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 to be performed by the driven control. Must be either π/4, π/2, or π.
- maximum_rabi_rate (float) – The maximum Rabi frequency Ωmax for the driven control.
- azimuthal_angle (float , optional) – The azimuthal angle ϕ for the rotation. Defaults to 0.
- name (str , optional) – An optional string to name the control. Defaults to
None.
Returns
The driven control {(δtn,Ωn,ϕn,Δn)}.
Return type
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 is the unnormalized sinc function.
References
[1] H. K. Cummins, G. Llewellyn, and J. A. Jones, Physical Review A 67, 042308 (2003).