Enhancing information retrieval in quantum-optical critical systems via quantum measurement backaction

TL;DR

The paper introduces a quantum-sensing protocol that leverages measurement backaction in open quantum-optical sensors near dissipative critical points to push frequency-estimation precision toward the quantum Cramér-Rao bound. By analyzing an open Kerr parametric oscillator under general-dyne monitoring, the authors identify backaction-evading critical points and show that the continuous-monitoring Fisher information dramatically increases near these points. They develop a deterministic, Gaussian-state formalism to compute the relevant Fisher informations: the continuous FI $F(\varphi,s)$ and the global QFI $I_G$, showing linear growth in time with identifiable growth rates $k_F$ and $k_G$. An optimization strategy over measurement parameters $(\varphi,s)$ enables the conditional state to match the global information in the long-time limit, offering a practical route to quantum-enhanced sensing in dissipative-critical quantum-optical systems.

Abstract

Continuous monitoring of open quantum-optical systems offers a promising route towards quantum-enhanced estimation precision. In such continuous-measurement-based sensing protocols, the ultimate precision limit is dictated, through the quantum Cramér-Rao bound, by the global quantum Fisher information associated with the joint system-environment state. Reaching this limit with established continuous measurement techniques in quantum optics remains an outstanding challenge. Here we present a sensing protocol tailored for open quantum-optical sensors that exhibit dissipative criticality, enabling them to significantly narrow the gap to the ultimate precision limit. Our protocol leverages a previously unexplored interplay between the quantum criticality and the quantum measurement backaction inherent in continuous general-dyne detection. We identify a performance sweet spot, near which the ultimate precision limit can be efficiently approached. Our protocol establishes a new pathway towards quantum-enhanced precision in open quantum-optical setups and can be extended to other sensor designs featuring similar dissipative criticality.

Figures (10)

• Figure 1: Phase diagram of the open KPO without continuous general-dyne measurement. The black solid curve at $\delta\epsilon=0$ marks the phase boundary separating the normal phase (N) and the symmetry-broken phase (SB). The insets illustrate that under homodyne detection, a backaction-evading CP (red diamond) emerges at $(\omega_\text{be},\epsilon_\text{be})$ (given by Eq. (\ref{['eq:epsilonomega']})), when the squeezing angle $\theta_0$ of the unconditional steady-state in the normal phase match the angle $\varphi$ (here $\varphi=0.6$). The green crosses are described in Fig. \ref{['fig:becpnumerics']}.
• Figure 2: (a) Covariance component $[\mathbf{\Sigma}_\text{ss}]_p$ evaluated (left) on the phase boundary $\delta\epsilon=0$ and (right) near the phase boundary $\delta\epsilon=0.03\kappa$ for different detection efficiency $\eta$. Vertical dashed lines indicate the location of the backaction-evading CP for $\varphi=0.6$. Note that, the curve corresponding to $\eta=0$ is not shown in the left panel as $[\mathbf{\Sigma}_\text{ss}]_p$ diverges on the phase boundary in the unconditional case. (b) Time evolution of the variance of the integrated photocurrent $\mathbb{E}[\mathbf{y}_t^\intercal\mathbf{y}_t]$ for selected $\omega$ along $\delta\epsilon=0.03\kappa$. Inset shows the current profile at $\kappa t=100$. The minimum location $\omega\approx0.1825\kappa$ in this case, alongside those for $\delta\epsilon/\kappa=0.02,0.01,0.005$, are shown as green crosses in Fig. \ref{['fig:figbecp']}. All simulations correspond to homodyne detection with $s=0$ and $\varphi=0.6$.
• Figure 3: (a) The long-time growth rate $k_F$ of the FI $F(\varphi,s)$ under homodyne detection as a function of $\omega$ and $\epsilon$. The red diamond corresponds to the backaction-evading CP for $\varphi=0.6$. (b) Optimization of $k_F$ over the parameters $\varphi$ and $s$ for $(\omega,\delta\epsilon)=(0.2\kappa,0.03\kappa)$, marked by the green circle in (a). The optimal general-dyne measurement is identified as $(s_\text{opt},\varphi_\text{opt})=(0,0.583)$ (blue star). The inset compares the FI $F(\varphi_\text{opt},s_\text{opt})$ under this optimal measurement and the corresponding global QFI denoted as $I_G$ . All simulations assume ideal detection efficiency $\eta=1$.
• Figure 4: (a) The growth rates $k_F^\text{opt}$ (symbols) and $k_G$ (lines) and (b) their ratio $k_F^\text{opt}/k_G$ as functions of $\omega$ for $\delta\epsilon/\kappa = 0.06$, $0.03$ and $0.02$. The solid curve in (b) represents the linear extrapolation of $k_F^\text{opt}/k_G$ to the phase boundary $\delta\epsilon=0$. (c) Four selected examples illustrating the linear extrapolation of $k_F^\text{opt}/k_G$. All simulations assume ideal detection efficiency $\eta=1$.
• Figure 5: (a) Optimization of $k_F$ for $(\omega,\delta\epsilon)=(0.2\kappa,0.03\kappa)$ with non-ideal detection efficiency $\eta=0.8$. The optimal general-dyne measurement occurs at $(s_\text{opt},\varphi_\text{opt})=(0.022,0.574)$ (blue star) while the optimal homodyne is achieved $(s,\varphi)=(0,0.56)$ (green triangle). (b) Time evolution of the corresponding FI for the optimal homodyne and general-dyne detection schemes in (a), compared with photon counting with the same efficiency.