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Physical Review B

Logic and functional operations using a near-field optically coupled quantum-dot system

Suguru Sangu, Kiyoshi Kobayashi, Akira Shojiguchi, Motoichi Ohtsu

Published Mar 26, 2004• 82 citations
Publisher

Abstract

This paper investigates the exciton dynamics in a three-quantum-dot system coupled via an optical near field. The system consists of two identical quantum dots coupled coherently (the coherent operation part) and a third quantum dot with exciton sublevels (the output part). It provides certain characteristic functional operations depending on the initial excitation, as well as symmetry of the coupling strengths or the spatial arrangement. First, we analytically obtain the coupling strength between two quantum dots via an optical near field and give a numerical estimation for a CuCl quantum-cube system. Then, a resonance condition between the two parts is shown; this depends on the initial excitation in the coherent operation part. Using this condition, which can be realized by adjusting the energy level of a quantum dot in the output part, AND- and XOR-logic operations can be demonstrated in a symmetrically arranged quantum-dot system. We also discuss how the asymmetry of the system affects the energy transfer through certain coupled states in the coherent operation part that would be forbidden in a symmetrically arranged system. Although the asymmetry degrades the signal contrast for logic operations, it is expected to open up new techniques for novel device technologies where quantum entangled states are mediated in the operations.

DOI
10.1103/physrevb.69.115334

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•Jan 1, 2003•0 citations
This paper investigates the exciton dynamics in a three-quantum-dot system coupled via an optical near field. The system consists of two identical quantum dots coupled coherently (the coherent operation part) and a third quantum dot with exciton sublevels (the output part). It provides certain characteristic functional operations depending on the initial excitation, as well as symmetry of the coupling strengths or the spatial arrangement. First, we analytically obtain the coupling strength between two quantum dots via an optical near field and give a numerical estimation for a CuCl quantum-cube system. Then, a resonance condition between the two parts is shown; this depends on the initial excitation in the coherent operation part. Using this condition, which can be realized by adjusting the energy level of a quantum dot in the output part, AND- and XOR-logic operations can be demonstrated in a symmetrically arranged quantum-dot system. We also discuss how the asymmetry of the system affects the energy transfer through certain coupled states in the coherent operation part that would be forbidden in a symmetrically arranged system. Although the asymmetry degrades the signal contrast for logic operations, it is expected to open up new techniques for novel device technologies where quantum entangled states are mediated in the operations.
We investigate the population dynamics in a three quantum-dot system coupled via an optical near field, which consists of a coherent operation part and an output part. We analytically show that a resonance condition between the two parts depends on initial excitation in the coherent operation part. Using this feature, AND- and XOR-gate operations are demonstrated in the case of symmetrically arranged quantum dots. We also evaluate the effects of asymmetric arrangement on these operations, and show that the coherence plays an important role in an asymmetric system.
Using density operator formalism, we discuss interdot excitation energy transfer dynamics driven by the optical near-field and phonon bath reservoir, as well as coherent excitation dynamics of a quantum dot system. As an effective interaction between quantum dots induced by the optical near-field, the projection operator method gives a renormalized dipole interaction, which is expressed as a sum of the Yukawa functions and is used as the optical near-field coupling of quantum dots. We examine one- and two-exciton dynamics of a three-quantum dot system suggesting a nanometric photonic switch, and numerically obtain a transfer time comparable with the recent experimental results for CuCl quantum dots.
In nanophotonic device operations, characteristic features on a nanometer scale, such as locally excited states, dependence on the excitation number, and spatial symmetry of a system, play an important role. Using these features, selective excitation energy transfer via an optical near field is shown for a quantum-dot system with discrete energy levels. This selectivity strongly depends on a dipole-inactive state of an exciton, which cannot be excited by the far-field light. Operation principles of logic gates, photon storage, and quantum information processing device, which are based on the selectivity, are proposed, and the temporal dynamics are investigated analytically and numerically by using quantum theory. Nanophotonic devices, which are constructed from quantum mechanical and classical dissipative systems, are expected to become one of a key technologies in future device architecture.
Potential application of elementary excitation in semiconductor quantum dot to quantum computation is discussed. We propose a scalable hardware and all optical implementation of a logic gate that exploits the discrete nature of electron–hole states and their well-concentrated oscillator strength for ultrafast gate operation. A multiple-bit gate function is based on the nearest neighbour dipole–dipole coupling. Rabi population oscillation and long-lived coherence of an excitonic two-level system in an isolated InxGa1−xAs quantum dot guarantees quantum gate functions. Technologies that will realize and facilitate the exciton quantum computing are discussed.
Energy transfer and exciton population dynamics in a two-quantum dot system coupled with a phonon heat-bath system are examined using the density matrix formalism. In such a system, optical near-field interactions induce energy transfer between quantum dots, and exciton–phonon interactions guarantee the unidirectional excitation energy transfer. Our theoretical investigation shows that the population dynamics change drastically depending on the coupling strengths due to optical near-field interactions and exciton–phonon heat-bath interactions. The temperature effect promotes frequent energy back-transfer from the heat-bath to the quantum dot system. Applying our theoretical formulation, we numerically calculate the time evolution of populations, and estimate energy transfer time or state-filling time for a CuCl quantum dot system. The estimated time is suitable for the elements in our proposed optical nano-switch and nano-photonic devices.
Quantum dots have been the focus of both fundamental and applied research due to their atomic-like properties. The delta-function-like density of states along with strong nonlinear optical properties have made quantum dots the focus of novel opto-electronic devices and of quantum computing proposals. The key issue for implementing quantum dots in devices such as quantum computers is the ability to coherently entangle separately localized quantum dot states. Using continuous wave coherent nonlinear optical spectroscopy techniques, this thesis focuses on creating coherent super-position states built from separately localized quantum dot states. The narrow bandwidths and mutual coherence of the applied laser fields allow for the creation of radiative and nonradiative coherences which can be understood from the coherent nonlinear optical response. The quantum dots under study are formed due to the width fluctuations of a thin quantum well. By applying nondegenerate mutually coherent fields on the sample in the traditional pump and probe geometry and homodyne detecting the nonlinear signal field, nonradiative coherences between two laterally coupled quantum dots are created and the coupling between their states examined. The coherent nonlinear optical response is compared with theoretical predictions based on the density matrix formalism for the interacting two exciton model. From this comparison, binding energies of the two-exciton bound state created with separately localized excitons is found to be on the order of 20 mueV for like-polarized excitons and on the order of 100 mueV for unlike-polarized excitons. A second order coherence between the ground and two-exciton state is also noted in the experimental data after comparison with theory. Further work attempting to study a vertically coupled quantum dot system was unsuccessful. The spectrum of a quantum dot is further understood from the comparison of the linear and nonlinear excited state spectra. Excited states which appear in both spectra imply a Coulomb interaction between them and their respective ground states. Coherent nonlinear optical signatures of excited states correlated with their linear excitation spectra are presented, and the importance of such states for a quantum computer read-out is described.