This thesis, mostly experimental, is based on two fundamental pillars: nonlinear interferometers and Optical Coherence Tomography (OCT). Nonlinear interferometers are a class of interferometers that exhibit nonclassical phenomena brought on by nonlinear elements, such as optical parametric amplifiers and parametric down-conversion (PDC) nonlinear crystals. OCT is a non-invasive imaging technique that allows to obtain images with high axial and cross-sectional resolution of a wide variety of samples.

The first novel contribution of this thesis is an experimental scheme that combines the two ideas: an OCT scheme based on a nonlinear interferometer. In these new approach the reflectivity of the sample translates in a loss of first-order coherence between two beams, that is the variable that is measured. In addition, it allows probing the sample with a wavelength different from the one that is measured. In this way, the penetration depth in the sample can be enhanced using longer wavelengths while using light at the optimal wavelength for detection.

We present and implement two different experimental configurations. The first is a nonlinear interferometer based on induced coherence, or Mandel-type interferometer, that works in the low parametric gain regime of parametric down-conversion (PDC). The results presented here are a proof-of-concept, that can potentially offer new applications for OCT, but that are not meant to substitute traditional OCT systems. 

The second OCT scheme overcomes some of the limitations of the first scheme discussed above. It is an SU(1,1), or Yurke-type interferometer, that operates in the high parametric gain regime of parametric down-conversion. In addition to taking advantage of the salutary features of this new approach, it also enables obtaining values of power and axial resolution comparable to those of conventional OCT.

The second novel contribution of this thesis is related to fundamental aspects at the heart of nonlinear interferometers. We discuss two experiments that study two important concepts behind the idea of induced coherence: quantum distinguishability and parametric amplification (stimulated emission). In the first experiment we propose a new experimental measure of quantum distinguishability and derive a complementarity relation between distinguishability and first-order coherence. In the second experiment, we contribute to the ongoing debate about the true role of quantum distinguishability and stimulated emission in explaining the induced coherence effect.

Finally, we put forward theoretically a new scheme to retrieve transverse spatial information of a sample using a nonlinear interferometer, based on projecting the outgoing photons in selected spatial modes. We call this new proposal spatial spectroscopy, and it does not require a physical mechanical scan of the sample. We demonstrate the feasibility of the technique with a simple example. This last contribution constitutes a future proposal to be carried out with nonlinear interferometers, evidencing their great versatility and potential applications in new areas.

Thesis Director: Prof Dr. Juan Pérez Torres