Quantum Enhanced Precision Estimation of Transmission with Bright Squeezed Light

Squeezed light enables measurements with sensitivity beyond the quantum noise limit (QNL) for optical techniques such as spectroscopy, gravitational wave detection, magnetometry, and imaging. Precision of a measurement—as quantified by the variance of repeated estimates—has also been enhanced beyond the QNL using squeezed light. However, sub-QNL sensitivity is not sufficient to achieve sub-QNL precision. Furthermore, demonstrations of sub-QNL precision in estimating transmission have been limited to picowatts of probe power. Here we demonstrate simultaneous enhancement of precision and sensitivity to beyond the QNL for estimating modulated transmission with a squeezed amplitude probe of $0.2$ mW average ($25$ W peak) power, which is 8 orders of magnitude above the power limitations of previous sub-QNL precision measurements of transmission. Our approach enables measurements that compete with the optical powers of current classical techniques, but have both improved precision and sensitivity beyond the classical limit.

Figure 1

Modeling enhanced precision measurement of ${\delta }_m$, and experimental setup. (a)–(c) Plots of spectral noise power illustrating the effect of amplitude squeezing and modulation on a typical laser source, with the quadrature diagrams showing a coherent state defined by $\hat{x}$, $\hat{p}$ at $\pm \mathrm{\Omega }$. (d) Theoretical model of the Fisher information per detected photon ${\mathcal{F}}^{\prime }({\delta }_m)$ for typical laser light that is quantum noise limited at $\mathrm{\Omega }$ (solid line) and squeezed light (dashed lines): $-1.6$ and $-2.6$ dB are the measured and inferred generated squeezing levels in our experiment, $-5.7$ dB is amplitude squeezing previously achieved using an asymmetric Kerr interferometer [31], and $-15$ dB is the highest measured squeezing to date [9]. For each plot, $M=1$, $P=0.2$ mW, $\lambda =740$ nm, $\eta =1$, ${\delta }_m=1\times {10}^{-4}$ and $\mathrm{Var}(\mathrm{Re}[\mathcal{H}])=1\times {10}^{-5}$. (e) Schematic of the experiment and SEM image representative of the birefringent photonic crystal fiber (PCF) structure. A pulsed laser at $740$ nm propagates into a Sagnac interferometer for squeezed state generation. A PCF provides the nonlinear medium for Kerr squeezing. An electro-optic modulator (EOM) combined with polarizing beam splitter (PBS) are used to generate AM, which is measured with a spectrum analyzer (SA).

Figure 2

Observing a precision enhancement in parameter estimation using amplitude squeezed light. In each panel, the black dashed line represents the QNL. (a) $10$-MHz AM measured by direct detection. The red trace corresponds to $-1.2$ dB of squeezing and the blue trace to $2.7$ dB of antisqueezing. (b) Measured quantum precision enhancement of experimentally estimated ${\delta }_m$, $\mathcal{Q}({\hat{\delta }}_m)$, for different squeezing $\mathrm{\Phi }$. The red line corresponds to ${\mathcal{Q}}_{\mathrm{opt}}$. (c) Measured $\mathcal{Q}({\hat{\delta }}_m)$ with varied RBW $B$, for an average $-1.3$ dB of squeezing.