Fourier transform spectroscopy: A tool for quantum optics studies

Most of the experimental interferometric setup are based on the Mach-Zehnder geometry. Usually in the experimental configurations the photons travel in air, at a speed v independent of λ. An integrated optics approach appears necessary both for practical applications and because it can be useful for fundamental optics studies because the transmitted photons are in a spatial coherent state. We exploited a hybrid setup integrating optical fibres and monolithic optical waveguides to implement an asymmetric nonlinear Mach-Zehnder Interferometer (ANLI). One arm of the interferometer was equipped with a single mode Er:LiNbO3 waveguide, acting as nonlinear component whereas the other arm was an undoped LiNbO3 single mode waveguide, used to obtain a phase shift through the application of a voltage ramp. We injected in the ANLI a 980 nm laser radiation to collect interferograms that could be ascribed exclusively to the pump photons, as all frequency conversion events are localized only in one arm of the interferometer. The Fourier Transform analysis of the experimental data allowed us to perform a n Interaction-Free Quantum Optics experiment. This is a novel approach that can be used because in quantum mechanics the wave functions of a state, expressed in terms of two conjugate variables, are Fourier Transform pairs. In fact, operating in the Fourier Transform time-frequency space-domain, we recovered the spectral composition, in the wavenumber space-domain, of the photons generated by the excitation of an Er3+ doped crystal placed in one arm of the interferometer.