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.
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.
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.
Solid-state spin defects, particularly the nitrogen-vacancy (NV) center in diamond, have emerged as powerful platforms for exploring quantum many-body physics and quantum metrology. Their exceptional coherence properties and strong dipolar interactions offer unique opportunities to simulate complex quantum dynamics and engineer entangled states for enhanced sensing beyond the standard quantum limit. However, achieving scalable entanglement in these systems is notoriously difficult due to intrinsic disorder and the complex nature of long-range dipole-dipole interactions. This thesis presents both theoretical and experimental advancements in harnessing quantum dynamics in interacting spin ensembles for quantum-enhanced metrology. A central result is the experimental realization of spin squeezing in a dense ensemble of NV centers, demonstrating a clear path toward overcoming classical limits in solid-state platforms. To further formalize and scale these phenomena, this work develops theoretical frameworks for generating robust spin squeezing under realistic experimental conditions. We show that finite-temperature easy-plane magnetism can be actively leveraged to create scalable squeezed states for the dipolar spin systems on regular lattices. Building upon this, we further extend the result to spatially disordered quantum dipoles. We demonstrate that strongly coupled spin pairs suppress squeezing through dynamical heating, and we propose a selective shelving protocol to mitigate this problem. Furthermore, we also propose a universal protocol for quantum-enhanced sensing that exploits information scrambling, utilizing the natural, scrambling dynamics of strongly interacting many-body systems to effectively amplify weak external signals. Together, the findings detailed in this thesis establish a foundational paradigm for controlling and utilizing solid-state spin ensembles, paving the way for entanglement-enhanced quantum sensors.
We investigate phase transitions in the nonequilibrium dynamics of power-law interacting spin-1/2 bilayer XXZ models, which have recently been shown to allow generation of entanglement in the form of two-mode squeezing. We find a transition between a collective phase characterized by Heisenberg limited squeezing and a partially collective phase with scalable squeezing. We identify universal scaling of the squeezing dynamics in terms of system parameters and a divergent timescale, establishing these as distinct dynamical phases within the framework of nonequilibrium critical phenomena. Our Letter demonstrates a novel dynamical phase transition with potential applications in quantum sensing and quantum simulation in cold-atomic, molecular, or Rydberg platforms.
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.
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.