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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Maximally entangled spin states in equivalent-neighbor systems of quantum dots in a microcavity

Adam Miranowicz, Şahin Kaya Özdemir, Yu-xi Liu, W. Leoński, Masato Koashi, Nobuyuki Imoto, Y. Hirayama, J. Bajer

Published Nov 21, 2003• 0 citations
Publisher

Abstract

We analyze generation of maximally entangled states (EPR and W states) of the conduction-band electron spins in systems of an arbitrary number of semiconductor quantum dots under equivalent-neighbor interactions mediated by a single-mode cavity field. We show that the perfect EPR states in bipartite systems and perfect W states in multipartite ones can only be generatcd in systems of up to six and four dots, respectively, with single or equivalently, all dots except one excited.

DOI
10.1117/12.545067

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We analyze generation of maximally entangled states (EPR and W states) of the conduction-band electron spins in systems of an arbitrary number of semiconductor quantum dots under equivalent-neighbor interactions mediated by a single-mode cavity field. We show that the perfect EPR states in bipartite systems and perfect W states in multipartite ones can only be generatcd in systems of up to six and four dots, respectively, with single or equivalently, all dots except one excited.
Equivalent-neighbor interactions of the conduction-band electron spins of quantum dots in the model of Imamo\ifmmode \bar{g}\else \={g}\fi{}lu et al. [Phys. Rev. Lett. 83, 4204 (1999)] are analyzed. An analytical solution and its Schmidt decomposition are found and applied to evaluate how much the initially excited dots can be entangled with the remaining dots if all of them are initially disentangled. It is demonstrated that perfect maximally entangled states (MES's) can only be generated in systems of up to six dots with a single dot initially excited. It is also shown that highly entangled states, approximating the MES's with good accuracy, can still be generated in systems of odd numbers of dots with almost half of them excited. A sudden decrease of entanglement is observed on increasing the total number of dots in a system with a fixed number of excitations.
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.
We investigate the generation of multipartite entangled state in a system of N quantum dots embedded in a microcavity and examine the emergence of genuine multipartite entanglement by three different characterizations of entanglement. At certain times of dynamical evolution one can generate multipartite entangled coherent exciton states or multiqubit W states by initially preparing the cavity field in a superposition of coherent states or the Fock state with one photon, respectively. Finally, we study environmental effects on multipartite entanglement generation and find that the decay rate for the entanglement is proportional to the number of excitons.
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