AtomicDensityMatrix`
AtomicDensityMatrix`

EffectiveHamiltonian

EffectiveHamiltonian[h,u,t]

returns the effective Hamiltonian corresponding to the Hamiltonian h under a (possibly time dependent) transformation u, assuming time variable t.

Details and Options

  • EffectiveHamiltonian finds the operator that satisfies the Schrödinger equation in the frame determined by the transformation matrix, even if that frame is non-inertial.
  • The formula for the effective Hamiltonian is .
  • EffectiveHamiltonian is called by RotatingWaveApproximation.

Examples

Basic Examples  (1)

Define a system with Zeeman structure:

Find the Hamiltonian assuming a single optical field of frequency ω:

Find a unitary transformation for performing the rotating-wave approximation using RotatingWaveTransformMatrix:

This matrix can be supplied to the function EffectiveHamiltonian to transform the Hamiltonian to the rotating frame without dropping the fast-oscillating terms: