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.

Access to collective excitations lies at the heart of our understanding of quantum many-body systems. We study the Higgs and Goldstone modes in a supersolid quantum gas that is created by coupling a Bose-Einstein condensate symmetrically to two optical cavities. The cavity fields form a U(1)-symmetric order parameter that can be modulated and monitored along both quadratures in real time. This enables us to measure the excitation energies across the superfluid-supersolid phase transition, establish their amplitude and phase nature, as well as characterize their dynamics from an impulse response. Furthermore, we can give a tunable mass to the Goldstone mode at the crossover between continuous and discrete symmetry by changing the coupling of the quantum gas with either cavity.Collective excitations are crucial for describing the dynamics of quantum many-body systems. They provide unified explanations of phenomena studied in different disciplines of physics, such as in condensed matter [1] or particle physics [2], or in cosmology [3]. The symmetry of the underlying effective Hamiltonian determines the character of the excitations, which changes in a fundamental way when a continuous symmetry is broken at a phase transition. Excitations can now appear both at finite and zero energy.In the paradigmatic case of models with U(1)-symmetry breaking, the system can be described by a complex scalar order parameter in an effective potential as illustrated in Fig. 1(A-B) [4]. In the normal phase, the potential is bowl-shaped with a single minimum at vanishing order parameter, and correspondingly two orthogonal amplitude excitations. Within the ordered phase, the potential shape changes to a 'sombrero' with an infinite number of minima on a circle. Here, fluctuations of the order parameter reveal two different excitations: a Higgs (or amplitude) mode, which stems from amplitude fluctuations of the order parameter and shows a finite excitation energy, and a Goldstone (or phase) mode, which stems from phase fluctuations of the order parameter and has zero excitation energy. The former should yield correlated fluctuations in the two squared quadratures of the order parameter, whereas the latter should show anticorrelated behavior.Condensed matter systems typically do not provide access to both quadratures of the order parameter, and Higgs and Goldstone modes have to be excited and detected by incoherent processes. In addition, the idealized situation is often disguised by further interactions that reduce the number of distinct modes [1, 6]. For charged particles, the minimal coupling to a vector potential can even completely suppress the Goldstone mode through the Anderson-Higgs mechanism [2]. In chargedensity wave compounds, a persisting Higgs mode has been observed as a well-defined resonance [7][8][9]. In superfluid Helium [10] and Bose-Einstein condensates [11] * donner@phys.ethz.ch Illustration of the experiment. A Bose-Einstein condensate (blue stripes) cut into slices by a transverse pump lattice potential (red stripes)...

We present an optical setup with focus-tunable lenses to dynamically control the waist and focus position of a laser beam, in which we transport a trapped ultracold cloud of 87 Rb over a distance of 28 cm. The scheme allows us to shift the focus position at constant waist, providing uniform trapping conditions over the full transport length. The fraction of atoms that are transported over the entire distance comes near to unity, while the heating of the cloud is in the range of a few microkelvin. We characterize the position stability of the focus and show that residual drift rates in focus position can be compensated for by counteracting with the tunable lenses. Beyond being a compact and robust scheme to transport ultracold atoms, the reported control of laser beams makes dynamic tailoring of trapping potentials possible. As an example, we steer the size of the atomic cloud by changing the waist size of the dipole beam.

We investigate a Bose-Einstein condensate strongly coupled to an optical cavity via a repulsive optical lattice. We detect a stable self-ordered phase in this regime, and show that the atoms order through an antisymmetric coupling to the P-band of the lattice, limiting the extent of the phase and changing the geometry of the emergent density modulation. Furthermore, we find a non-equilibrium phase with repeated intense bursts of the intra-cavity photon number, indicating non-trivial driven-dissipative dynamics. arXiv:1905.10377v1 [cond-mat.quant-gas]

Controlling matter to simultaneously support coupled properties is of fundamental and technological importance (for example, in multiferroics or high-temperature superconductors). However, determining the microscopic mechanisms responsible for the simultaneous presence of different orders is difficult, making it hard to predict material phenomenology or modify properties. Here, using a quantum gas to engineer an adjustable interaction at the microscopic level, we demonstrate scenarios of competition, coexistence and mutual enhancement of two orders. For the enhancement scenario, the presence of one order lowers the critical point of the other. Our system is realized by a Bose-Einstein condensate that can undergo self-organization phase transitions in two optical resonators, resulting in two distinct crystalline density orders. We characterize the coupling between these orders by measuring the composite order parameter and the elementary excitations and explain our results with a mean-field free-energy model derived from a microscopic Hamiltonian. Our system is ideally suited to explore quantum tricritical points and can be extended to study the interplay of spin and density orders as a function of temperature.