Toward nuclear physics on a spin quantum simulator by detecting quantum phase transitions in the Agassi model

A central challenge in nuclear physics is understanding quantum many-body systems governed by the strong nuclear force. The inherent complexity of these systems, combined with the limitations of classical computational methods, underscores the need for new approaches to study nuclear structure and dynamics. Here, we demonstrate that a spin-based digital quantum simulator using nuclear magnetic resonance, where nuclear spins simulate interacting fermions, offers a powerful tool to address this challenge. As a first step, we experimentally simulate the Agassi model, which encapsulates the interplay between collective and single-particle behaviors in finite nuclei. By representing nucleons as both bosons (nucleon pairs) and fermions (individual unpaired nucleons), the Agassi model captures highly non-linear interactions and is particularly suited for studying nuclear phase transitions, such as those between spherical and deformed shapes. We experimentally measure the correlation function as an order parameter during the evolution of the many-body system, successfully detecting a quantum phase transition. Specifically, we observe a sharp transition between the symmetric phase and the broken symmetry phase. This work underscores the potential of quantum simulation as a transformative tool in nuclear physics, particularly for exploring complex quantum many-body systems with applications in nuclear structure and reaction dynamics.