Two-Photon Induced Coherence without Induced Emission

TL;DR

The paper addresses realizing quantum-enhanced phase sensitivity in induced coherence without induced emission by employing a two-photon Fock state in a nonlinear interferometer to induce coherence among two-photon SPDC amplitudes. An applied phase $φ_I$ on undetected 1016 nm idler photons produces a $2φ_I$ modulation in the detected 632 nm signal photons, corresponding to a fringe period of 508.2 nm, confirming two-photon induced coherence without induced emission. Coincidence measurements show a two-photon interference visibility of 22%, with reductions attributed to temporal/mode mismatch; a control experiment demonstrates absence of induced emission. The approach enables quantum-enhanced metrology and imaging with undetected photons, expanding access to challenging wavelength regimes and enabling multi-photon induced coherence-based sensing.

Abstract

At the heart of recent breakthroughs in quantum imaging and spectroscopy utilizing undetected photons lies the quantum optical effect known as induced coherence without induced emission. This fundamental quantum interference effect has unlocked new possibilities in accessing challenging wavelength regimes for advanced imaging and spectroscopic analysis. Despite these advancements, the full spectrum of quantum metrology's capabilities, particularly the enhanced phase sensitivity offered by quantum optical Fock states or N00N states, has yet to be realized. This is due to the fact that, until now, the exploration of induced coherence has been confined to phenomena involving single photons. In this study, we present the observation of two-photon induced coherence without induced emission. This advancement hinges on a two-photon Fock state that creates quantum coherence between pairs of two-photon spontaneous emission amplitudes. The result is a doubling of the interferometric phase modulation compared to what is observed with single photons. Specifically, we show that a phase change $φ$ applied to undetected 1016 nm near-infrared photons leads to $2φ$ modulation in the detection of the 632 nm visible photons, verifying two-photon induced coherence without induced emission. These findings pave the way for innovative high-resolution quantum metrological applications leveraging multi-photon induced coherence without induced emission.

Figures (5)

• Figure 1: (a) Ordinary induced coherence without induced emission is observed at detector $D_1$ or $D_2$ as single-photon interference. (b) Proposed two-photon induced coherence without induced emission. The effect is observed in coincidence between detectors $D_1$ and $D_2$.
• Figure 2: Experimental setup corresponding to the schematic shown in Fig. \ref{['fig1']}(b). The idler modes $I_1$ and $I_2$ are overlapped by reflecting $I_1$ with the Idler mirror. DM: dichroic mirror, IF: interference filter, BS: beam splitter,
• Figure 3: Experimental results. Quantum interference at $D_1$, (a), and $D_2$, (b) corresponds to the usual induced coherence without induced emission. (c) Two-photon induced coherence without induced emission observed in coincidence counts. The signal photon exhibits $2 \phi_I$ phase modulation, the hallmark effect for quantum-enhanced sensing in quantum metrology. The solid lines represent the sinusoidal fits to the data points.
• Figure 4: Effects of temporal mode mismatch. (a) Maximum and minimum coincidence counts are recorded for a few different Idler mirror positions. The error bars represent one standard deviation. The solid lines represent the Gaussian fits to the data points, showing the envelope of the two-photon induced coherence. (b) Numerical simulation of two-photon interference fringes, showing the full envelope of the two-photon induced coherence. The inset shows the interference fringe at the center, exhibiting a period of 508.2 nm.
• Figure 5: Single count and two-photon coincidence count rates in $S_2$ mode before and after unblocking the undetected photon mode $I_1$. The data confirm the absence of induced two-photon emission in our experiment.