Scalable Spin Squeezing Achieves Robustness in XXZ Models with Disorder, up to 646

Spin squeezing, a technique vital for enhancing the precision of quantum sensors, typically relies on systems with strong, all-encompassing interactions. Recent research indicates that spin squeezing can also emerge in systems governed by power-law interactions, opening avenues for implementation in platforms such as Rydberg atoms and trapped ions. Samuel E. Begg, Bishal K. Ghosh, Chong Zu, Chuanwei Zhang, and Michael Kolodrubetz, from The University of Texas at Dallas and Washington University, investigate how positional disorder impacts the scalability of this squeezing effect. Their work demonstrates the existence of robust, scalable spin squeezing in two-dimensional lattices with a degree of missing sites, up to a specific disorder threshold. This research provides a crucial phase diagram for achieving scalable squeezing and offers an explanation for limitations observed in nitrogen-vacancy centre experiments, ultimately highlighting controlled defect creation as a pathway towards practical quantum sensing.

Scalable Squeezing Despite Positional Disorder

Scientists demonstrate the possibility of scalable spin squeezing within power-law interacting XXZ models, even when accounting for positional disorder. The research addresses a critical limitation observed in recent experiments with nitrogen vacancy (NV) centers in diamond, where disorder significantly hindered the achievement of practical squeezing advantages. This study employed semi-classical modeling to investigate spin squeezing in two-dimensional lattices containing a fraction of unoccupied lattice sites, revealing that scalable squeezing persists up to a specific disorder threshold. The team successfully generated a phase diagram delineating the conditions necessary for scalable squeezing, offering an explanation for the lack of scalability previously observed in the NV experiment.

The work establishes a clear understanding of the maximum tolerable disorder for realizing scalable spin squeezing across various quantum simulators. Researchers utilized the XXZ model with power-law interactions, specifically a 1/r interaction coefficient, to simulate spin dynamics within 2D lattices incorporating randomly positioned vacancies. Through semi-classical modeling with the discrete truncated Wigner approximation, they demonstrated that squeezing scales with system size until a disorder threshold is surpassed, at which point scalability is lost. This transition correlates with a change in the presence of order at later time scales, aligning with expectations based on U(1) symmetry principles.

Experiments show that the spin squeezing parameter, ξ, and magnetization, Mxy, exhibit distinct behaviours depending on the vacancy probability. For a disorder-free system, the study predicts optimal squeezing scaling of ξ opt ∼N⁻/⁵, though one-axis-twisting scaling of ξ opt ∼N⁻/ may be observed for smaller systems. The research highlights that the initial state of the system, an x-aligned state, is crucial for ensuring thermalization to the easy-plane ferromagnetic phase, a prerequisite for observing scalable squeezing. The simulations were conducted across a range of system sizes, approximately N ∈{10, 10⁴}, with results averaged over multiple disorder realizations and samples to ensure statistical robustness.

This breakthrough reveals a minimal disorder requirement for achieving scalable spin squeezing in diverse quantum simulators, offering valuable insights for future experimental designs. The team’s findings explain why the NV center experiment failed to demonstrate scalable squeezing and pinpoint favorable regions within the phase diagram for targeted experimentation. Furthermore, the research identifies controlled defect creation as a promising strategy for mitigating the effects of positional disorder and realizing scalable squeezing in solid-state systems, opening new avenues for advancements in quantum metrology and precision measurement.

Disorder’s Impact on Scalable Spin Squeezing

The study investigates the robustness of spin squeezing in two-dimensional lattices containing vacant sites, addressing a critical limitation observed in nitrogen-vacancy (NV) center experiments where positional disorder significantly hinders scalability. Researchers developed a semi-classical modeling approach, utilizing the power-law interacting XXZ model, to demonstrate the existence of scalable squeezing up to a specific disorder threshold. This model, defined by the Hamiltonian H = − Σi To characterize squeezing, the team employed the spin squeezing parameter ξ2 = Nminn⊥xVar[n. S] ⟨Sx⟩2, where Sα represents the collective spin and the variance is minimized along the x-direction.

