Entanglement-enhanced quantum metrology via alternating in-phase and quadrature modulation

Abstract

Quantum metrology harnesses quantum entanglement to improve measurement precision beyond standard quantum limit. Although nonlinear interaction is essential for generating entanglement, during signal accumulation, it becomes detrimental and therefore must be suppressed. To address this challenge, we propose an alternating in-phase and quadrature modulation (AIQM) scheme, designed to operate under a fixed nonlinear interaction. During signal accumulation, our time-interleaved approach sequentially applies the in-phase and quadrature driving fields, thereby eliminating the effects of nonlinear interaction on signal accumulation. Our AIQM scheme achieves better metrological performance than conventional schemes, particularly under strong nonlinear interaction and prolonged signal accumulation, with pronounced robustness against parameter variations. By selectively eliminating and utilizing nonlinear interactions via AIQM, our work enables high-precision and high-accuracy entanglement-enhanced sensing without the need for active control of the nonlinear interaction.

Figures (4)

• Figure 1: (a) Schematic of an ensemble of interacting two-level particles under in-phase and quadrature driving fields. (b) Energy level diagram of the particle. Here, $\chi$ stands for atom-atom interaction strength, $\omega_{0}$ is the transition frequency to be estimated, $\omega_{c}$ is the carrier frequency, and $\omega_{m}$ is the modulation frequency. (c) Time sequence of alternating in-phase and quadrature modulation (AIQM) during a signal accumulation duration of $t_s=2mnT$. The in-phase and quadrature Rabi frequencies are periodically alternated between $\left[ \Omega_{I}(t)=\Omega, \Omega_{Q}(t)=0 \right]$ and $\left[\Omega_{I}(t)=0, \Omega_{Q}(t)=\Omega\right]$ at the intervals of $nT=2n\pi/\omega_{m}$. (d) State evolution during signal accumulation with and without AIQM.
• Figure 2: (a) The population imbalance expectation $\langle \hat{J}_z \rangle$, (b) the population imbalance uncertainty $\Delta\hat{J}_z$, and (c) the estimation precision $\Delta\omega_{0}$ for a OAT system with AIQM (cyan solid line) and without AIQM (purple dotted line). The dependence of $\Delta \omega_{0}$ on (d) the rescaled signal accumulation time $\chi t_s$ and the interaction strength $\chi$ for (e) $t_s = 0.01\delta^{-1}$) and (f) $t_s = 0.1\delta^{-1}$. The black dashed lines are obtained from the effective Hamiltonian \ref{['H_eff_s']}. The gray dash-dotted line indicates the SQL. Here, $N=100$, $\omega_{m}=2\pi\times 20N\chi$, $t_s=0.01\chi^{-1}$, $\chi=1$ for (a)-(d), $\delta=1$ for (d)-(f).
• Figure 3: The robustness of estimation precision $\Delta \omega_{0}$ against different control parameters: (a) the modulation frequency $\omega_{m}$, (b) the ratio of Rabi frequencies $\Omega/\omega_{m}$, and (c) the phase $\alpha=\arctan(\Omega_{Q}/\Omega_{I})$ in the second period. Here, $N=100$, $t_s=0.01\chi^{-1}$, $\omega_{m}=2\pi\times 20N\chi$, $\delta=\chi=1$.
• Figure 4: The full-stage AIQM protocol for quantum metrology via selective utilization and suppression of OAT interaction. Under a fixed OAT interaction, the AIQM is applied in the whole procedure: (a) entanglement preparation, (b) signal accumulation, and (c) interaction-based readout. (d) The performance of schemes with (the cyan solid line) and without (the purple dotted line) AIQM. The result of effective time-independent Hamiltonians (the black dashed line) is shown for comparison. (e) The precision scaling versus the particle number $N$. The pink dashed line is the fitted for the AIQM protocol with $\Delta \omega_{0} /\chi=270 N^{-0.95}$. (f) The robustness against the detection noise for $t_s=0.01\chi^{-1}$. Here, $N=100$, $\omega_{m}=2\pi\times 100N\chi$, and $\delta=\chi=1$.