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Journal of Physics Conference Series

Quantum entanglement in lateral GaAs/AlGaAs quantum dot molecules

Vlastimil Křápek, Petr Klenovský, Armando Rastelli, Oliver G. Schmidt, D. Munzar

Published Sep 1, 2010• 16 citations
Publisher

Abstract

We calculate the excitonic structure of pairs of GaAs/AlGaAs quantum dots forming lateral molecules and obtain the entanglement of exciton states. The following advantages of the lateral geometry over the vertical one are found: (1) The energy structures of the dots forming a molecule can be in principle identical. (2) Comparable tunneling of electrons and holes ensures a high entanglement of antisymmetric excitons. A drawback of existing structures are very low tunneling energies, which make the entanglement vulnerable against differences in the sizes and shapes of both dots.

DOI
10.1088/1742-6596/245/1/012027

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We calculate the excitonic structure of pairs of GaAs/AlGaAs quantum dots forming lateral molecules and obtain the entanglement of exciton states. The following advantages of the lateral geometry over the vertical one are found: (1) The energy structures of the dots forming a molecule can be in principle identical. (2) Comparable tunneling of electrons and holes ensures a high entanglement of antisymmetric excitons. A drawback of existing structures are very low tunneling energies, which make the entanglement vulnerable against differences in the sizes and shapes of both dots.
Currently there is strong interest in realizing implementations of quantum computation and quantum cryptography in a solid state environment. One of the systems that are actively studied are semiconductor quantum dots (QDs). Due to their discrete energy level structure, they are often called artificial atoms, and they attract immediately interest of quantum information science since they allow to mimic the design developed for atomic physics systems such as ions in traps or atoms in cavities. However, despite of the similarities, one has to keep in main that any elementary excitation in a QD has a generic many-body character. An essential building block of a quantum processor is a quantum gate which entangles the states of two quantum bits. Recently it has been proposed that a pair of vertically aligned QDs could be used as an optically driven quantum gate: The quantum bits are individual carriers either on dot zero or dot one. The different dot indices play the same role as a "spin," therefore we term them "isospin." Quantum mechanical tunneling between the dots rotates the "isospin" and leads to superposition of two quantum dot states. The quantum gate is built when two different particles, an electron and a hole, are created optically. The two particles form entangled isospin states. The entanglement can be controlled by application of an electric field along the heterostructure growth direction. Here we present spectroscopic studies on single quantum dot molecules (QDMs) with different vertical separation between the dots that support the feasibility of this proposal. The comparison of the evolution of the excitonic recombination spectrum with the results of calculations allows us to demonstrate coherent tunneling of electrons and holes across the separating barrier and the formation of entangled exciton states. For a given barrier width, we find only small variations of the tunneling induced splitting between the entangled states demonstrating a good homogeneity within the obtained QDM ensembles.
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)
Establishing the hybrid entanglement among a growing amount of matter and photonic quantum bits is necessary for scalable quantum computation and long-distance quantum communication. Here we demonstrate that charged excitonic complexes forming in strongly correlated quantum dot molecules are able to generate tripartite hybrid entanglement under proper carrier quantization. The mixed orbitals of the molecule construct multi-level ground states with sub-meV hole tunneling energy and relatively large electron hybridization energy. We show that appropriate size and interdot spacing keeps the electron particle weakly localized, opening extra recombination channels by correlating ground-state excitons. This allows for creation of higher order entangled states. Nontrivial hole tunneling energy, renormalized by multi-particle interactions, facilitates the realization of the energy coincidence among only certain components of the molecule optical spectrum. This translates to the emergence of favorable spectral components in a multi-body excitonic complex which sustain principal oscillator strengths throughout the electric field-induced hole tunneling process. We particularly analyze whether the level broadening of favorable spin configurations could be manipulated to eliminate the distinguishability of photons.
Exciton states and optical spectra in a pair of vertically stacked InGaAs∕GaAs\mathrm{InGaAs}∕\mathrm{GaAs}InGaAs∕GaAs quantum dots are studied with a proposed variation-diagonalization technique. The spectra obtained are in good agreement with experiments. The tunnel coupling and the exciton entanglement are also investigated. It is found that at short barrier widths, the entanglement is small due to the coupling between the intradot and interdot orbitals. At large barrier widths, large entanglement appears in coupled identical quantum dots; however, such an entanglement can be easily destroyed by the broken symmetry because of the weak tunneling of the hole.
It has been suggested (Giavaras et al 2007 Phys. Rev. B 75 085302) that a quantum dot structure, which consists of a small open dot formed within a larger dot, can generate spin entanglement between two electrons and filter singlet–triplet states as a consequence of Coulomb interaction and the Pauli exclusion principle. In this work, we show via numerical modelling how to form the dot structure in an AlGaAs/GaAs/AlGaAs quasi-one-dimensional channel using top and back gates. We calculate the confining potential of the dot and the corresponding low-lying two-electron states and demonstrate a way of controlling the degree of entanglement and filtering by tuning the dot potential with the voltage applied to a back gate.
Energy spectra, spin configurations, and entanglement characteristics of a system of four electrons in lateral double quantum dots are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field, and strength of interelectron repulsion. A distinctly different quantum behavior is found compared to that of circular single quantum dots. As a function of the magnetic field, the energy spectra exhibit a low-energy band consisting of a group of six states, with the number six being a consequence of the conservation of the total spin of the four electrons and the ensuing spin degeneracies. These six states appear to cross at a single value of the magnetic field, with the crossing point becoming sharper for larger interdot distances. As the strength of the Coulomb repulsion increases, the six states tend to become degenerate and a well defined energy gap separates them from the higher-in-energy excited states. The appearance of the low-energy band is a consequence of the formation of a Wigner supermolecule, with the four electrons (two in each dot) being localized at the vertices of a rectangular parallelogram. Using the spin-resolved pair-correlation functions, one can map the EXD many-body wave functions onto the spin functions associated with the four localized electrons. Analogies with nanomagnets, such as finite Heisenberg clusters, are discussed. The ability to determine associated spin functions enables investigations concerning entanglement properties of the system of four electrons. In particular, the formation of Wigner supermolecules generates EXD solutions belonging to the class of strongly entangled states referred to as N-qubit Dicke states in the quantum-information literature.