Any physical meaning that the electric field operator consists of creation and annihilation operators?
Answers
Quantum optics textbooks say that the electric field operator is written as a superposition as the positive frequency part and negative frequency part, e.g., for a single mode field, E^=Ek(r)a^(t)+E∗k(r)a^†(t) where Ek(r) is the position-dependent classical mode function determined by a given physical structure and a^(a^†) is the annihilation (creation) operator. Then, one question immediately came to my mind, what does the fact that the electric field consists of creation and annihilation operator mean? Is it like the electric field is the superposition of two physical processes such as absorption (by a^) and emission (by a^†)? Someone said to me that they correspond, when compared to the classical complex representation, to a classical amplitude and its complex conjugate. However, I see this statement would be true only when a coherent state of light |α⟩ is considered. Is there any better way to understand the terms a^ and a^† in the electric field operator? or do they represent any actual physical processes that eventually constitute the electric field? or is it related to the process to measure the electric field?