arc.alkali_atom_functions.AlkaliAtom.breitRabi#

AlkaliAtom.breitRabi(n, l, j, B)[source]#

Returns exact Zeeman energies math:E_z for states \(\vert F,m_f\rangle\) in the \(\ell,j\) manifold via exact diagonalisation of the Zeeman interaction \(\mathcal{H}_z\) and the hyperfine interaction \(\mathcal{H}_\mathrm{hfs}\) given by equations

\(\mathcal{H}_Z=\frac{\mu_B}{\hbar}(g_J J_z+g_I I_z)B_z\)

and

\(\mathcal{H}_\mathrm{hfs}=A_\mathrm{hfs}I\cdot J + B_\mathrm{hfs}\frac{3(I\cdot J)^2+3/2 I\cdot J -I^2J^2}{2I(2I+1)2J(2J+1)}\).

Parameters
  • n – principal,orbital, total orbital quantum numbers

  • l – principal,orbital, total orbital quantum numbers

  • j – principal,orbital, total orbital quantum numbers

  • B – Magnetic Field (units T)

Returns

State energy \(E_z\) in SI units (Hz), state f, state mf

Return type

float