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Physical Review A

Quantum metrology via Floquet-engineered two-axis twisting and turning dynamics

Jihao Ma, Yi Shen, Jiahao Huang, Chaohong Lee

Published Sep 29, 2025• 5 citations
Publisher

Abstract

This work demonstrates a Heisenberg-limited metrology protocol via Floquet-engineered two-axis twisting and turning dynamics. Furthermore, the approach allows for efficient interaction-based readout without inverting the nonlinear interaction, thereby enhancing the robustness against detection noise.
DOI
10.1103/32n5-mhk1

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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.
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-axis twisting (OAT) and two-axis twisting (TAT) are well-known methods for achieving entanglement-enhanced quantum metrology, and their time-reversal echo offers a potent tool for approaching the Heisenberg limit even with detection noise. However, flipping the sign of interaction to implement the time-reversal echo is generally challenging. Here, we propose an echo protocol based on synthetic TAT from interaction-fixed OAT in a pseudospin-1/2 ensemble to achieve time-reversal quantum metrology. By applying modulation pulses around two different orthogonal directions, the effective TAT and its echo can be realized without changing the interaction. We demonstrate that this protocol not only outperforms the OAT echo scheme in both metrological gain and evolution time but is also robust against detection noise. Our protocol presents a TAT echo scheme that effectively avoids flipping the sign of interaction, providing a viable method for improving precision and robustness of quantum metrology.
Quantum error correction has been successfully applied to enhance the precision of parameter estimation in the presence of noise. Nonetheless, existing methods require a number of noiseless, controllable ancillae and lack efficient encoding and decoding procedures. In this Letter, we demonstrate that subsystem error correction provides a new direction that can substantially simplify the metrological protocol. We derive general conditions under which subsystem stabilizer codes achieve the Heisenberg limit and show that, for broad classes of noise, this can be realized by syndrome-free protocols using at most a single ancilla qubit. Furthermore, we extend this framework to dynamical error correction and show that Floquet codes can protect time-dependent metrological signals in reaching the Heisenberg limit.
Spin cat states are promising candidates for quantum-enhanced measurement. Here, we analytically show that the ultimate measurement precision of spin cat states approaches the Heisenberg limit, where the uncertainty is inversely proportional to the total particle number. In order to fully exploit their metrological ability, we propose to use the interaction-based readout for implementing phase estimation. It is demonstrated that the interaction-based readout enables spin cat states to saturate their ultimate precision bounds. The interaction-based readout comprises a one-axis twisting, two $\frac{\ensuremath{\pi}}{2}$ pulses, and a population measurement, which can be realized via current experimental techniques. Compared with the twisting echo scheme on spin squeezed states, our scheme with spin cat states is more robust against detection noise. Our scheme may pave an experimentally feasible way to achieve Heisenberg-limited metrology with non-Gaussian entangled states.