The goal of this thesis is to investigate the viability of reflection-based biphoton Hong-Ou-Mandel Interferometry (HOMI) for measuring a sub-nanometer step size. We attempt to push this technology forward by designing for larger separation than has been done before in the literature, resulting in higher possible precision.
This is a Fisher-information-based estimation method. We show that the Quantum Cramér-Rao (QCR) bound can be saturated with our proposed measurement. We propose a mostly common-path interferometer design, where the two optical paths are distinct in polarization instead of spatial mode. This reduces the risk of creating accidental which-path information.
For the production of the photon superposition, we propose a novel biphoton source design specialized for large detuning between the two downconverted wavelengths, similar to the more common beamdisplacer entangled photon sources. The proposed photon source can be designed for type-0 and type-II SPDC.
We suggest a detection system based on a combination of visible and NIR single-photon detectors to handle larger detunings than is possible with a single type of detector. The best combination of detectors and type of SPDC was Si-SPAD (visible) and SNSPD (NIR) with weak downconversion focusing (ξ ≪ 1).
This experiment has an expected measurement time of 7.4 seconds for 0.1 nm precision. We conclude that biphoton HOMI is indeed feasible for high-precision metrology.

The behavior of light is well understood and well documented in many different scenarios. Nonetheless the situations can get more complicated. We can easily calculate the electromagnetic field confined to a cubic volume by solving the wave equations. However, this is not so easy for arbitrary geometries of the boundary. The wave equation most likely does not have well defined Eigenmodes for arbitrary shape of the boundary and conditions on this boundary. This complex situation can give a chaotic field. In this bachelor thesis we are going to investigate this situation for a 2-dimensional cavity in the shape of a quarter stadium, in which light can move freely and is reflected on the boundaries. The shape of our cavity is expected to result in a really chaotic field, whose properties will be studied in detail below. We will introduce ergodicity and compare the behaviors of a chaotic and non-chaotic cavity using ergodic properties and looking at the divergence of two neighboring trajectories. Furthermore we will look at the onset of chaos in the wave field inside the cavity and suggest a test to determine if a field is completely chaotic.