Two-Photon Induced Coherence without Induced Emission

Abstract: At the heart of recent advances in quantum imaging and spectroscopy with undetected photons is the quantum optical effect known as induced coherence without induced emission. This quantum interference effect has enabled access to challenging wavelength regimes for imaging and spectroscopic applications. However, the potential of undetected photon quantum metrology, particularly the enhanced phase sensitivity offered by Fock or N00N states, has not yet been realized, as prior work focused only on single-photon phenomena. Here, we report the observation of two-photon induced coherence without induced emission. Using a two-photon Fock state, we establish quantum coherence between pairs of two-photon spontaneous emission amplitudes, resulting in a doubling of interferometric phase modulation. Specifically, we show that a phase shift $\phi$ applied to undetected 1016 nm photons leads to a $2\phi$ modulation in the detection of 632 nm photons. This demonstrates genuine two-photon induced coherence without induced emission and opens possibilities for quantum-enhanced phase measurements using multi-photon coherence without detecting the modulated photons.