Nonlinear suppression of relaxation in dynamic localization phenomenon in a double quantum dot

The role of decoherence in controllable electron dynamics in a double quantum dot, influenced by external ac and dc electric fields, has been analyzed. Using the quasienergy formalism we have obtained the reduced density matrix of the electron subsystem and found the time evolution of the occupation probabilities in each quantum dot. It was shown that the dissipation caused by the phonon environment disappears under certain relations between electric field parameters. In this case one may perform a dynamic localization and form stable electron states localized within one of the dots. The suppression of dissipation is essentially a nonlinear effect, which is possible only in strong electric fields.

Figure 1

Schematic representation of the system for an arbitrary fixed time. One of the phonon modes is shown as an oscillator with frequency $\omega \left(\mathbf{k}\right)$.

Figure 2

Occupation probability for the left quantum dot for various values of the $\mid {\Delta }_{-1}∕\delta \mid$ ratio: (a) 3.0, (b) 1.0, (c) 0.3, (d) 0.01. For all the cases $\gamma ∕\epsilon$ has been kept constant and equal to 0.1. One can see that, independently of $\mid {\Delta }_{-1}∕\delta \mid$, the mean value of ${\rho }_{LL}$ tends to 0.5.

Figure 3

Reciprocal relaxation time in units of $4\gamma$ for various dimensionless resonance detunings $\eta$ as a function of parameter $\lambda$, which is proportional to the ac field magnitude $F$ (see the text). ${\omega }_0∕\Delta =30$.