Figure 1

Fidelity dynamics of a 10-level atomic system under control of regular and noisy pulse sequences. The target state \(|A\rangle =\sum _{j=0}^{n-1}a_j|j\rangle\) is such chosen as \(|a_j|^2=1/10\). The parameters are chosen as \(\kappa _j=0.1\omega\), \(E_{j\ne 0}=0\) and \(E_0(t)=\omega\). For regular rectangular pulse, \(|c(t)|=\Phi /\Delta\) for \(m\tau -\Delta \le t\le m\tau\), where \(m\ge 1\) is an integer; otherwise, \(|c(t)|=0\). \(\Phi\), \(\Delta\), and \(\tau\) are the strength, duration and period of pulse, respectively. Here \(\tau =0.02\omega t\) and \(\Delta /\tau =0.5\). For noisy pulse, \(|c(t)|\rightarrow |c(t)|[1+G\mathcal {N}(t)]\) where G (here \(G=50\%\)) is a dimensionless parameter measuring the white noise strength \(\mathcal {N}(t)\in (-1, 1)\). The environment correlation function is taken as \(\beta (t,s)=\frac{\gamma }{2}e^{-\gamma |t-s|}\), where \(\gamma\) is inversely proportional to the environmental memory time. A smaller \(\gamma\) indicates a stronger non-Markovian environment.