Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid

Abstract

Quantum anomalies are violations of classical scaling symmetries caused by quantum fluctuations. Although they appear prominently in quantum field theory to regularize divergent physical quantities, their influence on experimental observables is difficult to discern. Here, we discovered a striking manifestation of a quantum anomaly in the momentum-space dynamics of a 2D Fermi superfluid of ultracold atoms. We measured the position and pair momentum distribution of the superfluid during a breathing mode cycle for different interaction strengths across the BEC-BCS crossover. Whereas the system exhibits self-similar evolution in the weakly interacting BEC and BCS limits, we found a violation in the strongly interacting regime. The signature of scale-invariance breaking is enhanced in the first-order coherence function. In particular, the power-law exponents that characterize long-range phase correlations in the system are modified due to this effect, indicating that the quantum anomaly has a significant influence on the critical properties of 2D superfluids.Symmetries and their violations are fundamental concepts in physics. A prominent type is conformal symmetry which gives rise to the peculiar effect of scaleinvariance, where the properties of a system are unchanged under a transformation of scale. For instance, a Hamiltonian H(x) is said to be scale-invariant when H(λx) = λ α H(x), where λ is a scaling factor and α is a real number. Intriguingly, scaling symmetries such as these can be violated by quantum fluctuations, which is known as a quantum anomaly. Such anomalous symmetry breaking is widely discussed in quantum field theory [1], as they have fundamental implications in a wide range of scenarios, such as high-energy physics and phase transitions. However, experimental signatures of this effect, particularly in many-body systems, have so far been elusive. Here, we report the direct observation of a quantum anomaly in the dynamics of a two-dimensional Fermi superfluid.Two-dimensional systems with contact interactions, V (x) ∝ δ 2 (x), are particularly interesting in the context of scale-invariance violation, because the δ 2 potential does not introduce a characteristic scale to the Hamiltonian. At the classical level, the transformation x → λx rescales the interaction potential as V (λx) = λ −2 V (x) exactly the same way as the kinetic energy and therefore the classical 2D gas is intrinsically scale-invariant [2,3]. However at the quantum mechanical level, this is no longer true since the δ 2 scattering potential supports a two-body bound state for arbitrarily weak attraction. This additional binding energy scale E B and the associated scattering length scale a 2D effectively break the scaling relation between interaction and kinetic energy, which leads to a quantum anomaly.An important question is, how does this quantum anomaly influence the behavior of 2D systems at macroscopic scales? This is especially relevant for 2D superfluids which exhibit algebraic -hence scale-free -decay of phase correlations [4,5]...

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

“…If we do a simple linear extrapolation of (2, 2) and (3, 3) results towards the 1/N tot = 0 limit, the extrapolated results agree reasonably well with the manybody AFQMC result shown in hollow symbols. The good agreement encourages us to perform the same extrapolation for the data with effective range k 2 F R s = −0.620, which is the realistic effective range in recent two 6 Li experiments [10,11,13]. This is shown in Fig.…”

“…This discrepancy is probably caused by the large temperature of the 40 K Fermi gas in the experiment [7], as suggested by virial expansion studies [8,9]. In two most recent experiments with 6 Li atoms, the 2D Fermi gas was cooled down to one-tenth of Fermi temperature, to avoid any dominant finite temperature effect [10,11]. Surprisingly, the measured quantum anomaly, about 2 − 3%, is still at the same level as in the first observation [7].…”

“…The initial idea of a weakly-interacting 2D Bose gas [1,2] does not work since the breathing mode frequency shift is too small to be observable. A strongly interacting twocomponent 2D Fermi gas of 40 K and 6 Li atoms appears to be a better candidate [4][5][6]. However, the early observation of about 1% frequency shift from 2ω [7] is much smaller than the 10% anomaly predicted for zero-range contact interaction at zero temperature [4,5].…”

“…-The main motiva- tion for this work is the discrepancy between the large quantum anomaly (∼ 10%) predicted with zero-range model and the much smaller quantum anomaly (< 3%) observed in the experiments [10,11]. In both Heidelberg and Swinburne experiments, two hyperfine states of 6 Li are cooled to deep quantum degeneracy in a 2D trap. It has been shown that the effective range in those setups are non-negligible [13].…”

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].…”