Universal and robust quantum coherent control based on a chirped-pulse driving protocol

We propose a chirped-pulse driving protocol and reveal its exceptional property for quantum coherent control. The nonadiabatic passage generated by the driving protocol, which includes the population inversion and the nonadiabaticity-induced transition as its ingredients, is shown to be robust against pulse truncation. We further demonstrate that the protocol allows for universal manipulation on the qubit system through designing pulse sequences with either a properly adjusted sweeping frequency or pulsing intensity.

Figure 1

Chirped-pulse driving protocol specified by the Hamiltonian (1). (a) Field component ${\mathrm{\Omega }}_z\left(t\right)$ (solid line) and ${\mathrm{\Omega }}_x$ (dashed line) of the driving protocol. (b) The nonadiabatic energy described by $E_{\pm }\left(t\right)/\eta =\mp \frac{1}{2}cos\phi csc\theta$ with $\nu /\eta =1$ (solid line) and adiabatic energy levels in the limit $\nu /\eta \to 0$ (dashed line). The corresponding gaps at the crossing point $t=0$ are shown to be $\mathrm{\Delta }=1/\sqrt{2}$ and ${\mathrm{\Delta }}_{ad}=1$, respectively.

Figure 2

Fidelities of coherent operations yielded by the driving protocol with pulse truncation. (a) $F(U_0,U_{\delta })$ of the evolution operator with $\eta /\nu =1$ (blue solid line) and $\sqrt{3}$ (red dashed line). (b) Fidelity between ${\tilde{U}}_0$ and ${\tilde{U}}_{\delta }$ accounting for the nonadiabaticity-induced transition in the evolution operator. (c) $F_{\epsilon }(\eta /\nu )$ between the desired evolution $U_0(\eta /\nu )$ and the one $U_0(\tilde{\eta }/\tilde{\nu })$ with deviation of the control parameter $\tilde{\eta }/\tilde{\nu }=\eta /\nu +\epsilon$.

Figure 3

Schematic to illustrate the universality of the rotation $\mathcal{R}({\eta }^{\prime }/{\nu }^{\prime },\eta /\nu )$ acting on ${\sigma }_y$ and ${\sigma }_z$. (a) Parameter surfaces of $\mathit{S}({\eta }^{\prime }/{\nu }^{\prime },\eta /\nu )$ in which the domains of $\eta /\nu$ and ${\eta }^{\prime }/{\nu }^{\prime }$ responsible for the left, middle, and right panels are $\eta /\nu \in (-1,1),(-2,2),(-3,3)$ and ${\eta }^{\prime }/{\nu }^{\prime }\in (-1,1),(-2,2),(-3,3)$, respectively. (b) Parameter surfaces of $\mathit{T}({\eta }^{\prime }/{\nu }^{\prime },\eta /\nu )$ with respect to the same domains of $\eta /\nu$ and ${\eta }^{\prime }/{\nu }^{\prime }$ specified in (a) for the left to right panels.