Long-range interacting spin systems can be used to generate metrologically useful entanglement in the form of spin squeezing resulting in quantum enhanced sensitivity. This work considers power-law spin exchange interactions to generate two-mode squeezing in a bilayer geometry. It shows how spatial control over the geometry allows for achieving the same sensitivity with power-law interactions as with infinite-range interactions, and how spatially Floquet-engineered interactions allow for achieving the ultimate Heisenberg scaling of sensitivity.
Long-range interacting spin systems can be used to generate metrologically useful entanglement in the form of spin squeezing resulting in quantum enhanced sensitivity. This work considers power-law spin exchange interactions to generate two-mode squeezing in a bilayer geometry. It shows how spatial control over the geometry allows for achieving the same sensitivity with power-law interactions as with infinite-range interactions, and how spatially Floquet-engineered interactions allow for achieving the ultimate Heisenberg scaling of sensitivity.
This dissertation presents theoretical and computational investigations into non-equilibrium quantum dynamics in engineered systems, with a central focus on entanglement generation for quantum metrology. The primary contributions establish the scalable and robust generation of entanglement in the form of two-mode squeezing in bilayers of power-law interacting quantum spins and uncover a novel dynamical phase transition. We develop a Floquet protocol utilizing spatio-temporal control to engineer spin-spin interactions tailored to the initial state and desired entanglement dynamics, thereby improving the standard quantum limit of 1/√N scaling of the sensitivity in system size N to approach the ultimate Heisenberg limit of 1/N. For a wide range of power-law interactions (1/rα), this approach creates exponentially fast entangled pairs of excitations between the layers. We then reveal a dynamical phase transition in the two-mode squeezing dynamics by identifying universal scaling in terms of system parameters and a divergent time-scale. We establish two distinct phases: a fully collective phase exhibiting Heisenberg-limited squeezing and a partially collective phase with scalable but sub-Heisenberg squeezing. A full set of critical exponents is derived, and a universal scaling collapse of the dynamics is demonstrated, framing entanglement generation within the theory of non-equilibrium critical phenomena. We also apply advanced computational methods to other quantum and classical engineered systems. We investigate quantum transport that maps conductivity to the disorder-driven phase diagram of two-dimensional Dirac fermions. We also design a high-efficiency, lead-free tandem photovoltaic cell. Collectively, this research provides a framework for harnessing quantum control to probe and enhance functionality in complex systems, from fundamental quantum sensing to applied materials design.
We demonstrate a general mechanism to generate scalable, metrologically useful entanglement in the form of generalized spin squeezing in multi-level (qudit) spin systems with power-law interactions. We demonstrate this for spin-changing dynamics, extending the physics of spin-nematic squeezing known from spinor BECs to spatially extended lattice geometries. In the absence of all-to-all connectivity, the dynamics generally suffers from leakage into non-collective finite-momentum modes, destroying Heisenberg scaling. We show that introducing local su(D) exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling ξ2∝1/N in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.
Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/rα) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α=0) case. This indifference to the interaction range persists up to a critical value α=2D/3, above which squeezing degrades continuously. Boundary-induced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.
Entanglement can improve the measurement precision of quantum sensors beyond the shot noise limit. Neutral atoms, the basis of some of the most precise and accurate optical clocks and interferometers, do not naturally exhibit the all-to-all interactions traditionally used to generate such entangled states. On the other hand, these systems exhibit exceedingly high degrees of experimental control over parameters such as temperature, spatial entropy, and itinerancy. In this work, we investigate spin squeezing in a highly coherent itinerant system of neutral atoms with magnetic dipole-dipole interactions. We achieve 7.1 dB of metrologically useful squeezing using finite-range spin-exchange interactions in an erbium quantum gas microscope, and we demonstrate that introducing atomic motion, realizing a dipolar t − J model, protects the spin sector coherence at low fillings, significantly improving the achievable spin squeezing in a 2D dipolar system. This work’s protocol can be implemented with most neutral atoms, opening the door to quantum-enhanced metrology in other itinerant dipolar systems, such as molecules or optical lattice clocks, and serves as a novel method for studying itinerant quantum magnetism with long-range interactions.
Spin squeezing serves as both a fundamental witness of quantum entanglement and a critical resource for quantum-enhanced metrology. While generating substantial spin squeezing in finite-range interacting systems remains challenging, such capability is important for advancing quantum technologies. In this work, we develop an optimal control strategy for achieving enhanced spin squeezing in a two-dimensional XX model with dipolar interactions. Leveraging rotor-spin-wave theory for periodic boundary conditions, we circumvent computational bottlenecks to explore control strategies at unprecedented scales. Remarkably, optimizing a single collective transverse field is sufficient to achieve substantial squeezing enhancement, exceeding the two-axis-twisting benchmark. The optimized control field achieves this breakthrough by dynamically suppressing inter-subspace mixing induced by the finite-range interactions, thereby confining the system evolution predominantly within the maximal spin subspace. We further extend rotor-spin-wave theory to open boundary conditions and incorporate dephasing noise, providing a scalable framework for realistic systems. Under these conditions, the optimized protocol remains effective, highlighting its robustness and suitability for experimental implementation.
Long-range spin-spin interactions are known to generate nonequilibrium dynamics that can squeeze the collective spin of a quantum spin ensemble in a scalable manner, leading to states whose metrologically useful entanglement grows with system size. Here, we show theoretically that scalable squeezing can be produced in 2D U(1)-symmetric systems even by short-range interactions, i.e., interactions that at equilibrium do not lead to long-range order at finite temperatures, but rather to an extended Berezinskii-Kosterlitz-Thouless critical phase. If the initial state is a coherent spin state in the easy plane of interactions, whose energy corresponds to a thermal state in the critical Berezinskii-Kosterlitz-Thouless phase, the nonequilibrium dynamics exhibits critical slowing down, corresponding to a power-law decay of the collective magnetization in time. This slow decay protects scalable squeezing, whose scaling reveals in turn the decay exponent of the magnetization. Our results open the path to realizing massive entangled states of potential metrological interest in many relevant platforms of quantum simulation and information processing-such as Mott insulators of ultracold atoms, or superconducting circuits-characterized by short-range interactions in planar geometries.