Laser light is known to produce "coherent state light," which consists of a superposition of different photon numbers. However, wouldn't the entanglement between the atoms and the light suggest that photons become distinguishable, preventing the probability amplitudes from coherently adding to produce coherent state light?
The emission of a photon by an atom transitioning to the ground state can be represented as $$ p_1|\text{ground}\rangle|1\rangle + p_2|\text{excited}\rangle|0\rangle, $$ where $p_1$ and $p_2$ are the probability amplitudes.
Given multiple atoms in a medium each emitting photons, the quantum states of these photons could, in theory, be influenced by the spatial distribution of their source atoms.
So in summary, my question is: How does the process of photon emission in lasers overcome the potential for distinguishability due to the spatial variance of atoms, ensuring the photons' states remain indistinguishable and preserve the overall coherence of the laser light?
