Thermodynamics of the Ramsey Zone

We carry out a study on thermodynamics properties as entropy and heat $J_{Q}$ and work $J_{W}$ fluxes involved in a Ramsey zone, i.e., a mode field inside a low quality factor cavity that behaves classically and promotes rotations on atomic states. Focusing on the atomic dynamic only, here we show that $J_{W}$ predominates when the atomic state evolves maintaining its maximum purity, as computed by von Neumann entropy, in which case the rotation is successfully applied. On the other hand, $J_{Q}$ is the quantity that stands out when the atomic state ceases to be pure due to its entanglement with the cavity field mode state. We describe those limits in terms of the driving strength, the atom-field coupling and the cavity field dissipation rate, and interpret the quantum-to-classical transition in light of the heat and work fluxes. Besides, we show that for a driven-dissipative cavity mode to work out as a Ramsey zone (classical field), a very large amount of photons, of the order of $10^{6}$, need to cross the leaky cavity, which explains the classical behavior of the intra-cavity mode field even though, on average, it has a number of photons of the order of unity [Phys. Rev. Lett. 82, 4737 (1999)]