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Chinese Physics B

Symmetry and size effects on energy and entanglement of an exciton in coupled quantum dots

Man Shen, Yan-Kui Bai, Xing‐Tao An, Jian-Jun Liu

Published Apr 1, 2013• 3 citations
Publisher

Abstract

We study theoretically the essential properties of an exciton in vertically coupled Gaussian quantum dots in the presence of an external magnetic field. The ground state energy of a heavy-hole exciton is split into four energy levels due to the Zeeman effect. For the symmetrical system, the entanglement entropy of the exciton state can reach a value of 1. However, for a system with broken symmetry, it is close to zero. Our results are in good agreement with previous studies.

DOI
10.1088/1674-1056/22/4/047101

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We study theoretically the essential properties of an exciton in vertically coupled Gaussian quantum dots in the presence of an external magnetic field. The ground state energy of a heavy-hole exciton is split into four energy levels due to the Zeeman effect. For the symmetrical system, the entanglement entropy of the exciton state can reach a value of 1. However, for a system with broken symmetry, it is close to zero. Our results are in good agreement with previous studies.
Using the one-dimensional effective potential method, we theoretically study the properties of an exciton in vertically coupled quantum dots (VCQDs) under the influence of an applied magnetic field. The ground state transition energies of the heavy-hole exciton are calculated in a single quantum dot and in VCQDs, respectively. Our results are in good agreement with those of experiments. In symmetrical VCQDs, the entanglement of the exciton state monotonously increases with increasing barrier width, and can even attain the value of the maximally entangled state. When the symmetry of the VCQDs is broken, the entanglement of the exciton state almost entirely breaks down under the combined influences of tunneling and the Coulomb interactions.
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.
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)
The relation between the excitonic purity and the concurrence in a system of two coupled large semiconduction quantum dots mediated by a single-mode cavity field is investigated by using linear entropy theory. The results show the difference in describing two modes of excitonic entanglement between linear entropy and concurrence. The relation between nonclassical property of cavity field and the entanglement degree of excitons is also discussed. The results show that two modes of exciton can reach maximal entanglement when the cavity exhibits an antibunching effect.
We study the dynamics of entanglement and mixedness of the excitons in a system of the two driven quantum dots coupled to a single-model cavity field by means of the concurrence and the linear entropy.We show that in the absence of the external driving field,excitonic entanglement and mixedness exhibit a periodic oscillation.When the external field is applied,state entanglement and mixedness will reduce,but if the Ω/g is selected a reasonable value,we can effectively suppress the mixedness and prepare a pure excitonic entangled state.
The dynamics of the entanglement for coherent excitonic states in the system of two, coupled, large semiconductor quantum dots ${(R/a}_{B}\ensuremath{\gg}1)$ mediated by a single-mode cavity field is investigated. Maximally entangled coherent excitonic states can be generated by cavity field initially prepared in odd coherent state. The entanglement of the excitonic coherent states between two dots reaches maximum when no photon is present in the cavity. The effects of the zero-temperature environment on the entanglement of excitonic coherent state are also studied using the concurrence for two subsystems of the excitons.