Classical limit of the interaction of a quantum system with the electromagnetic field
Lars Braun, Walter T. Strunz, J S Briggs · Physical Review A · 2004
The interaction of nonrelativistic matter with the quantized electromagnetic field is investigated in the classical limit of large photon numbers. Quantization of both matter, say an atom, and the field results in a time-independent Schr\"odinger equation (TISE). However, for very strong fields (quantum mechanically, large photon numbers) this is impractical to solve. The standard approach then is simply to replace the quantized field by a classical field to give a time-dependent Schr\"odinger equation (TDSE) for the atom alone. Here we show how this TDSE can be derived from the TISE for atom plus field, illustrating at each stage the approximations that are necessary to treat the field classically. An important difficulty at the semiclassical stage is a breakdown of the approximation at classical turning points. We show how the use of coherent field states can circumvent this problem. In the limit that the field can be treated classically, time emerges from the Maxwell equations and a TDSE for the atom alone results.