Anomalous Breaking of Scale Invariance in a Two-Dimensional Fermi Gas

Abstract

The frequency of the breathing mode of a two-dimensional Fermi gas with zero-range interactions in a harmonic confinement is fixed by the scale invariance of the Hamiltonian. Scale invariance is broken in the quantized theory by introducing the two-dimensional scattering length as a regulator. This is an example of a quantum anomaly in the field of ultracold atoms and leads to a shift of the frequency of the collective breathing mode of the cloud. In this work, we study this anomalous frequency shift for a two component Fermi gas in the strongly interacting regime. We measure significant upwards shifts away from the scale invariant result that show a strong interaction dependence. This observation implies that scale invariance is broken anomalously in the strongly interacting two-dimensional Fermi gas.Symmetries are an indispensable ingredient to any attempt of formulating a fundamental theory of nature. Yet, it is not allways true that one can make accurate predictions about the behaviour of some complex system based on the symmetries of its Hamiltonian alone. The fundamental reason behind this is the concept of symmetry breaking [1]. Symmetry violations often have drastic effects on the state of the system, for example when some metal breaks rotational invariance and becomes ferromagnetic. There are three different mechanisms through which a given system may violate some of the symmetries of its Hamiltonian: explicit, spontaneous and anomalous symmetry breaking [2].Quantum anomalies are violations of an exact symmetry of a classical action in the corresponding quantized theory [3]. They may occur when a cut-off has to be introduced to regularize divergent terms. This regulator may explicitly break some symmetry of the theory. If this symmetry is not restored even after the cut-off is removed at the end of the renormalization procedure, the symmetry is broken anomalously.Quantum anomalies are ubiquitous in quantum field theories and provide, important constraints on physical gauge theories like the standard model [4, 5] or on string theories [6, 7]. Whereas the formalisms of explicit and spontaneous symmetry breaking are frequently applied across many fields in physics [8][9][10], anomalous symmetry breaking is typically associated only with high energy physics. One exception was found in molecular physics [11,12] and here we report an observation of a quantum anomaly in the field of cold atom physics.A particular class of anomalies, called conformal anomalies, break the scale invariance of a theory, that is invariance of the Hamiltonian under r → λr. The most prominent examples are found in field theories like QED or QCD where the renormalized coupling constants depend on the energy scale and thus break scale invariance explicitly. In ordinary quantum mechanics the 1/r 2 -and the δ 2 -potential in 2D are well-known examples of conformal anomalies [13,14].Notably, the δ 2 -potential is used to model contact in-teractions in cold atom gases in two-dimensions as V int ∝ g 0 δ 2 (r i − r j ). Including the kinetic...

Bulk Viscosity and Contact Correlations in Attractive Fermi Gases

“…In a generic interacting fluid, instead, a nonzero value of the bulk viscosity quantifies the breaking of scale invariance in physical systems ranging from QCD [4-7] to condensed matter [8][9][10][11][12][13][14]. An intriguing example is the twodimensional dilute Fermi gas, where the classical model is scale invariant but a quantum scale anomaly breaks this symmetry [15][16][17][18]; this has recently been observed via breathing dynamics in cold-atom experiments [19][20][21].The bulk viscosity is necessary to understand and predict the real-time evolution and hydrodynamic modes of dissipative quantum fluids and to quantitatively interpret current experiments. However, measurements of the bulk viscosity remain challenging even for classical fluids [22].…”

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

“…The effective range is fixed to k Rs = −0.620. Upper and lower triangles show the experimental data by Peppler et al (Swinburne) [11] and Holten et al (Heidelberg)[10]. The solid line shows the zero-range AFQMC result in the many-body limit.…”

Effective theory for ultracold strongly interacting fermionic atoms in two dimensions

“…5). The puzzling quantitative and qualitative discrepancies, observed in the previous comparisons between experiment and theory [5,6,9,16,17], are therefore naturally resolved in a satisfactory way. Our results emphasize the important role played by the effective range of interactions in 2D strongly interacting Fermi systems, which may also be found in cuprate superconductors [18] and neutron stars [21].…”

“…Breathing mode and quantum anomaly. We now turn to consider the breathing mode frequency, which was recently measured in two experiments at N ≃ 0.2N 2D [16,17], as shown in Fig. 5 by green circles and blue squares.…”