Fröhlich versus Bose-Einstein Condensation in Pumped Bosonic Systems

Magnon-condensation, which emerges in pumped bosonic systems at room temperature, continues to garner great interest for its long-lived coherence. While traditionally formulated in terms of Bose-Einstein condensation, which typically occurs at ultra-low temperatures, it could potentially also be explained by Fröhlich-condensation, a hypothesis of Bose-Einstein-like condensation in living systems at ambient temperatures. This prompts general questions relating to fundamental differences between coherence phenomena in open and isolated quantum systems. To that end, we introduce a simple model of bosonic condensation in an open quantum system (OQS) formulation, wherein bosons dissipatively interact with an oscillator (phonon) bath. Our derived equations of motion for expected boson occupations turns out to be similar in form to the rate equations governing Fröhlich-condensation. Provided that specific system parameters result in correlations that amplify or diminish the condensation effects, we thereby posit that our treatment offers a better description of high-temperature condensation compared to traditional formulations obtained using equilibrium thermodynamics. By comparing our OQS derivation with the original uncorrelated and previous semi-classical rate equations, we furthermore highlight how both classical anti-correlations and quantum correlations alter the bosonic occupation distribution.