Coherent Control of Interacting Electrons in Quantum Dots via Navigation in the Energy Spectrum

Quantum control of the wave function of two interacting electrons confined in quasi-one-dimensional double-well semiconductor structures is demonstrated. The control strategies are based on the knowledge of the energy spectrum as a function of an external uniform electric field. When two low-lying levels have an avoided crossing, our system behaves dynamically to a large extent as a two-level system. This characteristic is exploited to implement coherent control strategies based on slow (adiabatic passage) and rapid (diabatic Landau-Zener transition) changes of the external field. We apply this method to reach desired target states that lie far in the spectrum from the initial state.

Figure 1

Energy spectrum of our system as a function of the external uniform electric field.

Figure 2

Spatial wave functions ${\varphi }_i(E,z_1,z_2)$ corresponding to labels (a)–(h) in Fig. 1. States (a) and (b) have one electron in each well, wave functions (c) and (d) are localized in the left well, and wave functions (e) and (f) have both electrons in the right well. States (a)–(f) are far from avoided crossings and therefore have well-defined localization properties. This is not the case for eigenstates (g) and (h), which are at avoided crossings.

Figure 3

(a) Schematic diagram of the intended path followed by the state. Short (long) arrows indicate slow (fast) variations of the electric field. The initial state is marked as ■ and the target state as ⊕. (b) External electric field (the control parameter) as a function of time. (c) Probabilities that the two electrons are in the same (left) well ($P_{LL}$) and in different wells ($P_{RL}$). (d) Absolute value of the overlap of the evolving state with the energy eigenstate ${\varphi }_i(E)$. (e) Spatial wave functions at various times indicated in (d).