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arXiv:2609.34559

Microsecond-Programmable Synthetic Quantum Matter: Circumventing the Adiabatic Bottleneck for Heisenberg-Limited Metrology

Soi-Chan Lei

quant-phSubmitted Sep 28, 2026• Announced Sep 29, 2026• 0 citations
arXivHTMLPDF

Abstract

Generating macroscopic quantum entanglement is central to quantum metrology. While traversing a quantum critical point yields Heisenberg-limited precision, adiabatic schemes are restricted by slow dynamics and decoherence. Here, we propose a non-adiabatic Floquet protocol in a single-cavity Bose-Einstein condensate to circumvent these limitations. By applying rapid rotations and phase jumps, we dynamically synthesize effective Two-Axis Twisting (TAT) interactions from native longitudinal couplings. To evaluate this beyond mean-field limits, we develop an exact finite-state automaton Matrix Product Operator (MPO) encoding that strictly bounds the virtual dimension to $\mathcal{O}(1)$, enabling exact DMRG and TDVP simulations for large systems. Tracking non-equilibrium Floquet TAT dynamics and environmental decoherence for $N=10^3$ ensembles, we demonstrate that the quench rapidly generates Heisenberg-limited spin squeezing ($ξ_R^2 \sim 1/N$). The microsecond timescale of this protocol decouples the generation process from typical millisecond decoherence, with phenomenological models revealing an optimal extraction time near $t \approx 3.26~μs$. This work establishes a feasible route for realizing Heisenberg-limited metrology in current cavity-QED platforms.

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arXiv:2208.04019•Physical Review A•Jan 24, 2023•18 citations
Generating macroscopic quantum entanglement is central to quantum metrology. While traversing a quantum critical point yields Heisenberg-limited precision, adiabatic schemes are restricted by slow dynamics and decoherence. Here, we propose a non-adiabatic Floquet protocol in a single-cavity Bose-Einstein condensate to circumvent these limitations. By applying rapid rotations and phase jumps, we dynamically synthesize effective Two-Axis Twisting (TAT) interactions from native longitudinal couplings. To evaluate this beyond mean-field limits, we develop an exact finite-state automaton Matrix Product Operator (MPO) encoding that strictly bounds the virtual dimension to O(1)\mathcal{O}(1)O(1), enabling exact DMRG and TDVP simulations for large systems. Tracking non-equilibrium Floquet TAT dynamics and environmental decoherence for N=103N=10^3N=103 ensembles, we demonstrate that the quench rapidly generates Heisenberg-limited spin squeezing (ξR2∼1/Nξ_R^2 \sim 1/NξR2​∼1/N). The microsecond timescale of this protocol decouples the generation process from typical millisecond decoherence, with phenomenological models revealing an optimal extraction time near t≈3.26 μst \approx 3.26~μst≈3.26 μs. This work establishes a feasible route for realizing Heisenberg-limited metrology in current cavity-QED platforms.
One core of quantum metrology is the utilization of entanglement to enhance measurement precision beyond the standard quantum limit. Here, we utilize the Floquet-engineered two-axis twisting (TAT) and turn dynamics to generate GHZ-like states for quantum metrology. Using both analytical semi-classical and quantum approaches, we find that the desired NNN-particle GHZ-like state can be produced in a remarkably short time topt∝ln⁡N/Nt_\mathrm{opt}\propto \ln{N}/{N}topt​∝lnN/N, and its quantum Fisher information FQopt∝N2F^\mathrm{opt}_\mathrm{Q}\propto N^2FQopt​∝N2 approaches the Heisenberg limit. Owing to the rapid state preparation, it shows outstanding robustness against decoherence. Moreover, using the Floquet-engineered anti-TAT-and-turn, one may implement an efficient interaction-based readout protocol to extract the signal encoded in this GHZ-like state. This Floquet-engineered anti-TAT-and-turn approach offers a viable method to achieve effective time-reversal dynamics to improve measurement precision and resilience against detection noise, all without the need to invert the sign of the nonlinear interaction. This study paves a way for achieving entanglement-enhanced quantum metrology via rapid generation of GHZ-like states at high particle numbers through continuous Floquet engineering.
Twist-untwist protocols for quantum metrology consist of a serial application of (1) unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), (2) parameterized dynamics $U(\ensuremath{\phi})$ (e.g., a collective rotation or phase space displacement), and (3) time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of $\ensuremath{\phi}$ even when the nonlinearities are applied for times much shorter than required to produce Schr\"odinger cat states. In this work, we prove that, asymptotically in the number of particles, twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only first and second moments of a total spin operator $\stackrel{P\vec}{n}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{J}$. We consider the following physical settings: all-to-all interactions generated by one-axis twisting Jz2{J}_{z}^{2}Jz2​ (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve 85% and 92% of the respective quantum Cram\'er-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of LLL without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an LLL layer quantum alternating operator ansatz.
Abstract Spin squeezing is a key resource in quantum metrology, allowing improvements of measurement signal-to-noise ratio. Its generation is a challenging task because the experimental realization of the required squeezing interaction remains difficult. Here, we propose a generic scheme to synthesize spin squeezing in non-squeezing systems. By using periodical rotation pulses, the original non-squeezing interaction can be transformed into squeezing interaction, with significantly enhanced interaction strength. The sign of the interaction coefficient is also flippable, facilitating time-reversal readout protocol for nonlinear interferometers. The generated spin squeezing is capable of achieving the Heisenberg limit with measurement precision ∝ 1/N for N particles and its robustness to noises of pulse areas and separations has been verified as well. This work offers a path to extending the scope of Heisenberg-limited quantum precision measurements in non-squeezing systems.
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.
The spin-squeezing protocols allow the dynamical generation of massively correlated quantum many-body states, which can be utilized in entanglement-enhanced metrology and technologies. We study a quantum simulator generating twisting dynamics realized in a two-component Bose-Hubbard model with dipolar interactions. We show that the interplay of contact and long-range dipolar interactions between atoms in the superfluid phase activates the anisotropic two-axis countertwisting mechanism, accelerating the spin-squeezing dynamics and allowing the Heisenberg-limited accuracy in spectroscopic measurements.