Selective coherent destruction of tunneling in a quantum-dot array

The coherent manipulation of quantum states is one of the main tasks required in quantum computation. In this paper we demonstrate that it is possible to control coherently the electronic position of a particle in a quantum-dot array. By tuning an external ac electric field we can selectively suppress the tunneling between dots, trapping the particle in a determined region of the array. The problem is treated nonperturbatively by a time-dependent Hamiltonian in the effective mass approximation and using Floquet theory. We find that the quasienergy spectrum exhibits crossings and anticrossings at certain field intensities that result in the selective suppression of tunneling.

Figure 1

(Color online) First Brillouin zone of quasienergies (in units of $\hslash \omega$) as function of ac field intensity $(eFd∕\hslash \omega )$, for $T_e∕\hslash \omega =0.2$. Left inset shows amplification of collapse region, showing crossings and anticrossing that follow a definite pattern according to dynamical symmetries. The two vertical lines indicate field intensity $F_1$ and $F_2$ and are used later in numerical simulation. Right inset shows the spatial component of the density probability of the Floquet eigenstates in the collapse region and their evolution with the field.

Figure 2

(Color online) Time evolution of probability to find one particle in each one of the QDs in a four-dot array for $e{F}_{1}d∕\hslash \omega \simeq 2.38$, and starting the system with the particle in: (a) dot 1, and (b) dot 2. Lower panel is a schematic representation of the dynamics of the system, as seen in the respective time evolution of the occupation probability of each dot. The full circle represents the position of the particle at time zero, crosses indicate the suppression of tunneling through that barrier and arrows indicate that tunneling is possible.

Figure 3

(Color online) Time evolution of the probability to find a particle in one of the QDs for ${eF}_{2}d∕\hslash \omega \simeq 2.40$, starting the system with the particle in: (a) dot 1, and (b) dot 2. Lower panel is a schematic representation of the dynamics. Here, the middle barrier tunneling is suppressed.

Figure 4

(Color online) (a) Crossing/anticrossing in the collapse region as indicated by vertical lines in the inset of Fig. 1, as function of the ratio $T_e∕\hslash \omega$. In the high frequency limit (lower ratio $T_e∕\hslash \omega$) the crossings/anticrossings occur basically at the same point (zeroes of Bessel function). Inset shows amplification of quasienergy spectrum for $T_e∕\hslash \omega =0.7$. (b) Escape probability for a particle initially in one region of the quantum-dot array. Solid red line is for the equivalent anticrossing and represents the escape probability of the QD 1, considering this dot as the initial condition. Dashed green line is for the crossing and represents escape probability of the first two QDs assuming that the system starts in QD 1.

Figure 5

(Color online) Collapse region of the first Brillouin zone of quasienergies (in units of $\hslash \omega$) as function of the ac field intensity ($eFd∕\hslash \omega$), for $T_e∕\hslash \omega =0.2$ for: (a) an array of six QDs and (b) an array of five QDs. Lower cartoons are the schematic representation of the dynamic of the respective arrays of QDs at field intensity given by $F_1$ and $F_2$.