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

Schema of |0>-> -> |e> -> |1> transition
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