# arc.alkali_atom_functions.AlkaliAtom.twoPhotonRydbergExcitation#

AlkaliAtom.twoPhotonRydbergExcitation(Pp, wp, qp, Pc, wc, qc, Delta, fg, mfg, ne, le, je, nr, lr, jr, mjr)[source]#

Returns two-photon Rabi frequency $$\Omega_R$$, ground AC Stark shift $$\Delta_{\mathrm{AC}_g}$$, Rydberg state AC Stark shift $$\Delta_{\mathrm{AC}_r}$$ and probability to scatter a photon during a $$\pi$$-pulse $$P_\mathrm{sc}$$ for two-photon excitation from $$\vert f_h,m_{f_g}\rangle\rightarrow \vert j_r,m_{j_r}\rangle$$ via intermediate excited state

$$\Omega_R=\displaystyle\sum_{f_e,m_{f_e}}\frac{\Omega_p^{g\rightarrow f_e}\Omega_c^{f_e\rightarrow r}}{2(\Delta-\Delta_{f_e})}$$

$$\Delta_{\mathrm{AC}_g} = \displaystyle\sum_{f_e,m_{f_e}}\frac{\vert\Omega_p^{g\rightarrow f_e}\vert^2}{4(\Delta-\Delta_{f_e})}$$

$$\Delta_{\mathrm{AC}_r} = \displaystyle\sum_{f_e,m_{f_e}}\frac{\vert\Omega_p^{g\rightarrow f_e}\vert^2}{4(\Delta-\Delta_{f_e})}$$

$$P_\mathrm{sc} = \frac{\Gamma_et_\pi}{2}\displaystyle\sum_{f_e,m_{f_e}}\left[\frac{\vert\Omega_p^{g\rightarrow f_e}\vert^2}{2(\Delta-\Delta_{f_e})^2}+\frac{\vert\Omega_c^{f_e\rightarrow r}\vert^2}{2(\Delta-\Delta_{f_e})^2}\right]$$

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

Parameters
• Pp – power (W) of probe laser $$\vert g \rangle\rightarrow\vert e\rangle$$

• wp – beam waist (m) of probe laser $$\vert g \rangle\rightarrow\vert e\rangle$$

• qp – polarisation (+1, 0 or -1 corresponding to driving $$\sigma^+$$,:math:pi and $$\sigma^-$$) of probe laser $$\vert g \rangle\rightarrow\vert e\rangle$$

• Pb – power (W) of coupling laser $$\vert e\rangle\rightarrow\vert r\rangle$$

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

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

• Delta – Detuning from excited state centre of mass (rad s:math:^{-1})

• fg – ground state hyperfine state

• mfg – projection of ground state hyperfine state

• f1 – upper hyperfine state

• mf1 – upper hyperfine state

• ne – principal quantum numbers of excited state

• le – orbital angular momentum of excited state

• je – total angular momentum of excited state

• nr – principal quantum number of target Rydberg state

• lr – orbital angular momentum of target Rydberg state

• jr – total angular momentum of target Rydberg state

• mjr – projection of total angular momenutm of target Rydberg state

Returns

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

Return type

float