The coupling of two-level quantum systems to the thermal environment is a fundamental problem with applications of such usually single-particle or fermionic systems ranging from qubit state preparation to spin models. The present Letter studies the elementary problem of the thermodynamics of an ensemble of bosons populating a two-level system. Using an optical dye microcavity platform, we thermalize photons in a two-mode system at conditions of tunable chemical potential, demonstrating the statistical mechanical problem of $N$ bosons populating a two-level system, coupled to a heat bath. Under pulsed excitation, we observe Josephson oscillations between the two quantum states, which verifies the possibility for coherent manipulation. In contrast, under stationary conditions, the thermalization of the two-mode system is observed, arising from radiative coupling of photons to the dye. As the energetic splitting between eigenstates is 2 orders of magnitude smaller than thermal energy, at low occupations, an almost equal distribution of the occupation of the modes is observed, as expected from Boltzmann statistics. For larger occupation, we observe efficient population of the ground state and saturation of the upper level at high filling, expected from quantum statistics. Our experiment holds promise for state preparation in quantum technologies as well as for quantum thermodynamics studies.

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• Open quantum systems
• Phase transitions
• Quantum optics
• Thermodynamics