Quantum Metrology via Floquet-Engineered Two-axis Twisting and Turn Dynamics

TL;DR

This work demonstrates that Floquet-engineered TAT-and-turn dynamics can rapidly generate GHZ-like states with Heisenberg-limited metrological potential in large spin ensembles, with preparation times scaling as t_opt ∝ (ln N)/N and QFI reaching F_Q^opt ∝ N^2. By tuning a transverse drive and detuning, an effective χ_eff and δ_eff yield a TAT-like amplification that outpaces conventional OAT-based schemes, while a Floquet-engineered anti-TAT-and-turn enables time-reversal readout without sign reversal of χ. The authors further develop an interaction-based readout framework that achieves near-QCRB precision and demonstrates robustness against detection noise. Together, these results provide a scalable, robust route to entanglement-enhanced quantum metrology using continuous Floquet engineering and GHZ-like states.

Abstract

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 $N$-particle GHZ-like state can be produced in a remarkably short time $t_\mathrm{opt}\propto \ln{N}/{N}$, and its quantum Fisher information $F^\mathrm{opt}_\mathrm{Q}\propto N^2$ 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.

Figures (7)

• Figure 1: (a) An ensemble of two-level particles ($\chi$ denoting the nonlinear interaction between particles) coupled via an external coupling field with detuning $\delta$ and (b) periodically modulated Rabi frequency $\Omega(t)=\Omega_{0} \cos(\omega t)$. (c) Schematic diagram of Floquet-engineered TAT-and-turn. The classical phase-space trajectory for (i) one-axis-twist $\chi \hat{J}_{z}^2$, (ii) rotation induced by energy imbalance $\delta \hat{J}_{z}$, (iii) rotation induced by modulated linear coupling $\Omega_{0} \cos(\omega t)\hat{J}_{\alpha}$. The combination of these three terms results in (iv) the effective TAT-and-turn dynamics.
• Figure 2: Maximum QFI achieved via Floquet-engineered TAT-and-turn dynamics. (a) The time-evolution of the maximum QFI $F_Q^\mathrm{max}$ for different $\delta$ with the particle number $N=100$, the driving frequency $\omega=2\pi\times10N\chi$ and the angle $\alpha=0$. (b) The time-evolution of the maximum QFI for the Floquet-engineered TAT-and-turn with $\delta_\mathrm{opt}$. The results of OAT, XYZ PhysRevLett.132.113402 and ideal TAT-and-turn are presented for comparison. (c) The enlarged area of (b) for $0\le\chi t \le 0.05\pi$. (d) The probability distribution $P_{m_{y}}=|\langle m_{y}|\psi\rangle|^2$ ($|m_{y}\rangle$ denoting the eigenstates of $\hat{J}_y$) and the Husimi distribution (inset) for the optimal state with largest QFI. (e) The critical detuning $\delta_\mathrm{opt}$ and (f) the critical evolution time $\chi t_\mathrm{opt}$ corresponding to (g) the optimal QFI $F_Q^\mathrm{opt}$ for different particle numbers $N$, in which the semi-classical predictions are $\delta_\mathrm{opt}^\mathrm{SC}/(N\chi)\approx0.3135$, $t_\mathrm{opt}^\mathrm{SC}={3(1.9+0.55\ln{N})}/{N}$ and $(F_Q^\mathrm{opt})^\mathrm{SC}/N\approx0.97N$, respectively. The fitted line for the optimal $F_Q^\mathrm{max}$ is $F_Q^\mathrm{opt}/N\simeq0.77N$. (h) The optimal QFI $F_Q^\mathrm{opt}$ versus the decoherence strength $\Gamma$ in generating GHZ or GHZ-like state by OAT, XYZ, and TAT-and-turn dynamics, respectively. The black dashed (dash-dotted) line indicates the SQL (HL)
• Figure 3: (a) Measurement precision yielded from Floquet-engineered anti-TAT-and-turn. The metrological gain is defined as $G=20 \log _{10} \left[{(\Delta \phi)_{\mathrm{SQL}}}/{\Delta \phi}\right]$ with $(\Delta \phi)_{\mathrm{SQL}}=1/{\sqrt{N}}$ denoting the measurement precision of SQL. (b) Robustness against detection noise. The green dashed line is the result of population measurement $\langle\hat{J}_{z}\rangle_{\sigma}$ after Floquet-engineered anti-TAT-and-turn with $\chi t=0.12$. The blue dash-dotted and yellow dotted lines are results of parity measurement $\langle\hat{\prod}\rangle_{\sigma}$ for GHZ-like and GHZ states generated by XYZ and OAT dynamics, respectively. Here, the black dashed (dash-dotted) line indicates the SQL (HL). The driving frequency is set to $\omega = 2\pi \times 100N\chi$, and $\alpha = \pi/2$. These parameters, along with a particle number of $N = 100$ and an estimated phase of $\phi = 1/1000$, are selected for the simulation of FE-TATNT.
• Figure 4: (a) The probability distributions of GHZ-like state generated by Floquet-engineered TAT-and-turn dynamics and its corresponding spin cat state with $\theta=\arccos{\overline{Z}}$ for particle number $N=100$. (b) The QFI of GHZ-like states generated by Floquet-engineered TAT-and-turn dynamics and their corresponding spin cat states with $\theta=\arccos{\overline{Z}}$ versus different particle number $N$.
• Figure 5: (a) The IBR and QCRB for TAT-and-turn. (b) The attainable measurement precision of TAT-and-turn at $t=0.12$ via IBR for $\phi$ approaching 0. (c) The time evolution of maximum QFI for OAT, OAT-and-turn, Floquet-engineered TAT, and Floquet-engineered TAT-and-turn. (d) The IBR without flipping the sign of nonlinear interaction for OAT, OAT-and-turn, Floquet-engineered TAT and Floquet-engineered TAT-and-turn. The metrological gain is defined as $G=20 \log _{10} \left[{(\Delta \phi)_{\mathrm{SQL}}}/{\Delta \phi}\right]$ with $(\Delta\phi)_{\mathrm{SQL}}=1/{\sqrt{N}}$ denoting the measurement precision of SQL. The phase $\phi=1/1000$ and particles number $N=100$ are chosen for simulation.