The project consists of an integrated theoretical and experimental program aimed at addressing open problems in quantum mechanics and its unification with gravity. The research focuses on analyzing the spin-statistics connection and the spontaneous collapse of the wave function, employing advanced atomic physics techniques across a series of experiments that leverage cutting-edge technologies. Within the scope of the project, innovative Silicon Drift Detectors (SDD) and High-Purity Germanium (HPGe) detectors are developed and utilized. Machine Learning (ML) algorithms and Convolutional Neural Networks (CNN) are optimized for pulse shape analysis, event selection, and data interpretation in order to identify deviations or unexpected spectral features that could indicate signals of new physics.

PAMQ places the strongest bounds on various models of quantum gravity and spontaneous collapse, providing a powerful tool to investigate the fundamental symmetries of nature and advancing our understanding toward a unified theory.

Violation of the spin-statistics connection – The Pauli Exclusion Principle (PEP) derives from the spin-statistics theorem, which is fundamental to the stability of quantum matter and linked to core principles of the Standard Model (SM) such as Lorentz invariance and CPT symmetry. Its phenomenological investigation constitutes an extremely sensitive test of the foundations of the SM. Possible violations of statistics have been explored since Fermi’s pioneering work; today, two main research avenues emerge:

• Quantum Gravity (QG) – QG represents a central challenge in modern physics, partly due to the direct experimental inaccessibility of the Planck scale. PAMQ has demonstrated that searching for PEP-violating atomic transitions allows for the testing of effective QG models, such as Non-Commutative QG (NCQG) and Minimal Length, imposing extremely stringent constraints with sensitivity reaching up to the Planck scale. In such theories, Lorentz invariance is deformed, implying violations of spin-statistics and the PEP.

• “Quon” model [Phys. Rev. Lett. 83, 4460 (1999)] – Subject to the Messiah-Greenberg (MG) superselection rule, this model allows for tests only within open systems by introducing test fermions into pre-existing systems. Its phenomenological nature requires the exploration of a broad spectrum of PEP-violating processes across the periodic table. Recent developments in parastatistics models [Nature 637, 314–318 (2025)] demand dedicated verification. PAMQ has established the most stringent limit to date [4].

Spontaneous collapse models – The superposition principle, while valid at the microscopic level, does not manifest macroscopically, giving rise to the measurement problem. PAMQ studies spontaneous collapse models, such as the gravitational models of Diósi and Penrose (DP) or the Continuous Spontaneous Localization (CSL) model, which resolve this issue [Rev. Mod. Phys. 85, 471 (2013)] and predict a characteristic spontaneous radiation. The DP model has stimulated developments in gravitational decoherence within QG [Nat. Comm. 12, 4449 (2021)] and [38], as well as Hybrid Dynamics [Phys. Rev. X 13, 041040 (2023)]. In this context, PAMQ is developing a new approach that combines spin-statistics and decoherence to test unified field theories.

The experimental activity of PAMQ is carried out within the framework of the VIP experiment, which utilizes advanced X-ray and gamma-ray detectors in the ultra-low background environment of the INFN Gran Sasso National Laboratories, where the PAMQ principal investigator also serves as the INFN national spokesperson.