Scalable squeezing is defined by ξ2 ∼N −ν, with ν ranging from 0 to 1, signifying the transition from the standard quantum limit to the Heisenberg limit. Simulations focused on identifying the minimum value of ξ2 during time evolution, termed ξ2 opt, which indicates maximal metrological utility. The researchers anticipated that disorder would lower the critical temperature, mirroring observations in systems with U(1) symmetry. Experiments began with an initially x-aligned state |ψ(0)⟩ = QN i |+⟩i, chosen for its low energy density and propensity to thermalize into an easy-plane ferromagnetic phase.

The team harnessed the discrete truncated Wigner approximation (dTWA) to simulate the model’s dynamics, a semi-classical method previously validated for long-range power-law interactions. Each simulation averaged data from 10 disorder realizations, each utilizing 6400 dTWA samples, to ensure statistical robustness. This innovative application of dTWA allows for the exploration of disorder effects on spin squeezing, revealing a phase diagram that explains the absence of scalable squeezing in prior NV center experiments and highlights regimes tolerant to disorder. The work demonstrates a clear relationship between vacancy probability and squeezing, with results presented for p values of 0, 0.5, 0.75, and 0.85, showing how squeezing parameter ξ2 and magnetization Mxy evolve over time for varying system sizes. The study’s findings pinpoint a minimal disorder requirement for scalable spin squeezing and propose controlled defect creation as a promising strategy for achieving this in solid-state quantum simulators.

Robust Scalable Squeezing in Disordered 2D Lattices

Scientists achieved scalable spin squeezing in two-dimensional lattices with a fraction of unoccupied sites, demonstrating robustness against positional disorder. The research team employed semi-classical modeling to explore the behaviour of power-law interacting XXZ models, revealing scalable squeezing up to a specific disorder threshold. Experiments measured the spin squeezing parameter, ξ2, to characterise the degree of squeezing, and data shows that scalable squeezing occurs when ξ2 scales inversely with system size N, specifically as ξ2 ∼N−ν, where ν can be 0 or 1. This work identifies a regime with substantial tolerance to disorder, offering a promising route for scalable squeezing in solid-state systems like nitrogen vacancy (NV) centres in diamond.

The study focused on systems with an average of N = fL2 spins, utilising 1/r3 interactions commonly observed in experiments. Results demonstrate that in the disorder-free case, the minimum value of the spin squeezing parameter, ξ2 opt, scales as ξ2 opt ∼N−2/3, consistent with one-axis-twisting (OAT) scaling. Tests prove that for a vacancy probability of p = 0, the squeezing parameter decreases with increasing system size, confirming the presence of scalable squeezing. However, at higher vacancy probabilities, such as p = 0.85, the team recorded a lack of scalable squeezing, with magnetization decaying as a power-law with increasing N, indicating thermalization to a disordered phase.

Further measurements confirm that at a vacancy probability of p = 0.5, the minimum squeezing parameter still exhibits a decrease with system size, maintaining a similar OAT scaling. The team observed that at p = 0.75, while an initial minimum is not scalable, a second local minimum does demonstrate scalable squeezing for sufficiently large systems, exceeding N ∼O(104). Analysis of the distribution of effective interaction strengths, Jeff, revealed that for weak disorder (p = 0.1), the largest interaction values are approximately double the smallest, while for strong disorder (p = 0.9), this ratio becomes significantly larger due to close spin pairings. The breakthrough delivers a phase diagram for scalable squeezing, explaining its absence in previous NV experiments and highlighting the importance of controlled defect creation. Scientists recorded the easy-plane magnetization, Mxy, alongside ξ2, finding that Mxy decays as Mxy ∼N−α within the disordered phase, aligning with analytic behaviour in L−1. These findings illustrate the maximum disorder allowed for realizing scalable spin squeezing, paving the way for advancements in quantum technologies and metrology.