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 2ω in two-dimensional harmonically trapped Fermi gases, where ω 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.

Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry

“…We would like to point out that our method can also be implemented to the few-body system, such as the study of the dynamics in the three-body problem [39][40][41]. By characterizing how strong the broken of the SU (1, 1) symmetry is, our method may also be valid to study the quantum anomaly [42][43][44][45][46][47]. Since our method does not depend on the configuration of the spatial confinement, it can also be implemented to the study of the parametric excitation in BEC [48].…”

Collective excitations of a spherical ultradilute quantum droplet

“…The accurate frequency measurement of collective modes is known as a powerful probe of the many-body state of ultracold quantum gases [15]. For example, for strongly interacting Fermi gases, the measurement of breathing modes provides the first indirect proof of fermionic superfluidity in three dimensions [16][17][18] and quantum anomaly in two dimensions [19][20][21][22]. For dipolar Bose gases, the most recent collective mode measurement in arrays of dipolar droplets clearly shows the symmetry breaking and the supersolid nature of the system [23,24].…”

Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement

“…First, the two-body systems are "minimum" interacting systems of trapped ultracold atoms, and one can obtain a primary understanding for the interaction physics of an ultracold gas from the analysis of such systems [14]. Second, the solutions to these problems can be directly used to calculate some important few-or manybody quantities [15][16][17][18][19][20][21][22][23][24][25][26], e.g., the 2nd virial coefficient which determines the high-temperature properties of the ultracold gases. Third, these systems have been already realized in many experiments [14,[27][28][29][30][31][32][33][34][35][36][37][38][39] where the trap of the two atoms can be created via an optical lattice site [27,28,31], an optical tweezer [32][33][34][35][36], or nano-structure [37][38][39].…”