Rotating-wave approximation

The rotating-wave approximation is an approximation used in <a href="/facts/Atom_optics/1tt6Nk8e">atom optics</a> and <a href="/facts/Nuclear_magnetic_resonance/pGYAn9Bz">magnetic resonance</a>. In this approximation, terms in a <a href="/facts/Hamiltonian_(quantum_mechanics)/5XwK2HmD">Hamiltonian</a> that oscillate rapidly are neglected. This is a valid approximation when the applied electromagnetic radiation is near resonance with an atomic transition, and the intensity is low. Explicitly, terms in the Hamiltonians that oscillate with frequencies 
 
 
 
 
 ω
 
 L
 
 
 +
 
 ω
 
 0
 
 
 
 
 {\displaystyle \omega _{L}+\omega _{0}}
 
 are neglected, while terms that oscillate with frequencies 
 
 
 
 
 ω
 
 L
 
 
 −
 
 ω
 
 0
 
 
 
 
 {\displaystyle \omega _{L}-\omega _{0}}
 
 are kept, where 
 
 
 
 
 ω
 
 L
 
 
 
 
 {\displaystyle \omega _{L}}
 
 is the light frequency, and 
 
 
 
 
 ω
 
 0
 
 
 
 
 {\displaystyle \omega _{0}}
 
 is a transition frequency.
The name of the approximation stems from the form of the Hamiltonian in the <a href="/facts/Interaction_picture/1StMw9yu">interaction picture</a>, as shown below. By switching to this picture the evolution of an atom due to the corresponding atomic Hamiltonian is absorbed into the system <a href="/facts/Bra%E2%80%93ket_notation/NDlKsaRh">ket</a>, leaving only the evolution due to the interaction of the atom with the light field to consider. It is in this picture that the rapidly oscillating terms mentioned previously can be neglected. Since in some sense the interaction picture can be thought of as rotating with the system ket only that part of the electromagnetic wave that approximately co-rotates is kept; the counter-rotating component is discarded.
The rotating-wave approximation is closely related to, but different from, the <a href="/facts/Redfield_equation/nNYeNADY">secular approximation</a>.

Rotating-wave approximation open-in-new

Rotating-wave approximation