Diosi-Penrose criterion for solids and electrical components in quantum superpositions and application to a single-photon detector

Abstract: The Diosi-Penrose criterion is applied to solids in quantum superpositions that are slightly displaced against each other or have different expansions in the superposed states. The calculations take the microscopic mass distribution of the solid's nuclei into account, where the spatial variation of the nuclei is calculated with Debye's model for acoustical phonons. The contribution resulting from the mass concentration in the solid's nuclei can be neglected for displacements larger than ten lattice constants but dominates the superposition's decay for displacements smaller than the spatial variation of the nuclei in the order of a tenth of an Angstroem. In this regime, the parameter-free Diosi-Penrose model predicts significantly higher decay rates than the version in which the mass density is averaged. With the results for solids, formulas for the decay of superposed electrical components, as plate capacitors, resistors, wires and piezo actuators, are derived, which are used to analyse how long a single-photon detector can stay in a superposition of a photon-detected and a no-photon-detected state, and how its lifetime shortens when it displaces a mass with a piezo actuator.