We investigate many-body spin squeezing dynamics in an XXZ model with interactions that fall off with distance r as 1/r^{α} in D=2 and 3 spatial dimensions. In stark contrast to the Ising model, we find a broad parameter regime where spin squeezing comparable to the infinite-range α=0 limit is achievable even when interactions are short ranged, α>D. A region of "collective" behavior in which optimal squeezing grows with system size extends all the way to the α→∞ limit of nearest-neighbor interactions. Our predictions, made using the discrete truncated Wigner approximation, are testable in a variety of experimental cold atomic, molecular, and optical platforms.
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.
We analyze the collective spin noise in interacting spin systems. General expressions are derived for the short-time behavior of spin systems with general spin-spin interactions, and we suggest optimum experimental conditions for the detection of spin squeezing. For Ising models with site-dependent nearest-neighbor interactions, general expressions are presented for the spin squeezing parameter for all times. The reduction of collective spin noise can be used to verify the entangling powers of quantum computer architectures based on interacting spins.
Spin squeezing in a many-body system is a witness for entanglement and can enable measurement sensitivities beyond those achievable by only classical correlations. Here, working with ultracold ^{7}Li atoms in an optical lattice, we demonstrate spin squeezing using short-range contact interactions in both one and three dimensions. In 1D, spin squeezing is shown to be insensitive to density fluctuations caused by holes. In 3D, however, we observe that holes strongly modify the squeezing dynamics, hindering the recently predicted emergence of scalable squeezing in 3D XXZ spin systems. By developing a new theoretical model to account for spin-density coupling, we obtain strong quantitative agreement with the observed squeezing dynamics, resulting in ≈2 dB at 7% hole fraction. Our observations highlight the importance of understanding spin-density coupling in the dynamics of many interacting spins and lay the groundwork for improved spin squeezing in systems with only short-range interactions.
Abstract Numerical techniques to efficiently model out-of-equilibrium dynamics in interacting quantum many-body systems are key for advancing our capability to harness and understand complex quantum matter. Here we propose a new numerical approach which we refer to as generalized discrete truncated Wigner approximation (GDTWA). It is based on a discrete semi-classical phase space sampling and allows to investigate quantum dynamics in lattice spin systems with arbitrary S ≥ 1/2. We show that the GDTWA can accurately simulate dynamics of large ensembles in arbitrary dimensions. We apply it for S > 1/2 spin-models with dipolar long-range interactions, a scenario arising in recent experiments with magnetic atoms. We show that the method can capture beyond mean-field effects, not only at short times, but it also can correctly reproduce long time quantum-thermalization dynamics. We benchmark the method with exact diagonalization in small systems, with perturbation theory for short times, and with analytical predictions made for models which feature quantum-thermalization at long times. We apply our method to study dynamics in large S > 1/2 spin-models and compute experimentally accessible observables such as Zeeman level populations, contrast of spin coherence, spin squeezing, and entanglement quantified by single-spin Renyi entropies. We reveal that large S systems can feature larger entanglement than corresponding S = 1/2 systems. Our analyses demonstrate that the GDTWA can be a powerful tool for modeling complex spin dynamics in regimes where other state-of-the art numerical methods fail.
Recent work has identified a dynamical squeezing phase transition in power-law interacting bilayer XXZ spin models, separating a fully collective phase with Heisenberg-limited squeezing from a partially-collective phase with universal critical scaling. Here we test and establish the universality of this transition along two qualitatively different microscopic axes: lattice geometry, by studying square, triangular, and honeycomb
2D bilayers as well as
1D ladders, and a symmetry-preserving rescaling
λ of the interlayer couplings relative to the intralayer ones. Combining a Bogoliubov instability analysis with discrete truncated Wigner simulations, we find that the transition persists across all four lattice geometries and over a wide range of
λ with critical exponents consistent within error, providing strong evidence for a genuine non-equilibrium universality class. The Bogoliubov theory recovers the previously identified scaling
aZ∗∝L in the long-range interacting regime
α<d+2, and yields an analytical scaling
aZ∗∝L2/(α−d) for the critical aspect ratio with system size for
α>d+2, with
α the power-law exponent in dimension
d. This uncovers a previously unrecognized sub-linear regime for short-range interactions. By tuning
λ we vary the interlayer coupling strength at fixed layer spacing, demonstrating that the dynamical transition can be driven purely through interaction engineering without modifying the underlying geometry. These findings provide a versatile route toward controlling entanglement generation in Rydberg-array, polar molecule, and trapped-ion platforms with applications in quantum sensing and simulation.
We propose a new protocol for preparing spin squeezed states in controllable atomic, molecular, and optical systems, with particular relevance to emerging optical clock platforms compatible with Rydberg interactions. By combining a short-ranged, soft-core potential with an external drive, we can transform naturally emerging Ising interactions into an XX spin model while opening a many-body gap. The gap helps maintain the system within a collective manifold of states where metrologically useful spin squeezing can be generated at a level comparable to the spin squeezing generated in systems with genuine all-to-all interactions. We examine the robustness of our protocol to experimentally-relevant decoherence and show favorable performance over typical protocols lacking gap protection.