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 \(\tau_\pi=\pi/\Omega_R\).

Schema of |g-> -> |e> -> |r> transition
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