The violation of the Pauli Exclusion Principle (PEP) is a direct consequence of the spin-statistics theorem, a pillar of modern physics. It is responsible for the stability of quantum matter and is connected to the fundamental principles of the Standard Model of particle physics, such as Lorentz invariance and CPT symmetry.

To date, the two main theoretical frameworks that predict a violation of spin-statistics are:

1. The “Quon” model, which is subject to the Messiah-Greenberg (MG) superselection rule. This rule allows for its experimental verification exclusively using open systems. We do this by introducing test fermions into a pre-existing system of fermions and testing the resulting state of symmetry.

2. Quantum Gravity (QG). Despite a century of effort, QG remains one of the most complex challenges in modern physics. This is made worse by the inability to conduct direct experimental investigations near the Planck scale. PAMQ has shown that the experimental verification of effective QG models (such as Non-Commutative QG, or NCQG, and Minimal Length models) by searching for PEP-violating atomic transitions sets the absolute strongest constraints on various QG theories, with a sensitivity that can reach the Planck scale.

Models of Spontaneous Collapse

The superposition principle allows for coherent superpositions of distinguishable physical configurations, a direct consequence of the linearity of the Schrödinger equation. This principle has been verified with remarkable precision at the microscopic level. However, we do not observe superpositions at the macroscopic level, and the mechanism responsible for the quantum-to-classical transition is not encoded in the original framework of Quantum Theory (QT).

PAMQ investigates spontaneous collapse models (Continuous Spontaneous Localization (CSL) and the gravity-induced collapse models developed by Diosi and Penrose, or DP), which offer a rigorous phenomenological approach [Rev. Mod. Phys. 85, 471 (2013)]. A new phenomenological/experimental approach is being developed to test unified field theories.

The experimental activity of PAMQ is conducted in the context of the INFN VIP experiment (for which the PAMQ leader is also the INFN national leader). This experiment operates several cutting-edge apparatuses for very low-background X and gamma rays at the LNGS laboratories.

Today, the study of PEP violation is placing even stronger limits on QG models.

PAMQ has analyzed the entire complex of PEP-violating K-shell electronic transitions in an ultra-radio-pure Roman lead target, improving the sensitivity by about two orders of magnitude compared to existing data. At CREF, the first-ever experimental study of the Triply Special Relativity QG model and the spin-statistics implications of Minimal Length models was also conducted. This demonstrated that this approach improves existing limits by several orders of magnitude.

In the context of the Quon model, investigation through open systems can be carried out by monitoring fermions that have never interacted with any other fermions. The VIP-open-systems experiment, on the other hand, is based on introducing new electrons via a continuous current into a Cu target, using Silicon-Drift-Detectors (SDD) with a thickness of 0.45 mm to measure the X-rays emitted in atomic transitions. The experiment monitors PEP-violating Kα1​ and Kα2​ transitions, whose characteristic energy is 300 eV lower than standard transitions. With this strategy, PAMQ has set the most stringent limit in the literature.

Currently, our group is upgrading the VIP-open-systems experiment. This upgrade is based on the development of innovative SDD detectors to investigate elements of intermediate atomic number.

The intense experimental activity dedicated to spontaneous collapse models is based on a plethora of methodologies (cold atoms, optomechanical setups, phonon excitations in crystals, gravitational wave detectors, or measurements of “spontaneous radiation” in the X or gamma range). PAMQ primarily studies the spontaneous radiation emitted in the (1-15) keV range (an intrinsic effect of the spontaneous collapse dynamics that imposes a diffusive motion on particles), establishing the strongest limits in the literature.

The goal of the PAMQ project is to investigate open problems in quantum mechanics, particularly the relationship between the quantum world and gravity. We aim to push our experimental sensitivity to the threshold of the Planck scale, where quantum properties of the gravitational field might emerge. The implications are enormous, affecting our understanding of the foundations of the Standard Model and of theories that seek to explain the collapse of the wave function.

PAMQ intends to discriminate among various proposed Quantum Gravity (QG) theories, providing experimental guidance for model development. It has the potential to measure a QG signal for the very first time.

The VIP-open-systems experiment, with its improved apparatus, is producing limit values for PEP violation that are orders of magnitude better than what is currently known.

As for the spontaneous collapse models, PAMQ will increase the sensitivity of spontaneous radiation measurements. It will do this from both a theoretical standpoint, by applying the new theory to generalized (non-Markovian) collapse models, and from an experimental standpoint, with a new germanium detector that will make it possible to explore recent unified models of gravity and quantum mechanics.