arc.alkali_atom_functions.AlkaliAtom.twoPhotonRydbergExcitation#
- AlkaliAtom.twoPhotonRydbergExcitation(Pp: float, wp: float, qp: int, Pc: float, wc: float, qc: int, Delta: float, fg: int, mfg: int, ne: int, le: int, je: float, nr: int, lr: int, jr: float, mjr: float) Tuple[ndarray[Any, dtype[_ScalarType_co]], ndarray[Any, dtype[_ScalarType_co]], ndarray[Any, dtype[_ScalarType_co]], ndarray[Any, dtype[_ScalarType_co]]] [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: