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: