new_corpse_in_scrofulous_control
qctrlopencontrols.new_corpse_in_scrofulous_control(rabi_rotation, maximum_rabi_rate, azimuthal_angle=0.0, name=None)Creates a CORPSE concatenated within SCROFULOUS (CORPSE in SCROFULOUS) driven control.
CORPSE in SCROFULOUS 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 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
SEE ALSO
new_corpse_control, new_scrofulous_control
Notes
A CORPSE in SCROFULOUS driven control 1 consists of a SCROFULOUS control with each segment replaced by a CORPSE control, which yields nine segments:
| $\delta t_n$ | $\Omega_n$ | $\phi_n$ | $\Delta_n$ |
| $\Gamma^{\theta_1}_1/\Omega_{\rm max}$ | $\Omega_{\rm max}$ | $\phi+\phi_1$ | $0$ |
| $\Gamma^{\theta_1}_2/\Omega_{\rm max}$ | $\Omega_{\rm max}$ | $\phi+\phi_1+\pi$ | $0$ |
| $\Gamma^{\theta_1}_3/\Omega_{\rm max}$ | $\Omega_{\rm max}$ | $\phi+\phi_1$ | $0$ |
| $\Gamma^{\theta_2}_1/\Omega_{\rm max}$ | $\Omega_{\rm max}$ | $\phi+\phi_2$ | $0$ |
| $\Gamma^{\theta_2}_2/\Omega_{\rm max}$ | $\Omega_{\rm max}$ | $\phi+\phi_2+\pi$ | $0$ |
| $\Gamma^{\theta_2}_3/\Omega_{\rm max}$ | $\Omega_{\rm max}$ | $\phi+\phi_2$ | $0$ |
| $\Gamma^{\theta_3}_1/\Omega_{\rm max}$ | $\Omega_{\rm max}$ | $\phi+\phi_3$ | $0$ |
| $\Gamma^{\theta_3}_2/\Omega_{\rm max}$ | $\Omega_{\rm max}$ | $\phi+\phi_3+\pi$ | $0$ |
| $\Gamma^{\theta_3}_3/\Omega_{\rm max}$ | $\Omega_{\rm max}$ | $\phi+\phi_3$ | $0$ |
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) $$(with sinc(x)=sin(x)/x the unnormalized sinc function) are the SCROFULOUS angles, and
\Gamma^{\theta'}_1 &= 2\pi + \frac{\theta'}{2} - \sin^{-1} \left[ \frac{\sin(\theta'/2)}{2}\right] \Gamma^{\theta'}_2 &= 2\pi - 2\sin^{-1} \left[ \frac{\sin(\theta'/2)}{2}\right] \Gamma^{\theta'}_3 &= \frac{\theta'}{2} - \sin^{-1} \left[ \frac{\sin(\theta'/2)}{2}\right]are the CORPSE angles corresponding to each SCROFULOUS angle θ′∈{θ1,θ2,θ3}.
References
[1] T. Ichikawa, M. Bando, Y. Kondo, and M. Nakahara, Physical Review A 84, 062311 (2011).