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arXiv:2409.17398 · Physical Review Letters

Observation of Spin Squeezing with Contact Interactions in One- and Three-Dimensional Easy-Plane Magnets

Yoo Kyung Lee, Maxwell Block, Hanzhen Lin, Vitaly Fedoseev, Philip J. D. Crowley, Norman Y. Yao, Wolfgang Ketterle

Published May 14, 2025• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/jqvz-kpwg

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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.
We describe a theoretical scheme for generating scalable spin squeezing with nearest-neighbor interactions between spin-1/2 particles in a three-dimensional (3D) lattice, which are naturally present in state-of-the-art 3D optical lattice clocks. We propose to use strong isotropic Heisenberg interactions within individual planes of the lattice, forcing the constituent spin-1/2s to behave as large collective spins. These large spins are then coupled with XXZXXZXXZ anisotropic interactions along a third direction of the lattice. This system can be realized via superexchange interactions in a 3D optical lattice subject to an external linear potential, such as gravity, and in the presence of spin-orbit coupling to generate spin anisotropic interactions. We show there is a wide range of parameters in this setting where the spin squeezing improves with increasing system size even in the presence of holes.
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.
Spin squeezed entanglement enables metrological precision beyond the classical limit. Understood through the lens of continuous symmetry breaking, dipolar spin systems exhibit the remarkable ability to generate spin squeezing via their intrinsic quench dynamics. To date, this understanding has primarily focused on lattice spin systems; in practice however, dipolar spin systems$\unicode{x2014}$ranging from ultracold molecules to nuclear spin ensembles and solid-state color centers$\unicode{x2014}$often exhibit significant amounts of positional disorder. Here, we develop a theory for scalable spin squeezing in a two-dimensional randomly diluted lattice of quantum dipoles, which naturally realize a dipolar XXZ model. Via extensive quantum Monte Carlo simulations, we map out the phase diagram for finite-temperature XY order, and by extension scalable spin squeezing, as a function of both disorder and Ising anisotropy. As the disorder increases, we find that scalable spin squeezing survives only near the Heisenberg point. We show that this behavior is due to the presence of rare tightly-coupled dimers, which effectively heat the system post-quench. In the case of strongly-interacting nitrogen-vacancy centers in diamond, we demonstrate that an experimentally feasible strategy to decouple the problematic dimers from the dynamics is sufficient to enable scalable spin squeezing.
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.
While spin squeezing has been traditionally considered in all-to-all interacting models, recent works have shown that it can also occur in systems with power-law interactions, enabling direct tests in Rydberg atoms, trapped ions, ultracold atoms, and nitrogen-vacancy (NV) centers in diamond. For the latter, Wu et al. Nature 646 (2025) demonstrated that spin squeezing is heavily affected by positional disorder, reducing any capacity for a practical squeezing advantage, which requires scalability with the system size. In this Letter we explore the robustness of spin squeezing in two-dimensional lattices with a fraction of unoccupied lattice sites. Using semiclassical modeling, we demonstrate the existence of scalable squeezing in power-law interacting XXZ models up to a disorder threshold, above which squeezing is not scalable. We produce a phase diagram for scalable squeezing, and explain its absence in the aforementioned NV experiment. Our work illustrates the maximum disorder allowed for realizing scalable spin squeezing in a host of quantum simulators, highlights a regime with substantial tolerance to disorder, and identifies controlled defect creation as a promising route for scalable squeezing in solid-state systems.
The recent experimental realization of a three-dimensional (3D) optical lattice clock not only reduces the influence of collisional interactions on the clock's accuracy but also provides a promising platform for studying dipolar many-body quantum physics. Here, by solving the governing master equation, we investigate the role of both elastic and dissipative long-range interactions in the clock's dynamics and study its dependence on lattice spacing, dimensionality, and dipolar orientation. For small lattice spacing, i.e., ${k}_{0}a\ensuremath{\ll}1$, where aaa is the lattice constant and k0{k}_{0}k0​ is the transition wave number, a sizable spin squeezing appears in the transient state which is favored in a head-to-tail dipolar configuration in 1D systems and a side-by-side configuration in 2D systems, respectively. For large lattice spacing, i.e., ${k}_{0}a\ensuremath{\gg}1$, the single atomic decay rate can be effectively suppressed due to the destructive dissipative emission of neighboring atoms in both 1D and 2D. Our results will not only aid in the design of the future generation of ultraprecise atomic clocks but also illuminates the rich many-body physics exhibited by radiating dipolar system.