Towards Quantum Superpositions of a Mirror: An Exact Open Systems Analysis

We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirror’s dynamics contains a nonunitary term of the Lindblad-type proportional to $-[q,[q,\rho ]]$, with $q$ the position operator for the center of mass of the mirror, and $\rho$ the statistical operator. We derive an exact formula for the fringe visibility for this system. We discuss the consequences of our result for tests of environmental decoherence and of collapse models. In particular, we find that with the conventional parameters for the continuous spontaneous localization model of state vector collapse, maintenance of coherence is expected to within an accuracy of at least 1 part in ${10}^8$. Increasing the apparatus coupling to environmental decoherence may lead to observable modifications of the fringe visibility, with time dependence given by our exact result.