Rotating wave approximation  The rotating wave approximation is an approximation used in atom optics and magnetic resonance. In this approximation, terms in a Hamiltonian which 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 which oscillate with frequencies formula_1 are neglected, while terms which oscillate with frequencies formula_2 are kept, where formula_3 is the light frequency and formula_4 is a transition frequency. The name of the approximation stems from the form of the Hamiltonian in the interaction picture, as shown below. By switching to this picture the evolution of an atom due to the corresponding atomic Hamiltonian is absorbed into the system ket, 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. For simplicity consider a two-level atomic system with ground and excited states formula_5 and formula_6, respectively (using the Dirac bracket notation). Let the energy difference between the states be formula_7 so that formula_8 is the transition frequency of the system. Then the unperturbed Hamiltonian of the atom can be written as  Suppose the atom experiences an external classical electric field of frequency formula_10, given by formula_11, e.g. a plane wave propagating in space. Then under the dipole approximation the interaction Hamiltonian between the atom and the electric field can be expressed as  where formula_13 is the dipole moment operator of the atom. The total Hamiltonian for the atom-light system is therefore formula_14 The atom does not have a dipole moment when it is in an energy eigenstate, so formula_15 This means that defining formula_16 allows the dipole operator to be written as  where formula_20 is the Rabi frequency and formula_21 is the counter-rotating frequency. To see why the formula_22 terms are called `counter-rotating' consider a unitary transformation to the interaction or Dirac picture where the transformed Hamiltonian formula_23 is given by  where formula_25 is the detuning between the light field and the atom. This is the point at which the rotating wave approximation is made.