Figure 1. The three relevant length scales for quantum information processing using single electron quantum dots.
Figure 1. The three relevant length scales for quantum information processing using single electron quantum dots.

A broad program is underway to use single-electron quantum dots in silicon for quantum information processing. A theoretical description of this system is necessarily multiscale, ranging from density functional theory at the atomic level to time-dependent model Hamiltonian calculations of many-dot systems. Optimal experimental designs to minimize decoherence will be examined.

We are pursuing many complementary directions toward using electrons in quantum dots for quantum information processing. One approach is to confine quantum dots in silicon using a ferroelectric thin film grown on the silicon. Thin films of SrTiO3 grown on Si will be patterned with an AFM to generate the confining potential for "designer" quantum dots in the Si. The compressively strained SrTiO3 has ferroelectric polarization normal to the plane of the substrate. The fundamental quantum gate operations will be controlled by properly shaping sub-bandgap optical pulses in position and time; these pulses will reduce the ferroelectric polarization between the dots, thus lowering the confining barrier between them. We are providing theoretical guidance for this endeavor in the following ways:

At the atomic length scale, the polarization of the ferroelectric layer will be calculated so that the electric field induced in the Si may be computed. These "designer" quantum dots confined by a patterned ferroelectric film have never been made before. A series of density functional calculations will be performed to compute the polarization and resulting electric potential at all points in the actual experimental configuration. The results will be used to design efficient patterning for the ferroelectric films. Finally the effects of adding buffer layers of (Ba,Sr)O between the ferroelectric and Si on the band offsets will be examined.

At the quantum-dot length scale, the evolution of interacting dots as the laser field reduces the barrier between them will be calculated. The many-body states will be integrated in time to simulate the quantum swap and other operations. An efficient parallel representation of many-body Hilbert spaces is already in place, and this will be generalized for time-dependent Hamiltonians. The geometry of the confining ferroelectric domains and of the spatiotemporal pulse will be optimized theoretically to produce efficient quantum-gate operations with low decoherence rates.
Principal Investigator: Steve Hellberg