arc.alkali_atom_functions.AlkaliAtom.getSphericalMatrixElementHFStoFS#

AlkaliAtom.getSphericalMatrixElementHFStoFS(j1: float, f1: float, mf1: float, j2: float, mj2: float, q: int) → float[source]#

Spherical matrix element for transition from hyperfine resolved state to unresolved fine-structure state \(\langle f,m_f \vert\mu_q\vert j',m_j'\rangle\) in units of \(\langle j\vert\vert\mu\vert\vert j'\rangle\)

Parameters:

  • j1 – total orbital, fine basis (total atomic) angular momentum, and projection of total angular momentum for state 1

  • f1 – total orbital, fine basis (total atomic) angular momentum, and projection of total angular momentum for state 1

  • mf1 – total orbital, fine basis (total atomic) angular momentum, and projection of total angular momentum for state 1

  • j2 – total orbital, fine basis (total atomic) angular momentum, and projection of total orbital angular momentum for state 2

  • mj2 – total orbital, fine basis (total atomic) angular momentum, and projection of total orbital angular momentum for state 2

  • q (int) – specifies transition that the driving field couples to, +1, 0 or -1 corresponding to driving \(\sigma^+\), \(\pi\) and \(\sigma^-\) transitions respectively.

  • s (float) – optional, total spin angular momentum of state. By default 0.5 for Alkali atoms.

Returns:

spherical dipole matrix element( \(\langle j\vert\vert\mu\vert\vert j'\rangle\))

Return type:

float