Philip Zupancic

We observe a structural phase transition between two configurations of a superradiant crystal by coupling a Bose-Einstein condensate to an optical cavity and applying imbalanced transverse pump fields. The transition can be interpreted as a transition between two nonpolar, centro-symmetric structures involving a change in polarization. We find that this first order phase transition is accompanied by transient dynamics of the order parameter which we measure in real time. The phase transition and the excitation spectrum can be derived from a microscopic Hamiltonian, in quantitative agreement with our experimental data.

We realize a nondegenerate two-mode Dicke model with competing interactions in a Bose-Einstein condensate (BEC) coupled to two orthogonal polarization modes of a single optical cavity. The BEC is coupled to the cavity modes via the scalar and vectorial part of the atomic polarizability. We can independently change these couplings and determine their effect on a self-organization phase transition. Measuring the phases of the system, we characterize a crossover from a single-mode to a two-mode Dicke model. This work provides perspectives for the realization of coupled phases of spin and density.

Controlling matter to simultaneously support coupled properties is of fundamental and technological importance¹ (for example, in multiferroics^2,3,4,5 or high-temperature superconductors^6,7,8,9). However, determining the microscopic mechanisms responsible for the simultaneous presence of different orders is difficult, making it hard to predict material phenomenology^10,11 or modify properties^{12,13,14,15,16}. 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 resonators¹⁷, 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 points¹⁸ and can be extended to study the interplay of spin and density orders¹⁹ as a function of temperature²⁰.

Breaking the symmetry in a supersolid: The concept of broken symmetry has relevance across all branches of physics, including particle and condensed matter physics. In many cases, the shape of the potential energy resembles a Mexican hat, and the symmetry of the system is broken when it chooses a particular spot along the “trough” of the hat. Out of this minimum-energy state, the system can undergo collective excitations either along the trough or perpendicular to it. Léonard et al. detected these so-called Goldstone and Higgs modes in a supersolid Bose-condensed atomic gas held in two crossed optical cavities. By monitoring the dynamics of the light field in each cavity, the oscillations of the order parameter associated with both modes were observed in real time. Science , this issue p. 1415

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.

High-resolution addressing of individual ultracold atoms, trapped ions or solid state emitters allows for exquisite control in quantum optics experiments. This becomes possible through large aperture magnifying optics that project microscopic light patterns with diffraction limited performance. We use programmable amplitude holograms generated on a digital micromirror device to create arbitrary microscopic beam shapes with full phase and amplitude control. The system self-corrects for aberrations of up to several λ and reduces them to λ/50, leading to light patterns with a precision on the 10⁻⁴ level. We demonstrate aberration-compensated beam shaping in an optical lattice experiment and perform single-site addressing in a quantum gas microscope for ⁸⁷Rb.

Quantum walkers under a microscope: Generations of physics students have been taught to think of one-dimensional random walks in terms of a drunken sailor taking random steps to the right or to the left. But that doesn't compare with the complexity of a quantum walker, who can propagate down multiple paths at the same time. Preisset al.detected particles in single sites of an optical lattice to study the dynamics of two interacting atoms of 87Rb performing a quantum walk (see the Perspective by Widera). Depending on the initial conditions and the interaction strength between the atoms, the atoms either ignored each other, stuck to each other, or tried to get as far away from each other as possible.Science, this issue p.1229; see also p.1200