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Cavity QED experiments are natural hosts for non-equilibrium phases of matter supported by photon-mediated interactions. In this work, we consider a cavity QED simulation of the BCS model of superfluidity, by studying regimes where the cavity photons act as dynamical degrees of freedom instead of mere mediators of the interaction via virtual processes. We find an enhancement of long time coherence following a quench whenever the cavity frequency is tuned into resonance with the atoms. We discuss how this is equivalent to enhancement of non-equilibrium superfluidity and highlight similarities to an analogous phenomena recently studied in solid state quantum optics. We also discuss the conditions for observing this enhanced resonant pairing in experiments by including the effect of photon losses and inhomogeneous coupling in our analysis. 

We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing (TMS) of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for the observation of continuous variable entanglement in atomic systems and associated applications in next-generation optical atomic clocks. 

Time of flight is an intuitive way to determine the velocity of particles and lies at the heart of many capabilities ranging from mass spectrometry to fluid flow measurements. Here we show time-of-flight imaging can realize tomography of a quantum state of motion of a single trapped atom. Tomography of motion requires studying the phase space spanned by both position and momentum. By combining time-of-flight imaging with coherent evolution of the atom in an optical tweezer trap, we are able to access arbitrary quadratures in phase space without relying on coupling to a spin degree of freedom. To create non-classical motional states, we harness quantum tunneling in the versatile potential landscape of optical tweezers, and our tomography both demonstrates Wigner function negativity and assesses coherence of non-stationary states. Our demonstrated tomography concept has wide applicability to a range of particles and will enable characterization of non-classical states of more complex systems or massive dielectric particles. 

Engineering a Hamiltonian system with tunable interactions provides opportunities to optimize performance for quantum sensing and explore emerging phenomena of many-body systems. An optical lattice clock based on partially delocalized Wannier-Stark states in a gravity-tilted shallow lattice supports superior quantum coherence and adjustable interactions via spin-orbit coupling, thus presenting a powerful spin model realization. The relative strength of the on-site and off-site interactions can be tuned to achieve a zero density shift at a `magic' lattice depth. This mechanism, together with a large number of atoms, enables the demonstration of the most stable atomic clock while minimizing a key systematic uncertainty related to atomic density. Interactions can also be maximized by driving off-site Wannier-Stark transitions, realizing a ferromagnetic to paramagnetic dynamical phase transition.