10. Open Problems in Quantum Mechanics (PAMQ)

The aim of the PAMQ project is to perform high sensitivity tests of:

1. The Pauli Exclusion Principle (PEP) for electrons.
2. Models of wave-function collapse.

1) The VIP-2 experiment consists in two, intertwined and complementary research branches, each of them characterized by a set of dedicated experiments:

1.1) VIP-2 Open Systems: is the most sensitive experimental test of the PEP for electrons, in the context of Local Quantum Field theories. Such models are constrained by the Messiah-Greenberg (MG) superselection rule, which forbids transitions among states with different symmetry, and can then only be tested in open systems. Such a condition is realized in VIP-2 by introducing new electrons in a pre-existing system of electrons, and testing the resulting symmetry state. The setups under use are characterized by: a) an electrolytic copper target coupled to Silicon Drift Detectors  b) an extreme radio-purity Roman target and High Purity Germanium Detectors. Both experiments are operated at the underground Gran Sasso National Laboratory of (INFN), where the cosmic rays background is reduced of about six orders of magnitude. Such an environment is ideal for the measurement of extremely low-rate physical processes. The experiments set the most competitive upper limits on the PEP violation probability for the models introduced above.

1.2) VIP-2 Closed Systems: according to a large class of  Quantum Gravity models, PEP should be violated at the space-time operators non-commutativity scale. Such models violate MG and can be tested with closed systems. We are presently realizing a new apparatus which is based on Broad Energy Germanium detectors. Our goal is to improve our current limit of four orders of magnitude, in order to be sensitive to the non-commutativity energy scale. This will either unveil a signal, or lead to a falsification of the models.

2) test of wave-function collapse models: the Continuous Spontaneous Localization (CSL) and the Diosi-Penrose (DP) models consist in non-linear and stochastic modifications to the Shrödinger equation, which induce the wave function collapse with a strength which is proportional to the collapsing quantum state’ mass. In both models the collapse is related to unavoidable emission of a characteristic “spontaneous radiation”, which is not present in standard quantum mechanics. We have recently falsified the DP model (gravity-related collapse), this research article was published in  Nature Physics. We also set the most stringent constraint on the CSL model, in a broad range of the parameters space. A new study is presently ongoing in order to challenge the ultimate limit, which is predicted by the CSL for the spontaneous radiation rate.

The figure shows: panel a) top – scheme of the VIP-2 copper experiment, inside the vacuum chamber the tagret, the Silicon Drift Detectors, the cooling system and the veto system are recognizable. Panel a) bottom – fit of the measured X rays spectrum and corresponding residuals, in the region of interest for the search of eventual PEP violating Kα transitions in copper (the calculated position for the violating line is indicated in by the red arrow). Panel b) top – energy spectrum measured with the High Purity Germanium detector; in the inset the 60Co lines are highlighted in green, the region of interest (ROI) for the spontaneous radiation emission, due to the gravitationally induced collapse, is indicated in grey. Panel b) bottom – representation of the inner components of the experimental apparatus: 1 – Ge crystal, 2 – Electric contact, 3 – Plastic insulator, 4 – Copper cup, 5 – Copper end-cup, 6 – Copper block and plate, 7 – Inner Copper shield, 8 – Lead shield.