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

TL;DR

This paper investigates how long isolated single-photon detectors can stay in quantum superpositions according to the Di"osi-Penrose criterion, proposing designs that maintain superpositions for seconds and enabling new tests of wavefunction collapse.

Contribution

It introduces a method to construct indirect single-photon detectors that remain in superposition for seconds, facilitating experimental tests of wavefunction collapse models.

Findings

Detectors can stay in superposition for seconds with specific design.

Proposes using these detectors to generate and study mirror superpositions.

Enables new experimental probes of wavefunction collapse mechanisms.

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.