new_scrofulous_control

qctrlopencontrols.new_scrofulous_control(rabi_rotation, maximum_rabi_rate, azimuthal_angle=0.0, name=None)

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 θ\theta to be performed by the driven control. Must be either π/4\pi/4, π/2\pi/2, or π\pi
  • maximum_rabi_rate (float) – The maximum Rabi frequency Ωmax\Omega_{\rm max}
  • azimuthal_angle (float , optional) – The azimuthal angle ϕ\phi
  • name (str , optional) – An optional string to name the control. Defaults to None.

Returns

The driven control {(δtn,Ωn,ϕn,Δn)}\{(\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

\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), $$

and sinc(x)=sin⁡(x)/x\mathrm{sinc}(x)=\sin(x)/x

References

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

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