Explore the vast range of titles available.

Quantum simulations offer opportunities both for studying many-body physics and for generating useful entangled states. However, existing platforms are usually restricted to specific types of interaction, fundamentally limiting the models they can mimic. Here we realize an all-to-all interacting model with an arbitrary quadratic Hamiltonian, thus demonstrating an infinite-range tunable Heisenberg XYZ model. This was accomplished by engineering cavity-mediated four-photon interactions between an ensemble of 700 rubidium atoms with a pair of momentum states serving as the effective qubit degree of freedom. As one example of the versatility of this approach, we implemented the so-called two-axis counter-twisting model, a collective spin model that can generate spin-squeezed states that saturate the Heisenberg limit on quantum phase estimation. Furthermore, our platform allows for including more than two relevant momentum states by simply adding additional dressing laser tones. This approach opens opportunities for quantum simulation and quantum sensing with matter–wave interferometers and other quantum sensors, such as optical clocks and magnetometers. Spin models that can be emulated by quantum simulators are usually restricted to systems with conserved total magnetization. The tuning of photon-mediated interactions between atoms in a cavity enables the implementation of more general models also useful for quantum sensing tasks.

Highly controllable atomic, molecular, and optical systems have emerged as an increasingly powerful toolkit in advancing the frontiers of quantum simulation, metrology, computation, and fundamental physics. In this thesis, we present theoretical work on manipulation of contact and photon-mediated interactions in optical lattice clocks and cavity QED systems, as well as explorations of their possible applications on problems relevant for quantum simulation and metrology.We start from an overview of the relevant theoretical background for this thesis, including optical lattices, contact interactions, spin systems, photon-mediated interactions and measurements, as well as metrological concepts. We then present research in three closely related directions.Firstly, we discuss theory ideas for optimizing the performance of optical lattice clocks via Hamiltonian engineering. Based on the tunable delocalization of Wannier-Stark states in tilted lattices, we can fine-tune the relative strength of on-site p-wave and nearest-neighbor s-wave interactions, leading to a minimization of density shifts in a 1D optical lattice clock. We also discuss the tunability of nearest-neighbor interactions by lattice geometry. Considering the improved sensitivity of optical lattice clocks, we further analyze the manifestation of general relativistic effects in a quantum many-body optical lattice clock and discuss protocols for their near-term observation.Additionally, we discuss theory ideas for exploring emergent collective behaviors and dynamical phases in interacting arrays. We utilize sideband transitions in trapped bosonic gases to engineer Lipkin-Meshkov-Glick model and identify dynamical phase transitions between ferromagnetic and paramagnetic phases. We also provide a theoretical proposal for correlated hopping processes facilitated by multilevel atoms in cavity QED systems, which features intriguing phenomena such as chiral transport and correlation spreading behaviors. We then consider protocols for the control and amplification of atomic Bloch oscillations via cavity-mediated interactions. Moreover, we realize the Bardeen–Cooper–Schrieffer (BCS) model, an iconic model that describes the behavior of superfluids and superconductors, by photon-mediated spin exchange interactions using the Anderson pseudospin mapping, and for the first time observe a dynamical phase with persistent oscillations of the BCS order parameter.Finally, we discuss theory ideas for entanglement generation via photon-mediated interactions and measurements. We provide a theory proposal for implementing homogeneous one-axis twisting interactions in a lattice-based atom interferometer using partial delocalized Wannier-Stark states in tilted lattices, which suppresses inhomogeneities in atom-light couplings at a magic lattice depth. We also compare two common approaches experimentally used to generate spin squeezing in cavity QED systems, quantum nondemolition measurements and unitary one-axis twisting dynamics. We derived simple criteria to determine the best protocol based on the detector's quantum efficiency.

In conventional Bardeen–Cooper–Schrieffer superconductors 1 , electrons with opposite momenta bind into Cooper pairs due to an attractive interaction mediated by phonons in the material. Although superconductivity naturally emerges at thermal equilibrium, it can also emerge out of equilibrium when the system parameters are abruptly changed 2 – 8 . The resulting out-of-equilibrium phases are predicted to occur in real materials and ultracold fermionic atoms, but not all have yet been directly observed. Here we realize an alternative way to generate the proposed dynamical phases using cavity quantum electrodynamics (QED). Our system encodes the presence or absence of a Cooper pair in a long-lived electronic transition in 88 Sr atoms coupled to an optical cavity and represents interactions between electrons as photon-mediated interactions through the cavity 9 , 10 . To fully explore the phase diagram, we manipulate the ratio between the single-particle dispersion and the interactions after a quench and perform real-time tracking of the subsequent dynamics of the superconducting order parameter using nondestructive measurements. We observe regimes in which the order parameter decays to zero (phase I) 3 , 4 , assumes a non-equilibrium steady-state value (phase II) 2 , 3 or exhibits persistent oscillations (phase III) 2 , 3 . This opens up exciting prospects for quantum simulation, including the potential to engineer unconventional superconductors and to probe beyond mean-field effects like the spectral form factor 11 , 12 , and for increasing the coherence time for quantum sensing. The dynamical phases of out-of-equilibrium Bardeen–Cooper–Schrieffer superconductors have been simulated using cold atoms levitated inside an optical cavity.

