  Nonlinear interferometers with correlated photons hold a promise to advance
optical characterization and metrology techniques by improving their
performance and affordability. Nonlinear interferometers offer the sub-shot
noise phase sensitivity and enable measurements in detection-challenging
regions using inexpensive and efficient components. The sensitivity of such
interferometers, defined by the ability to measure small shifts of interference
fringes, can be significantly enhanced by using multiple nonlinear elements, or
crystal superlattices. However, to date, the experiments with no more than two
nonlinear elements have been realized, thus hindering the potential of
nonlinear interferometers. Here, we build a nonlinear interferometer with up to
five nonlinear elements in a highly-stable and versatile configuration. We
study the modification of the interference pattern in different configurations
of the superlattice and perform a proof-of-concept gas sensing experiment with
enhanced sensitivity. Our approach offers a viable path towards broader
adoption of nonlinear interferometers with correlated photons for imaging,
interferometry, and spectroscopy.
