How long single-photon detectors stay in quantum superpositions during detection according to the Di\'osi-Penrose criterion

Abstract

For special single-photon detectors that are isolated from their environment during detection (so-called indirect detectors), it is investigated how long they stay in a superposition of a photon-detected and a no-photon-detected state according to the Di\'osi-Penrose criterion for wavefunction collapse. To suppress interactions with the environment during detection, the avalanche photodiodes of the indirect detectors are biased using plate capacitors rather than conventional voltage sources, and the detection outcome is read out a sufficient time after the superposition in the detector has reduced. For the analysis, the Di\'osi-Penrose criterion is applied to solids in quantum superpositions that are slightly displaced relative to each other or have slightly different expansions in the superposed states, where both the parameter-free Di\'osi-Penrose model and Di\'osi's version, in which the microscopic mass distribution is spatially averaged, are discussed. It is shown that indirect single-photon detectors can be constructed in such a way that they remain in superposition for seconds. It is proposed to use indirect detectors for the generation of mirror superpositions with the help of piezo-actuators, where the superposed mirror can have a displacement of about 50 Angstrom for approximately half a microsecond. Even though the superposed mirror states generated in this way are decoherent superpositions (improper mixtures) and therefore cannot be detected by conventional methods, their generation opens new perspectives for probing wavefunction collapse.