Two-Photon Induced Coherence without Induced Emission

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.