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Science

Optically Induced Entanglement of Excitons in a Single Quantum Dot

Gang Chen, N. H. Bonadeo, Duncan G. Steel, Dan Gammon, Douglas Scott Katzer, Daeui Park, Lu Jeu Sham

Published Sep 15, 2000• 242 citations
Publisher

Abstract

Optically induced entanglement is identified by the spectrum of the phase-sensitive homodyne-detected coherent nonlinear optical response in a single gallium arsenide quantum dot. The electron-hole entanglement involves two magneto-excitonic states differing in transition energy and polarization. The strong coupling needed for entanglement is provided through the Coulomb interaction involving the electrons and holes. The result presents a first step toward the optical realization of quantum logic operations using two or more quantum dots.

DOI
10.1126/science.289.5486.1906

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Optically induced entanglement is identified by the spectrum of the phase-sensitive homodyne-detected coherent nonlinear optical response in a single gallium arsenide quantum dot. The electron-hole entanglement involves two magneto-excitonic states differing in transition energy and polarization. The strong coupling needed for entanglement is provided through the Coulomb interaction involving the electrons and holes. The result presents a first step toward the optical realization of quantum logic operations using two or more quantum dots.
Summary form only given. A single quantum dot (QD) exciton is considered as a basic unit capable of carrying one bit of quantum information (qubit). Reference has demonstrated exciton Rabi oscillations in single QD's that are equivalent to single-bit rotations. To realize two-bit quantum logic operations in the next step, it is essential to identify and coherently manipulate two interacting single QD excitons. Our earlier work shows that two-exciton entangled states not involving the biexciton can be optically induced. This paper extends the entanglement to include the biexciton and show that all four basis states of the two-exciton system can be coherently manipulated based on a coherent nonlinear optical spectroscopy technique.
Recently a pair of vertically aligned quantum dots has been suggested as optically driven quantum gate. The later is built when two different particles, an electron and a hole, are created optically. The two particles form entangled states. We study theoretically the dynamics of a single heavy hole exciton confined in a small vertically coupled quantum dot. We use harmonic potentials to model the confining of electrons and holes and calculate the exciton's energy spectrum using the Hund-Mulliken approach, and including the Coulomb interaction. The entanglement may be controlled by the application of external electric field. At certain times of dynamical evolution one can generate a maximally entangled coherent exciton state by initially preparing the quantum dots in a superposition of coherent state. In ideal situations, entangled quantum states would not decohere during processing and transmission of quantum information. However, a real quantum system is inevitably influenced by its environment. Since, we study the decoherence effect caused by the interaction of the confined carriers with the acoustic phonon effects. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
Summary form only given. Two excitons can bind to form a biexciton through the Coulomb interaction. In a quantum dot (QD), the binding is greatly enhanced due to 3D confinement. Previous work has focused on luminescence from biexciton-to-exciton transitions. We report the first coherent nonlinear optical spectra of a biexcitonic system. Such types of studies provide vital information on the exciton/biexciton lifetime as well as the optically-induced quantum coherence and its decay. The realization of coherent optical devices based on QD systems, such as proposed for quantum logic operations, relies critically on these measurements.
The optically induced and detected entangled state involving an exciton Zeeman doublet with entanglement entropy as high as $\ensuremath{\sim}0.7$ was created using picosecond lasers in single GaAs\mathrm{GaAs}GaAs quantum dots. The temporal evolution of the nonradiative Raman coherence between two exciton states was directly resolved in quantum beats measured in the homodyne detected differential transmission experiment. The Raman coherence time, $66\ifmmode\pm\else\textpm\fi{}15\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$, was determined from the decay of the envelope of the quantum beats, and was found to be limited by the lifetimes of the exciton transitions, $50\ifmmode\pm\else\textpm\fi{}3\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$.