Cavity-QED Quantum Simulator of Dynamical Phases of a Bardeen-Cooper-Schrieffer Superconductor.

We propose to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are encoded via the internal states of the atoms, and attractive interactions are realized via the exchange of virtual photons between atoms coupled to a common cavity mode. Control of the interaction strength combined with a tunable dispersion relation of the effective Cooper pairs allows exploration of the full dynamical phase diagram of the BCS model as a function of system parameters and the prepared initial state. Our proposal paves the way for the study of the nonequilibrium features of quantum magnetism and superconductivity by harnessing atom-light interactions in cold atomic gases.

Exploring dynamical phase transitions with cold atoms in an optical cavity.

Interactions between atoms and light in optical cavities provide a means of investigating collective (many-body) quantum physics in controlled environments. Such ensembles of atoms in cavities have been proposed for studying collective quantum spin models, where the atomic internal levels mimic a spin degree of freedom and interact through long-range interactions tunable by changing the cavity parameters1-4. Non-classical steady-state phases arising from the interplay between atom-light interactions and dissipation of light from the cavity have previously been investigated5-11. These systems also offer the opportunity to study dynamical phases of matter that are precluded from existence at equilibrium but can be stabilized by driving a system out of equilibrium12-16, as demonstrated by recent experiments17-22. These phases can also display universal behaviours akin to standard equilibrium phase transitions8,23,24. Here, we use an ensemble of about a million strontium-88 atoms in an optical cavity to simulate a collective Lipkin-Meshkov-Glick model25,26, an iconic model in quantum magnetism, and report the observation of distinct dynamical phases of matter in this system. Our system allows us to probe the dependence of dynamical phase transitions on system size, initial state and other parameters. These observations can be linked to similar dynamical phases in related systems, including the Josephson effect in superfluid helium27, or coupled atomic28 and solid-state polariton29 condensates. The system itself offers potential for generation of metrologically useful entangled states in optical transitions, which could permit quantum enhancement in state-of-the-art atomic clocks30,31.

Protocol for Precise Field Sensing in the Optical Domain with Cold Atoms in a Cavity.

In the context of quantum metrology, optical cavity-QED platforms have primarily been focused on the generation of entangled atomic spin states useful for next-generation frequency and time standards. Here, we report a complementary application: the use of optical cavities to generate nonclassical states of light for electric field sensing below the standard quantum limit. We show that cooperative atom-light interactions in the strong collective coupling regime can be used to engineer generalized atom-light cat states which enable quantum enhanced sensing of small displacements of the cavity field even in the presence of photon loss. We demonstrate that metrological gains of 10-20 dB below the standard quantum limit are within reach for current cavity-QED systems operating with long-lived alkaline-earth atoms.

Robust Spin Squeezing via Photon-Mediated Interactions on an Optical Clock Transition.

Cavity QED is a promising avenue for the deterministic generation of entangled and spin-squeezed states for quantum metrology. One archetypal scheme generates squeezing via collective one-axis twisting interactions. However, we show that in implementations using optical transitions in long-lived atoms the achievable squeezing is fundamentally limited by collectively enhanced emission into the cavity mode which is generated in parallel with the cavity-mediated spin-spin interactions. We propose an alternative scheme which generates a squeezed state that is protected from collective emission, and investigate its sensitivity to realistic sources of experimental noise and imperfections.

Cavity-mediated collective spin-exchange interactions in a strontium superradiant laser.

Laser-cooled and quantum degenerate atoms are being pursued as quantum simulators and form the basis of today's most precise sensors. A key challenge toward these goals is to understand and control coherent interactions between the atoms. We observe long-range exchange interactions mediated by an optical cavity, which manifest as tunable spin-spin interactions on the pseudo spin-½ system composed of the millihertz linewidth clock transition in strontium. This leads to one-axis twisting dynamics, the emergence of a many-body energy gap, and gap protection of the optical coherence against certain sources of decoherence. Our observations will aid in the future design of versatile quantum simulators and the next generation of atomic clocks that use quantum correlations for enhanced metrology.

Magnetically Induced Optical Transparency on a Forbidden Transition in Strontium for Cavity-Enhanced Spectroscopy.

In this Letter we realize a narrow spectroscopic feature using a technique that we refer to as magnetically induced optical transparency. A cold ensemble of ^{88}Sr atoms interacts with a single mode of a high-finesse optical cavity via the 7.5 kHz linewidth, spin forbidden ^{1}S_{0} to ^{3}P_{1} transition. By applying a magnetic field that shifts two excited state Zeeman levels, we open a transmission window through the cavity where the collective vacuum Rabi splitting due to a single level would create destructive interference for probe transmission. The spectroscopic feature approaches the atomic transition linewidth, which is much narrower than the cavity linewidth, and is highly immune to the reference cavity length fluctuations that limit current state-of-the-art laser frequency stability.

Superradiance on the millihertz linewidth strontium clock transition.

Laser frequency noise contributes a significant limitation to today's best atomic clocks. A proposed solution to this problem is to create a superradiant laser using an optical clock transition as its gain medium. This laser would act as an active atomic clock and would be highly immune to the fluctuations in reference cavity length that limit today's best lasers. We demonstrate and characterize superradiant emission from the millihertz linewidth clock transition in an ensemble of laser-cooled 87Sr atoms trapped within a high-finesse optical cavity. We measure a collective enhancement of the emission rate into the cavity mode by a factor of more than 10,000 compared to independently radiating atoms. We also demonstrate a method for seeding superradiant emission and observe interference between two independent transitions lasing simultaneously. We use this interference to characterize the relative spectral properties of the two lasing subensembles.