A logarithmic signature Some one-dimensional disordered interacting quantum systems have been theoretically predicted to display a property termed many-body localization (MBL), where the system retains the memory of its initial state and fails to thermalize. However, proving experimentally that something does not occur is tricky. Instead, physicists have proposed monitoring the entanglement entropy of the system, which should grow logarithmically with evolution time in an MBL system. Lukin et al. observed this characteristic logarithmic trend in a disordered chain of interacting atoms of rubidium-87. This method should be generalizable to other experimental platforms and higher dimensions. Science , this issue p. 256

The concept of a supersolid state combines the crystallization of a many-body system with dissipationless flow of the atoms from which it is built. This quantum phase requires the breaking of two continuous symmetries: the phase invariance of a superfluid and the continuous translational invariance to form the crystal. Despite having been proposed for helium almost 50 years ago, experimental verification of supersolidity remains elusive. A variant with only discrete translational symmetry breaking on a preimposed lattice structure-the 'lattice supersolid'-has been realized, based on self-organization of a Bose-Einstein condensate. However, lattice supersolids do not feature the continuous ground-state degeneracy that characterizes the supersolid state as originally proposed. Here we report the realization of a supersolid with continuous translational symmetry breaking along one direction in a quantum gas. The continuous symmetry that is broken emerges from two discrete spatial symmetries by symmetrically coupling a Bose-Einstein condensate to the modes of two optical cavities. We establish the phase coherence of the supersolid and find a high ground-state degeneracy by measuring the crystal position over many realizations through the light fields that leak from the cavities. These light fields are also used to monitor the position fluctuations in real time. Our concept provides a route to creating and studying glassy many-body systems with controllably lifted ground-state degeneracies, such as supersolids in the presence of disorder.

Owing to thermal fluctuations, two-dimensional (2D) systems cannot undergo a conventional phase transition associated with the breaking of a continuous symmetry 1 . Nevertheless they may exhibit a phase transition to a state with quasi-longrange order via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism 2 . A paradigm example is the 2D Bose fluid, such as a liquid helium film 3 , which cannot condense at non-zero temperature although it becomes superfluid above a critical phase space density. The quasi-long-range coherence and the microscopic nature of the BKT transition were recently explored with ultracold atomic gases 4-6 . However, a direct observation of superfluidity in terms of frictionless flow is still missing for these systems. Here we probe the superfluidity of a 2D trapped Bose gas using a moving obstacle formed by a micrometre-sized laser beam. We find a dramatic variation of the response of the fluid, depending on its degree of degeneracy at the obstacle location.'Flow without friction' is a hallmark of superfluidity 7 . It corresponds to a metastable state in which the fluid has a non-zero relative velocity v with respect to an external body such as the wall of the container or an impurity. This metastable state is separated from the equilibrium state of the system (v = 0) by a large energy barrier, so that the flow can persist for a macroscopic time. The height of the barrier decreases as v increases, and eventually passes below a threshold (proportional to the thermal energy) for a critical velocity v c . The microscopic mechanism limiting the barrier height depends on the nature of the defect and is associated with the creation of phonons and/or vortices 7 . Whereas the quantitative comparison between experiments and theory is complicated for liquid 4 He, cold atomic gases in the weakly interacting regime are well suited for precise tests of many-body physics. In particular, superfluidity was observed in 3D atomic gases by stirring a laser beam or an optical lattice through bosonic [8][9][10][11][12] or fermionic 13 fluids and by observing the resulting heating or excitations. Here we transpose this search for dissipation-less motion to a disc-shaped, non-homogeneous 2D Bose gas. We use a small obstacle to locally perturb the system. The obstacle moves at constant velocity on a circle centred on the cloud, allowing us to probe the gas at a fixed density. We repeat the experiment for various atom numbers, temperatures and stirring radii and identify a critical point for superfluid behaviour.Our experiments are performed with 2D Bose gases of N = 35,000-95,000 87 Rb atoms confined in the vertical direction by the harmonic potential W (z) and in the horizontal plane by the radially symmetric harmonic potential V (r) (see ref. perturbed by a focussed laser beam, which moves at constant velocity on a circle centred on the cloud. The stirring beam has a frequency greater than the 87 Rb resonance frequency ('blue detuning' of ≈2 nm) and thus creates a repulsive potential which causes a dip in the d...