Quantum Control of Electron-Phonon Scatterings in Artificial Atoms

The phonon-induced dephasing dynamics in optically excited semiconductor quantum dots is studied within the frameworks of the independent boson model and optimal control. We show that appropriate tailoring of laser pulses allow complete control of the optical excitation despite the phonon dephasing, a finding in marked contrast to other environment couplings.

Figure 1

Results of our calculations with Gaussian $2\pi$ (dashed lines) and optimal-control (solid lines) laser pulses and for (a),(d) zero temperature, (b),(e) zero temperature and an electron-phonon coupling enhanced by a factor of $\sqrt{3}$, and (c),(e) finite temperature $T={\omega }_c\sim 10\mathrm{K}$. The upper graphs [(a)–(c)] show $|\Omega (t)|$, the lower ones [(d)–(f)] the time evolution of $u_3(t)$, and the insets the trajectories of the Bloch vector $\mathit{u}(t)$. For the Gaussian $2\pi$ pulse, Rabi flopping occurs but is damped due to electron-phonon interactions. For the optimal control dephasing losses are completely suppressed, and the system passes through the desired states of ${\widehat{\mathit{e}}}_3$ at time zero and $-{\widehat{\mathit{e}}}_3$ at $T$.

Figure 2

Time evolution of the different phonon occupancies in the excited state $\sum _{\lambda }|⟨x|a_{\lambda }|\psi (t)⟩{|}^2\delta (\omega -{\omega }_{\lambda })$ as a function of phonon energy $\omega$ and for the (a) Gaussian and (b) optimal control shown in Fig. 1b.