new_scrofulous_control

qctrlopencontrols.new_scrofulous_control(rabi_rotation: float, maximum_rabi_rate: float, azimuthal_angle: float = 0.0, name: Optional[str] = None) → qctrlopencontrols.driven_controls.driven_control.DrivenControl[source]

Creates a short composite rotation for undoing length over and under shoot (SCROFULOUS) driven control.

SCROFULOUS driven controls are robust to low-frequency noise sources that perturb the amplitude of the control field.

Parameters
  • rabi_rotation (float) – The total Rabi rotation \(\theta\) to be performed by the driven control. Must be either \(\pi/4\), \(\pi/2\), or \(\pi\).

  • maximum_rabi_rate (float) – The maximum Rabi frequency \(\Omega_{\rm max}\) for the driven control.

  • azimuthal_angle (float, optional) – The azimuthal angle \(\phi\) for the rotation. Defaults to 0.

  • name (str, optional) – An optional string to name the control. Defaults to None.

Returns

The driven control \(\{(\delta t_n, \Omega_n, \phi_n, \Delta_n)\}\).

Return type

DrivenControl

Notes

A SCROFULOUS driven control 1 consists of three control segments:

\(\delta t_n\)

\(\Omega_n\)

\(\phi_n\)

\(\Delta_n\)

\(\theta_1/\Omega_{\rm max}\)

\(\Omega_\rm{max}\)

\(\phi+\phi_1\)

\(0\)

\(\theta_2/\Omega_{\rm max}\)

\(\Omega_{\rm max}\)

\(\phi+\phi_2\)

\(0\)

\(\theta_3/\Omega_{\rm max}\)

\(\Omega_{\rm max}\)

\(\phi+\phi_3\)

\(0\)

where

\[ \begin{align}\begin{aligned}\theta_1 &= \theta_3 = \mathrm{sinc}^{-1} \left[\frac{2\cos (\theta/2)}{\pi}\right]\\\theta_2 &= \pi\\\phi_1 &= \phi_3 = \cos^{-1}\left[ \frac{-\pi\cos(\theta_1)}{2\theta_1\sin(\theta/2)}\right]\\\phi_2 &= \phi_1 - \cos^{-1} (-\pi/2\theta_1),\end{aligned}\end{align} \]

and \(\mathrm{sinc}(x)=\sin(x)/x\) is the unnormalized sinc function.

References

1

H. K. Cummins, G. Llewellyn, and J. A. Jones, Physical Review A 67, 042308 (2003).