Coherent Amplifier-Empowered Quantum Interferometer: Preserving Sensitivity and Quantum Advantage under High Loss

Abstract

Quantum interferometers offer phase measurement capabilities that surpass the standard quantum limit (SQL), with phase sensitivity and quantum enhancement factor serving as key performance metrics. However, practical implementations face severe degradation of both metrics due to unavoidable losses, representing the foremost challenge in advancing quantum interferometry toward real-world applications. To address this challenge, we propose a coherent-amplifier-empowered quantum interferometer. The coherent amplifier dramatically suppresses the decay of both sensitivity and quantum enhancement under high-loss conditions, maintaining phase sensitivity beyond the original SQL even for losses exceeding 90%. Using an injected 4.2 dB squeezed-vacuum state in experimental demonstration, our scheme reduces the quantum enhancement degradation under 90% loss from 3.7 dB in a conventional quantum interferometer (CQI) to only 1.5 dB. More importantly, the phase sensitivity degradation under the same loss is limited to 4.0 dB, markedly outperforming the 11.2 dB degradation observed in a CQI. This improvement is enabled by the coherent amplifier's phase-sensitive photon amplification and its protection of the quantum state. This breakthrough in amplifier-empowered quantum interferometry overcomes the critical barrier to practical deployment, enabling robust quantum-enhanced measurements in lossy environments.

Figures (4)

• Figure 1: Quantum interferometer schemes. (a) CQI: conventional quantum interferometer. The splitting ratio of the two beam splitters, BS1 and BS2, is 0.5:0.5, respectively. (b) $\mathrm{{QI_{T}^{G}}}$: quantum interferometer integrated with a coherent amplifier (CA) of gain factor $G$ and BS1 of adjustable splitting ratio $T:(1-T)$. The splitting ratio of BS2 is 0.5:0.5. $a_{0}$: input coherent state; $S_{0}(r)$: input squeezed vacuum state; $r$: squeezing degree; $l$: optical loss rate of arm $b_{1}$; $\phi=\phi_{1}-\phi_{2}$: phase shift. Blue shades: phase-space noise at each position.
• Figure 2: Theoretical results. (a-b) Signal and noise versus gain $G$ for QI$_{T}^{G}$ at $l$ = 0.2 and 0.9, respectively. Signal-$G$: the amplified signal; noise-$G$: the amplification-induced noise; noise-$l$: the loss-induced noise; noise-$t$: total noise, the sum of noise-$G$ and noise-$l$. (c-d) The relative signal-to-noise ratio (SNR) and quantum enhancement $M$ as functions of gain $G$ in QI$_{T}^{G}$, plotted for different loss rates $l$. The zero level is the result of CQI at $r=0, l=0$. (e-f) Optimal sensitivity and quantum enhancement versus loss rate $l$. Dashed, dotted and solid curves correspond to CQI, QI$^{G}$ ($G_{opt}$ and T=0.5), and QI$_{T}^{G}$ ($G_{opt}$ and $T_{opt}$), respectively. The green and black dash-dotted lines in (e) represent the SQL and the lossless CQI sensitivity, respectively. The SQL is obtained by $1/\sqrt{N}$ with $N=4\times 10^{14}$. The squeezing degree of the injected squeezed-vacuum state is 10 dB (r=1.15). $M=-20\log _{10}[\delta \phi _{r}/\delta \phi _{r\rightarrow 0}]$.
• Figure 3: Experimental setup of QI$_{T}^{G}$. (a) Experimental setup. Squeezed state generation is that the coherent field $a_{0}$ (red solid line, horizontal polarization) generates the squeezed vacuum field $S_{0}$ (red dashed line, vertical polarization) in the $^{87}$Rb atomic cell via polarization self-rotation effect. The frequencies and spatial modes of the $a_{0}$ and $S_{0}$ fields are the same. HWP: half-wave plate; PBS: polarization beam splitter; BS: beam splitter; EOM: electro-optic modulator; LE: laser etalon (filter out the unnecessary light); PZT: piezoelectric transducer; CA: coherent amplifier; GL: Glan polarizer (filtering the excessive pump field); VA: variable attenuator, simulating the loss $l$; M: mirror; PD: photoelectric detector; BD: balanced detection of intensity-difference; PID: proportional-integral-derivative phase-locking device; SA: spectrum analyzer; $P$: the pump field (blue line, horizontal polarization) for CA. This $P$ field derives from the $a_{0}^{\prime }$ after a 6.83 GHz frequency shift via the EOM. (b) Atomic energies of the CA. $b_{1}^{\prime }$ is the amplified $b_{1}$. $\left\vert g\right\rangle$: $\left\vert 5^{2}S_{1/2},F=1\right\rangle$; $\left\vert m\right\rangle$: $\left\vert 5^{2}S_{1/2},F^{\prime }=2\right\rangle$; $\left\vert e\right\rangle$: $\left\vert 5^{2}P_{1/2},F^{\prime \prime }=1\right\rangle$. $\Delta =600$ MHz.
• Figure 4: Experimental results. The signal (a), noise (b), phase sensitivity (c) and quantum enhancement (d) as functions of loss rate $l$ for CQI (red square), QI$^{G}$ (with $G_{opt}$, $T=0.5$, blue dot), and QI$_{T}^{G}$ (with $G_{opt}$ and $T_{opt}$, black triangle). The squeezing degree of the input squeezed-vacuum field is 4.2 dB. The solid lines represent the theoretical results with parameters $N=1.2\times 10^{15}, r=0.48$ (i.e., 4.2 dB squeezing).