# Is energy conservation violated in spontaneous absorption?

For a 2-level atom in a cavity with a single mode quantized electromagnetic field (in the zero photon state-Vacuum state) there exists QED Rabi oscillations, where the atom constantly emits and absorbs a photon. (from Jaynes-Cummings model)

The average vacuum energy is $$\hbar\omega/2$$ where $$\omega$$ is the frequency of the electromagnetic field. In the case of resonance, the frequency of transition is $$\omega=(E_{f}-E_{i})/\hbar$$, where $$E_{i}$$ and $$E_{f}$$ are the energy states of the atom and $$E_f > E_i$$.

The atom is said to exhibit spontaneous emission and absorption. I do not understand how the absorbed energy from the vacuum state is sufficient to raise it to the higher energy level.

• Spontaneous absorption is the case when there is a photon present in the field (over and above the vacuum energy), whose energy gets transferred to the atom. You seem to be implying that the vacuum energy itself can be used to excite the atom, which is not the case. What are your reasons for making that claim? I.e. what literature, or otherwise, gave you that impression? – Emilio Pisanty Jun 14 '17 at 11:45
• My reference is 'Introduction to Quantum Optics' by C.Gerry and PL Knight. – S.Ajay Jun 14 '17 at 12:19
• That's a pretty long book - you should be specific to the section and page level. – Emilio Pisanty Jun 14 '17 at 12:25
• While discussing the Jaynes Cummings model for an atom in a cavity with a single mode quantized electromagnetic field (in the zero photon state), there exists QED Rabi oscillations, where the atom constantly emits and absorbs a photon. This is what the author says, marks the difference between a semi-classical field and a quantum field. – S.Ajay Jun 14 '17 at 12:25
• You should incorporate that information into your question. – Emilio Pisanty Jun 14 '17 at 12:35

The model you are using evidently has a ground state energy as you say "the average vacuum energy is given by $\frac{1}{2}\hbar\omega$.