gravity - Does the potential energy for a given photon increase or decrease in quanta?

As a photon leaves a strong gravitational field, it loses energy and redshifts. Is the exchange in potential energy of a photon characterized by energy quanta?

Answer

No. A photon of a given frequency $f$ is exactly one quantum of energy. An electromagnetic wave has a total energy given by $E_\text{total} = \langle N\rangle hf$, where $\langle N\rangle$ is the number of photons in the wave.

When an EM wave escapes from a gravitational potential well (or falls into one), it's the energy of each individual photon that changes; in other words, the unit in which energy is quantized gets smaller or larger. The number of units (number of photons) stays the same.