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arXiv:quant-ph/0205030 · Physical Review A

Generation of maximum spin entanglement induced by a cavity field in quantum-dot systems

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

Published Jun 19, 2002• 52 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.65.062321

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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 generation of entanglement between two identical, interacting quantum dots---initially in ground states---by a coherent field and the subsequent time evolution of the entanglement are studied by calculating the concurrence between the two dots. The results predict that while it is possible to generate entanglement (or entanglement of formation, as defined for a mixed state) between the two dots, at no time do the dots become fully entangled to each other or is a maximally entangled Bell state ever achieved. We also observe that the degree of entanglement increases with an increase in the photon number inside the cavity and a decrease in the dot-photon coupling. The behavior of the two-dot system, initially prepared in an entangled state and interacting with thermal light, is also studied.
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.
The dynamical behaviors of the entanglement for the excitons in a system of two coupled quantum dots and a single-mode cavity field are investigated for two different initial conditions by means of the concurrence.It is shown that the direct coupling between the dots can reduce the degree of the entanglement for the excitons.For the initial cavity field being in the odd-coherent state,the degree of their entanglement decreases with the increase of the coherent intensity of cavity field.There is a trade-off for excitonic entanglement when cavity field is initially prepared in the even-coherent state.The relation between the average photon numbers of cavity field and quasi-maximally entangled excitonic coherent states is studied.