# arc.alkali_atom_functions.AlkaliAtom.groundStateRamanTransition#

AlkaliAtom.groundStateRamanTransition(Pa, wa, qa, Pb, wb, qb, Delta, f0, mf0, f1, mf1, ne, le, je)[source]#

Returns two-photon Rabi frequency $$\Omega_R$$, differential AC Stark shift $$\Delta_\mathrm{AC}$$ and probability to scatter a photon during a $$\pi$$-pulse $$P_\mathrm{sc}$$ for two-photon ground-state Raman transitions from $$\vert f_g,m_{f_g}\rangle\rightarrow\vert nL_{j_r} j_r,m_{j_r}\rangle$$ via an intermediate excited state $$n_e,\ell_e,j_e$$.

$$\Omega_R=\displaystyle\sum_{f_e,m_{f_e}}\frac{\Omega^a_{0\rightarrow f_e}\Omega^b_{1\rightarrow f_e}}{2(\Delta-\Delta_{f_e})},$$

$$\Delta_{\mathrm{AC}} = \displaystyle\sum_{f_e,m_{f_e}}\left[\frac{\vert\Omega^a_{0\rightarrow f_e}\vert^2-\vert\Omega^b_{1\rightarrow f_e}\vert^2}{4(\Delta-\Delta_{f_e})}+\frac{\vert\Omega^a_{1\rightarrow f_e}\vert^2}{4(\Delta+\omega_{01}-\Delta_{f_e})}-\frac{\vert\Omega^b_{0\rightarrow f_e}\vert^2}{4(\Delta-\omega_{01}-\Delta_{f_e})}\right],$$

$$P_\mathrm{sc} =\frac{\Gamma_e t_\pi}{2}\displaystyle\sum_{f_e,m_{f_e}}\left[\frac{\vert\Omega^a_{0\rightarrow f_e}\vert^2}{2(\Delta-\Delta_{f_e})^2}+\frac{\vert\Omega^b_{1\rightarrow f_e}\vert^2}{2(\Delta-\Delta_{f_e})^2}+\frac{\vert\Omega^a_{1\rightarrow f_e}\vert^2}{4(\Delta+\omega_{01}-\Delta_{f_e})^2}+\frac{\vert\Omega^b_{0\rightarrow f_e}\vert^2}{4(\Delta-\omega_{01}-\Delta_{f_e})^2}\right]$$

where $$\tau_\pi=\pi/\Omega_R$$.

Parameters
• Pa – power (W), of laser a $$\vert 0 \rangle\rightarrow\vert e\rangle$$

• wa – beam waist (m) of laser a $$\vert 0 \rangle\rightarrow\vert e\rangle$$

• qa – polarisation (+1, 0 or -1 corresponding to driving $$\sigma^+$$, $$\pi$$ and $$\sigma^-$$) of laser a $$\vert 0 \rangle\rightarrow\vert e\rangle$$

• Pb – power (W) of laser b $$\vert 1 \rangle\rightarrow\vert e\rangle$$

• wb – beam waist (m) of laser b $$\vert 1 \rangle\rightarrow\vert e\rangle$$

• qb – polarisation (+1, 0 or -1 corresponding to driving $$\sigma^+$$, $$\pi$$ and $$\sigma^-$$) of laser b $$\vert 1 \rangle\rightarrow\vert e\rangle$$

• Delta – Detuning from excited state centre of mass (rad $$\mathrm{s}^{-1}$$)

• f0 – Lower hyperfine level

• mf0 – Lower hyperfine level

• f1 – Upper hyperfine level

• mf1 – Upper hyperfine level

• ne – principal, orbital, total orbital quantum numbers of excited state

• le – principal, orbital, total orbital quantum numbers of excited state

• je – principal, orbital, total orbital quantum numbers of excited state

Returns

Two-Photon Rabi frequency $$\Omega_R$$ (units $$\mathrm{rads}^{-1}$$), differential AC Stark shift $$\Delta_\mathrm{AC}$$ (units $$\mathrm{rads}^{-1}$$) and probability to scatter a photon during a $$\pi$$-pulse $$P_\mathrm{sc}$$

Return type

float