Coupled Quantum Dots for Quantum Computing

Introduction: In digital computers, information is represented in classical 'bits' by either 0 or 1. Quantum information is represented in "quantum bits" with wavefunctions Ψ = α|0> + β|1>. These bits involve the continuous phase and thus contain much more information than the classical bit. The search for physical implementations for quantum information technologies is a major focus of current multidisciplinary research efforts. Quantum information technology can form the basis for powerful encryption schemes and secure communications, for code breaking through prime number factoring, and for ulta-powerful computation.

The key requirement for these technologies is physical implementations of qu-bits, particularly of the coupled qu-bits for quantum gates. Two qu-bit gates are the bases for manipulation of information in computations. Solid state implementations, particularly those from semiconductors, are especially needed for systems that can be scaled up to large numbers of qu-bits and integrated in current semiconductor technologies. Quantum dots with their sharp optical lines behave like artificial atoms and are of great interest as qu-bits. In them, the two states can be represented either by the two levels of a spin in the dot in a magnetic field or by the presence/absence of an exciton (an optically excited electron-hole pair). Although quantum dot implementations for qu-bits have been widely studied, appropriately coupled quantum dots for two qu-bit gates have not been achieved to date.

Coupled Quantum Dots for Gates: The requirements for coupling between quantum dots to make gates are that the coupling be coherent so that information not be lost during computation, and that the coupling can be turned on and off externally to carry out the information exchange in the gate. In work done jointly between NRL and researchers in Germany,¹ we have demonstrated coupled quantum dots for gates. Single "self-organized" InAs quantum dots were gown by molecular beam epitaxy between GaAs substrates and GaAs overlayers (Fig. 9(a)). InAs dots form at the interface due to strain from the mismatch of the lattice constants of the two materials. Pairs of such quantum dots are formed on closely spaced interfaces. The strain around the two quantum dots causes them to form above one another.

The energies of excited electron-hole pairs in these coupled dots are shown in the lower part of Fig. 9(b) as a function of distance between the dots. The dependence of the energies on separation arises from overlap of the electron and hole wavefunctions in the two dots, and Coulomb interactions between the electron and hole. This distance dependence is similar to the splitting between the bonding and antibonding electron states of a simple molecule, which is sketched in the upper part of Fig. 9(b). Our theoretical results for this distance dependence (Fig. 9(b)) are in agreement with recent photoluminescence experiments on these coupled dot structures. This indicates that the coupling between the dots is quantum mechanical and thus coherent. Additional experimental and theoretical results for the diamagnetic shifts and anticrossings in magneto-optical studies confirm that the coupling is indeed coherent.¹

FIGURE 9
Left-hand side shows transmission electron micrographs for an InAs/GaAs quantum dot grown by molecular beam epitaxy and for coupled pairs of quantum dots on adjacent layers. Lower panel on right-hand side gives energies of eletron hole pair in coupled pair of quantum dots as a function of distance between them. Upper panel on right-hand side sketches bonding and antibonding wavefunctions of two atoms.

We have also devised a simple method to control the coupling between these quantum dots with an electric field. This field brings the excitons in the two dots into and out of resonance, as illustrated in the upper part of Fig. 10. The structure is formed into a Schottky diode, with metal films on the top and bottom as illustrated in the bottom of Fig. 10, to apply an electric field to the coupled dots. The right-hand side of Fig. 11 shows calculations of the wave good quantitative agreement with the photoluminescence data shown in the left-hand side of Fig. 11, which exhibit one feature (intradot exciton) with decreasing in energy and intensity and another (interdot exciton) appearing with increasing field. The observed features result from modifications of the electron and the hole wavefunctions in the two dots, and these results demonstrate that a simple electric field controls their wavefunction mixings.

FIGURE 10
Upper panel shows a sketch of excitons in two coupled quantum dots being brought into and out of resonance with an electric field. Lower panel is a sketch of Schottky diode structure in which an electric field is applied to coupled quantum dots.

FIGURE 11
Right-hand panel gives wavefunctions of an electron and a hole in a coupled dot structure as functions of electron and hole coordinates for electric field E = 0 and E = 6.2 V/cm. Left-hand panel gives photoluminescence results for coupled quantum dot structure as a function of electric field. The calculations give a detailed explanation of experiment both for the energies and for the intensities of the features.

Conclusions: We have fabricated coupled quantum dot structures from closely spaced self-organized InAs quantum dots, and we have demonstrated that the coupling between the dots is coherent. We also have shown that a simple electric field controls the couplings between carriers in the two dots. Two qu-bit quantum gates will be made from these coupled quantum dots by doping spins into each dot. The gate operations needed in quantum information technologies will be carried by electric field pulses on the coupled dots.

[Sponsored by ONR and DARPA]