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...

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The nature of the normal phase of strongly correlated fermionic systems is an outstanding question in quantum many-body physics. We used spatially resolved radio-frequency spectroscopy to measure pairing energy of fermions across a wide range of temperatures and interaction strengths in a two-dimensional gas of ultracold fermionic atoms. We observed many-body pairing at temperatures far above the critical temperature for superfluidity. In the strongly interacting regime, the pairing energy in the normal phase considerably exceeds the intrinsic two-body binding energy of the system and shows a clear dependence on local density. This implies that pairing in this regime is driven by many-body correlations, rather than two-body physics. Our findings show that pairing correlations in strongly interacting two-dimensional fermionic systems are remarkably robust against thermal fluctuations.

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]...

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