We theoretically propose a tunable implementation of symmetry-protected topological phases in a synthetic superlattice, taking advantage of the long coherence time and exquisite spectral resolutions offered by gravity-tilted optical lattice clocks. We describe a protocol similar to Rabi spectroscopy that can be used to probe the distinct topological properties of our system. We then demonstrate how the sensitivity of clocks and interferometers can be improved by the protection to unwanted experimental imperfections offered by the underlying topological robustness. The proposed implementation opens a path to exploit the unique opportunities offered by symmetry-protected topological phases in state-of-the-art quantum sensors.

We propose a scheme to control and enhance atomic Bloch oscillations via photon-mediated interactions in an optical lattice supported by a standing-wave cavity with incommensurate lattice and cavity wavelengths. Our scheme uses position-dependent atom-light couplings in an optical cavity to spatially prepare an array of atoms at targeted lattice sites starting from a thermal gas. On this initial state we take advantage of dispersive position-dependent atom-cavity couplings to perform non-destructive measurements of single-particle Bloch oscillations, and to generate long-range interactions self-tuned by atomic motion. The latter leads to the generation of dynamical phase transitions in the deep lattice regime and the amplification of Bloch oscillations in the shallow lattice regime. Our work introduces new possibilities accessible in state-of-the-art cavity QED experiments for the exploration of many-body dynamics in self-tunable potentials.

It is well known that superradiant decay of an ensemble of \\(N\\) spins generates a complex non-classical state of light. Here, we consider the information content of a superradiant burst of photons: how is information encoded in the initial spin state distributed among the emitted photons, and can it be extracted using simple measurements? Despite the complexity of the photonic burst state, we show that a simple homodyne measurement combined with an optimized filter and linear estimator recovers the \\(N\\)-scaling of the quantum Fisher information of the initial spin state (including cases exhibiting \\(N^2\\) Heisenberg scaling). Even more surprising, the temporal mode with optimal information content contains a vanishing fraction of the total emitted photons in the large-\\(N\\) limit, suggesting an effective compressing of information. Our results and setup represent a new way to perform cavity based readout of solid-state spin ensembles that allows one to utilize resonant spin-photon interactions.

We propose a quantum enhanced interferometric protocol for gravimetry and force sensing using cold atoms in an optical lattice supported by a standing-wave cavity. By loading the atoms in partially delocalized Wannier-Stark states, it is possible to cancel the undesirable inhomogeneities arising from the mismatch between the lattice and cavity fields and to generate spin squeezed states via a uniform one-axis twisting model. The quantum enhanced sensitivity of the states is combined with the subsequent application of a compound pulse sequence that allows to separate atoms by several lattice sites. This, together with the capability to load small atomic clouds in the lattice at micrometric distances from a surface, make our setup ideal for sensing short-range forces. We show that for arrays of \\(10^4\\) atoms, our protocol can reduce the required averaging time by a factor of \\(10\\) compared to unentangled lattice-based interferometers after accounting for primary sources of decoherence.

We propose a new direction in quantum simulation that uses multilevel atoms in an optical cavity as a toolbox to engineer new types of bosonic models featuring correlated hopping processes in a synthetic ladder spanned by atomic ground states. The underlying mechanisms responsible for correlated hopping are collective cavity-mediated interactions that dress a manifold of excited levels in the far detuned limit. By weakly coupling the ground state levels to these dressed states using two laser drives with appropriate detunings, one can engineer correlated hopping processes while suppressing undesired single-particle and collective shifts of the ground state levels. We discuss the rich many-body dynamics that can be realized in the synthetic ladder including pair production processes, chiral transport and light-cone correlation spreading. The latter illustrates that an effective notion of locality can be engineered in a system with fully collective interactions.

We study the combined effects of measurements and unitary evolution on the preparation of spin squeezing in an ensemble of atoms interacting with a single electromagnetic field mode inside a cavity. We derive simple criteria that determine the conditions at which measurement based entanglement generation overperforms unitary protocols. We include all relevant sources of decoherence and study both their effect on the optimal spin squeezing and the overall size of the measurement noise, which limits the dynamical range of quantum-enhanced phase measurements. Our conclusions are relevant for state-of-the-art atomic clocks that aim to operate below the standard quantum limit.

An attractive approach for stabilizing entangled many-body spin states is to employ engineered dissipation. Most existing proposals either target relatively simple collective spin states, or require numerous independent and complex dissipative processes. Here, we show a surprisingly versatile scheme for many-body reservoir engineering that relies solely on fully collective single-excitation decay, augmented with local Hamiltonian terms. Crucially, all these ingredients are readily available in cavity QED setups. Our method is based on splitting the spin system into groups of sub-ensembles, and provides an easily tunable setup for stabilizing a broad family of pure, highly entangled states with closed-form analytic descriptions. Our results have immediate application to multi-ensemble quantum metrology, enabling Heisenberg-limited sensing of field gradients and curvatures. Notably, our approach solves an important challenge in differential quantum sensing by providing the first example of Heisenberg-limited differential sensing immune to common-mode noise and accessible with only simple one-body measurements. The same setup also allows the stabilization of an entire family of entangled states in a 1D chain of spin ensembles with symmetry-protected topological (SPT) order, and have a direct connection to the outputs of sequential unitary circuits. A special case of our protocol efficiently stabilizes the celebrated Affleck-Kennedy-Lieb-Tasaki (AKLT) state.