The Materials Computation Center, University of Illinois Duane Johnson and Richard Martin (PIs), NSF DMR Vc(meV) J(meV) OBJECTIVE: Understand many-body effects in quantum confined systems for applications in quantum information processing. APPROACH: Use combined computational techniques based on density functional theory to model the quantum dot (QD) potential, Exact diagonalization (ED) and/or quantum Monte Carlo to simulate accurately exchange and correlation of electrons in triple QDs. WHY IT MATTERS: Our work provides physical insight into many-body effects in a man-made environment to manipulate single quantum objects, which is fundamental to accomplishing tasks which can only be performed by quantum information processing, such as unconditionally secure transmission of information. Computational models, such as ours, complement experimental work in determining what can and cannot be done by quantum computing. Realistic Computational Approaches for Coupled Quantum Dots STRATEGY:We use a variational Monte Carlo (VMC) method to compute both singlet and triplet energies for two electrons in the triple QDs. For the trial wavefunction, we use a Slater-Jastrow form with single- particle orbitals consisting of harmonic oscillator s and p states. We include 65 variational parameters in our wavefunction. To optimize the expectation value of the energy, we use the Steepest Descent method. We get agreement with ED methods for exchange energy between two electrons in double QD as a function of magnetic field and interdot separation. Jean-Pierre Leburton and Richard Martin Postdoc: D.V. Melnikov Students: Jihan Kim RESULT: (upper) left: Schematic of three coupled QDs in triangle; right: Contour plot of the potential. (lower) Exchange energy between two electrons as a function of detuning of the upper dot for different upper dot radii. The kink around 25 meV indicates the electron transition from the 2 lower dots to the upper dot x(nm) y(nm) d rc

The Materials Computation Center, University of Illinois Duane Johnson and Richard Martin (PIs), NSF DMR OUTLOOK: We will include a magnetic field in our VMC and consider the presence of the third electron in the triple dot for which the determination of the ground state, either ferro- or anti-ferromagnetic is an important theoretical problem. Other consideration includes the effect of detuning between energy levels when the potential or the size of one dot is varied with respect to the other two, in order to control or detect spin states in the two other dots. PUBLICATIONS : D.V. Melnikov, L-X Zhang and J.P. Leburton “"Exchange Coupling Between Two Electrons in Double Quantum Dot Structures" invited review article in “Current Opinion in Solid State & Materials Science”, ELSEVIER, vol.10 (2007) (invited) D. V. Melnikov and J.P. Leburton, “ Transport Spectroscopy in Vertical Quantum Dots” in "Highlights on Spectroscopies of Semiconductors and Nanostructures", ‘Festschrift’ in honor of Angiolino Stella, Conference Proceedings 94, pp , Eds. G. Guizzetti, L. C. Andreani, F. Marabelli and M. Patrini, the Italian Physical Society (SIF) (2007). (Invited) D.V. Melnikov and J.P. Leburton, “ Single Particle State Mixing and Coulomb Localization in Two- Electron Realistic Coupled Quantum Dots”, Phys. Stat. Solidi, (c) 4, 578, (2007). Proc. ICSNN-06, Istanbul, TK July 30-Aug.4, L-X Zhang, D. V. Melnikov and J.P. Leburton, “Engineering Exchange Coupling in Coupled Elliptic Quantum Dots”, (cond-mat/ ) Special issue of the IEEE Transactions on Nanotechnology vol 6, pp (2007) of the IEEE-NANO-2006 Conference, Cincinnati, OH, July 16-21, 2006., RECOGNITION: “Spintronics in Quantum Dots”, Speaker of the 43 rd colloquium in the Forum on Semiconductor Science and Technology, Institute of Semiconductors, Chinese Academy of Science, Beijing, April 9, 2007 (J.P. Leburton) “Quantum Transport Spectroscopy in Few Electron Quantum Dots” Keynote address at the 70 th birthday celebration of Rector A. Stella, University di Pavia, Italy, June 13, 2007 (J.P. Leburton) “Spin-based quantum dots for quantum computing” Quantum Computing workshop, the 1 st WUN International Conference on Spintronic Materials and Technology, York, UK, Aug. 7-10, (J.P. Leburton- invited)