Retrieving Ideal Precision in Noisy Quantum Optical Metrology

Quantum metrology employs quantum effects to attain a measurement precision surpassing the limit achievable in classical physics. However, it was previously found that the precision returns the shot-noise limit (SNL) from the ideal Zeno limit (ZL) due to the photon loss in quantum metrology based on Mech-Zehnder interferometry. Here, we find that not only can the SNL be beaten, but also the ZL can be asymptotically recovered in a long-encoding-time condition when the photon dissipation is exactly studied in its inherent non-Markovian manner. Our analysis reveals that it is due to the formation of a bound state of the photonic system and its dissipative noise. Highlighting the microscopic mechanism of the dissipative noise on the quantum optical metrology, our result supplies a guideline to realize the ultrasensitive measurement in practice by forming the bound state in the setting of reservoir engineering.

Figure 1

(a) Scheme of MZI-based quantum metrology. Two fields interact at beam splitter ${\mathrm{BS}}_1$ and propagate along two arms. One of the fields couples to a system with the potential influence of quantum noise, by which the estimated parameter $\gamma$ is encoded. After interfering at ${\mathrm{BS}}_2$, the fields are detected by the detectors $D_1$ and $D_2$. (b) Long-time behavior of $|c(t)|$ (dark cyan circles) by solving Eq. (6), which coincides with $Z$ (red solid line) from the bound-state analysis. The inset shows the evolution of $|c(t)|$. (c) Energy spectrum of the whole system of the optical field and its environment. The parameters $s=1$, $\gamma =\pi {\omega }_0$, and $\eta =0.02$ are used.

Figure 2

(a) Evolution of $\delta \gamma (t)$ in the absence of (purple dot-dashed line) and in the presence of (cyan solid line) the bound state, where the local minima match with the curve (red dashed line) of Eq. (11) in long-time condition. Dependence of the local minima of $\delta \gamma (t)$ on time (b) and $N$ (c) in different ${\omega }_c$. Parameters are the same as Fig. 1 except $\beta =(2\sqrt{N}{)}^{-1}$, $N=100$ in (b), and $t=10{\omega }_0^{-1}$ in (c).

Figure 3

Dependence of $\min (\delta \gamma /{\omega }_0)$ on time (a) and $N$ (b) in difference $\eta$. The inset of (b) shows $Z$ (red solid line) coinciding with $|c(\infty )|$ (dark cyan circles) and the energy spectrum. Parameters are the same as Fig. 2 except ${\omega }_c=300{\omega }_0$.