new_corpse_in_bb1_control

qctrlopencontrols.new_corpse_in_bb1_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 CORPSE concatenated within BB1 (CORPSE in BB1) driven control.

CORPSE in BB1 driven controls are robust to both low-frequency noise sources that perturb the amplitude of the control field and low-frequency dephasing noise.

Parameters
  • rabi_rotation (float) – The total Rabi rotation \(\theta\) to be performed by the driven control.

  • 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 CORPSE in BB1 driven control 1 2 consists of a BB1 control with the first segment replaced by a CORPSE control, which yields six segments:

\(\delta t_n\)

\(\Omega_n\)

\(\phi_n\)

\(\Delta_n\)

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

\(\Omega_{\rm max}\)

\(\phi\)

\(0\)

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

\(\Omega_{\rm max}\)

\(\phi+\pi\)

\(0\)

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

\(\Omega_{\rm max}\)

\(\phi\)

\(0\)

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

\(\Omega_{\rm max}\)

\(\phi+\phi_*\)

\(0\)

\(2\pi/\Omega_{\rm max}\)

\(\Omega_{\rm max}\)

\(\phi+3\phi_*\)

\(0\)

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

\(\Omega_{\rm max}\)

\(\phi+\phi_*\)

\(0\)

where

\[ \begin{align}\begin{aligned}\theta_1 &= 2\pi + \frac{\theta}{2} - \sin^{-1} \left[ \frac{\sin(\theta/2)}{2}\right]\\\theta_2 &= 2\pi - 2\sin^{-1} \left[ \frac{\sin(\theta/2)}{2}\right]\\\theta_3 &= \frac{\theta}{2} - \left[ \frac{\sin(\theta/2)}{2}\right]\\\phi_* &= \cos^{-1} \left( -\frac{\theta}{4\pi} \right).\end{aligned}\end{align} \]

References

1

M. Bando, T. Ichikawa, Y Kondo, and M. Nakahara, Journal of the Physical Society of Japan 82, 1 (2012).

2

C. Kabytayev, T. J. Green, K. Khodjasteh, M. J. Biercuk, L. Viola, and K. R. Brown, Physical Review A 90, 012316 (2014).