arc.alkali_atom_functions.AlkaliAtom.getMagneticDipoleMatrixElementHFS

AlkaliAtom.getMagneticDipoleMatrixElementHFS(l, j, f1, mf1, f2, mf2, q, s=0.5)

Magnetic dipole matrix element \(\langle f_1,m_{f_1} \vert \mu_q \vert f_2,m_{f_2}\rangle\) for transitions from \(\vert f_1,m_{f_1}\rangle\rightarrow\vert f_2,m_{f_2}\rangle\) within the same \(n,\ell,j\) state in units of \(\mu_B B_q\).

The magnetic dipole matrix element is given by \(\langle f_1,m_{f_1}\vert \mu_q \vert f_2,m_{f_2}\rangle = g_J \mu_B B_q (-1)^{f_2+j+I+1+f_1-m_{f_1}} \sqrt{(2f_1+1)(2f_2+1)j(j+1)(2j+1)} \begin{pmatrix}f_1&1&f_2\\-m_{f_1} & -q & m_{f_2}\end{pmatrix} \begin{Bmatrix}f_1&1&f_2\\j & I & j\end{Bmatrix}\)

Args:

l, j, f1, mf1: orbital, total orbital,

fine basis (total atomic) angular momentum,total anuglar momentum and projection of total angular momentum for state 1

f2,mf2: principal, orbital, 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:

float: magnetic dipole matrix element (in units of \(\mu_BB_q\))