[Paper Review] Diosi-Penrose criterion for solids in quantum superpositions and a single-photon detector

Garrelt Quandt-Wiese|arXiv (Cornell University)|Jan 2, 2017

Mechanical and Optical Resonators18 references3 citations

TL;DR

This paper develops a formulary applying the Diosi-Penrose criterion to solids in quantum superpositions, accounting for both microscopic mass distribution and macroscopic shape. It demonstrates that a single-photon avalanche photodiode can remain in superposition for seconds when isolated, with lifetime tunable to microseconds via a piezoactuator, enabling controlled tests of gravity-induced wave function collapse.

ABSTRACT

A formulary for the application of the Diosi-Penrose criterion to solids in quantum superpositions is developed, which takes the solid's microscopic mass distribution (resulting from its nuclei) and its macroscopic shape into account, where the solid's states can differ by slightly different positions or extensions of the solid. For small displacements, smaller than the spatial variation of the solid's nuclei, the characteristic energy of the Diosi-Penrose criterion is mainly determined by the mass distribution of the nuclei. For large displacements, much larger than the solid's lattice constant, the solid can be idealised as a continuum, and the characteristic energy depends on the solid's shape and the direction of the displacement. In Diosi's approach, in which the mass density operator has to be smeared, the solid's microscopic mass distribution plays no role. The results are applied to a special single-photon avalanche photodiode detector, which interacts as little as possible with its environment. This is realised by disconnecting the detector from the measurement devices when it is in a superposition, and by biasing the photodiode by a plate capacitor, which is charged shortly before the photon's arrival. For a suitable choice of components, the detector can stay in a superposition for seconds; its lifetime can be shortened to microseconds with the help of a piezoactuator, which displaces a mass in the case of photon detection.

Motivation & Objective

• To develop a formulary for applying the Diosi-Penrose criterion to solids in quantum superpositions, incorporating both microscopic mass distribution and macroscopic shape.
• To analyze how the characteristic energy of the criterion depends on displacement scale—microscopic vs. macroscopic—relative to the lattice constant.
• To design a single-photon detector that minimizes environmental coupling, enabling long-lived superpositions for testing quantum gravity effects.
• To demonstrate experimental feasibility of maintaining superposition for seconds and reducing it to microseconds using a piezoactuator.

Proposed method

• Derives the characteristic energy of the Diosi-Penrose criterion based on the solid’s mass distribution for small displacements, where nuclear positions matter.
• Models large displacements as a continuum, showing shape and displacement direction determine the characteristic energy.
• Applies the formalism to a single-photon avalanche photodiode with minimal environmental coupling via capacitor biasing and disconnection during superposition.
• Uses a piezoactuator to induce controlled mass displacement upon photon detection, enabling tunable decoherence times.
• Considers the mass density operator in Diosi’s approach, where microscopic details are smeared, and compares with the current formulary’s sensitivity to nuclear structure.

Experimental results

Research questions

• RQ1 How does the characteristic energy of the Diosi-Penrose criterion depend on the solid’s mass distribution at small displacements?
• RQ2 How does the macroscopic shape and displacement direction affect the characteristic energy at large displacements?
• RQ3 Can a single-photon detector be engineered to remain in superposition for seconds while minimizing environmental interaction?
• RQ4 To what extent can the decoherence time of such a detector be controlled via mechanical displacement?

Key findings

• For displacements smaller than the spatial variation of nuclei, the characteristic energy is primarily determined by the distribution of the solid’s nuclei.
• For displacements much larger than the lattice constant, the solid behaves as a continuum, and the characteristic energy depends on the solid’s shape and displacement direction.
• The detector can remain in superposition for seconds when disconnected from measurement devices and biased via a plate capacitor charged shortly before photon arrival.
• The decoherence time can be reduced to microseconds by using a piezoactuator to displace a mass upon photon detection.
• The formulary accounts for microscopic mass distribution in the Diosi-Penrose criterion, which is neglected in Diosi’s original smearing approach.