is yet to be experimentally confirmed [62,64,65]. The main obstacle comes from the confinement-induced effective range R s , which is significant under the current experimental condition.…”

“…Therefore, the breathing mode frequency deviates from the classically invariant value of ω c , i.e., δω B = ω B − ω c = 0. This frequency shift is now referred to as quantum anomaly [59][60][61][62][63][64][65][66]. In our case of a resonantly interacting p-wave interaction, where the 2D scattering area disappears, we anticipate that the system may also have scale-invariant zero-energy wave-functions if there is no length scale set by interactions, and in the presence of isotropic harmonic trap it has the scale-invariant breathing mode frequency ω c .…”

Role of the confinement-induced effective range in the thermodynamics of a strongly correlated Fermi gas in two dimensions

“…However, in the strongly correlated regime it turns out that, the theoretical EoS determined by accurate auxiliary-field quantum Monte Carlo (AFQMC) simulations [31] slightly over-estimates the thermodynamics compared to the measured EoS [2,17,21], suggesting the inefficiency of the single-channel model. The necessity of using a more appropriate theoretical model was highlighted by the most recent measurements on the breathing mode [34][35][36], which present an interesting example of a quantum anomaly (i.e., violation of the classical scale invariance [6]). It was found that the measured breathing mode is notably lower than the prediction from the single-channel model [8,9].…”