Thermodynamical aspects of optically pumped dense atomic medium

Abstract: Optically Pumped Magnetometers use light to drive an atomic vapor into a Non-Equilibrium Steady State for sensing. This kind of state is achieved when spin-exchange collisions, together with optical pumping, dominate the relaxation dynamics, redistributing the atomic populations and thereby shaping the steady-state configuration. Despite the rapid advancement of atomic magnetometer technology, a comprehensive thermodynamic analysis of the state preparation is largely unexplored. We apply a thermodynamic framework to alkali atoms in a vapor cell, modeling their interactions with the pump laser and their relaxation via spin-exchange and spin-destruction collisions. We analyze how the pump rate and light polarization determine the non-equilibrium steady state, quantifying irreversibility via entropy production, assessing useful energy via ergotropy, and defining the spin-polarization efficiency. Finally, we establish a connection between metrological performance and the Quantum Fisher Information (QFI), demonstrating that a higher thermodynamic efficiency directly translates into an improved fundamental bound on magnetometer sensitivity. These results provide insights for optimizing state preparation in quantum sensors.