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