Effect of environment on the interferometry of clocks.

Mach-Zhender interferometry involving spatial superposition of a massive particle with its internal degrees of freedom (DOF) modelled as \textit{clocks} had been previously proposed as an experiment encapsulating genuine general relativistic effects on quantum systems. We have analysed a realistic model of the \textit{clocks} in which they are subject to the effects of environment leading to noise during their transit through the arms of the interferometer. By modelling the environment as quantum DOF interacting with the clock, we have shown that interferometric visibility is affected by the noise. We have shown that the visibility can increase or decrease depending on the type of noise and also the time scale and transition probabilities in the noise models. The quantification of the aforementioned effect on the visibility paves the way for a better estimate on the expected outcome of an experiment wherein the clocks cannot be effectively shielded from the noise.