Dissipationless Counterflow Currents above T_{c} in Bilayer Superconductors.

We report the existence of dissipationless currents in bilayer superconductors above the critical temperature T_{c}, assuming that the superconducting phase transition is dominated by phase fluctuations. Using a semiclassical U(1) lattice gauge theory, we show that thermal fluctuations cause a transition from the superconducting state at low temperature to a resistive state above T_{c}, accompanied by the proliferation of unbound vortices. Remarkably, while the proliferation of vortex excitations causes dissipation of homogeneous in-plane currents, we find that counterflow currents, flowing in the opposite direction within a bilayer, remain dissipationless. The presence of a dissipationless current channel above T_{c} is attributed to the inhibition of vortex motion by local superconducting coherence within a single bilayer, in the presence of counterflow currents. Our theory presents a possible scenario for the pseudogap phase in bilayer cuprates.

Condensate Formation in a Dark State of a Driven Atom-Cavity System.

We demonstrate the formation of a condensate in a dark state of momentum states, in a pumped and shaken cavity-BEC system. The system consists of an ultracold quantum gas in a high-finesse cavity, which is pumped transversely by a phase-modulated laser. This phase-modulated pumping couples the atomic ground state to a superposition of excited momentum states, which decouples from the cavity field. We demonstrate how to achieve condensation in this state, supported by time-of-flight and photon emission measurements. With this, we show that the dark state concept provides a general approach to efficiently prepare complex many-body states in an open quantum system.

Realization of a Periodically Driven Open Three-Level Dicke Model.

A periodically driven open three-level Dicke model is realized by resonantly shaking the pump field in an atom-cavity system. As an unambiguous signature, we demonstrate the emergence of a dynamical phase, in which the atoms periodically localize between the antinodes of the pump lattice, associated with an oscillating net momentum along the pump axis. We observe this dynamical phase through the periodic switching of the relative phase between the pump and cavity fields at a small fraction of the driving frequency, suggesting that it exhibits a time crystalline character.

Observation of a Dissipative Time Crystal.

We present the first experimental realization of a time crystal stabilized by dissipation. The central signature in our implementation in a driven open atom-cavity system is a period doubled switching between distinct checkerboard density wave patterns, induced by the interplay between controlled cavity dissipation, cavity-mediated interactions, and external driving. We demonstrate the robustness of this dynamical phase against system parameter changes and temporal perturbations of the driving.

Dynamical Control of Order in a Cavity-BEC System.

We demonstrate dynamical control of the superradiant transition of cavity-BEC system via periodic driving of the pump laser. We show that the dominant density wave order of the superradiant state can be suppressed, and that the subdominant competing order of Bose-Einstein condensation emerges in the steady state. Furthermore, we show that additional, nonequilibrium density wave orders, which do not exist in equilibrium, can be stabilized dynamically. Finally, for strong driving, chaotic dynamics emerge.

Light-Induced Coherence in an Atom-Cavity System.

We demonstrate a light-induced formation of coherence in a cold atomic gas system that utilizes the suppression of a competing density wave (DW) order. The condensed atoms are placed in an optical cavity and pumped by an external optical standing wave, which induces a long-range interaction mediated by photon scattering and a resulting DW order above a critical pump strength. We show that the light-induced temporal modulation of the pump wave can suppress this DW order and restore coherence. This establishes a foundational principle of dynamical control of competing orders analogous to a hypothesized mechanism for light-induced superconductivity in high-T_{c} cuprates.

Observation of a continuous time crystal.

Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. Although discrete time crystals have been extensively studied in periodically driven systems, the experimental realization of a continuous time crystal is still pending. We report the observation of a limit cycle phase in a continuously pumped dissipative atom-cavity system that is characterized by emergent oscillations in the intracavity photon number. The phase of the oscillation was found to be random for different realizations, and hence, this dynamical many-body state breaks continuous time translation symmetry spontaneously. Furthermore, the observed limit cycles are robust against temporal perturbations and therefore demonstrate the realization of a continuous time crystal.