### Abstract

We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction Jz is different from the lateral one Jl. We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = Jl - Jz between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.

Original language | English |
---|---|

Pages (from-to) | 1777-1786 |

Number of pages | 10 |

Journal | Molecular Physics |

Volume | 106 |

Issue number | 14 |

DOIs | |

Publication status | Published - 1 Jul 2008 |

Externally published | Yes |

### Fingerprint

### Keywords

- Decoherence
- Entanglement
- Quantum computing

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Condensed Matter Physics
- Biophysics
- Molecular Biology

### Cite this

*Molecular Physics*,

*106*(14), 1777-1786. https://doi.org/10.1080/00268970802290313

**Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot.** / Sadiek, Gehad; Huang, Zhen; Aldossary, Omar; Kais, Sabre.

Research output: Contribution to journal › Article

*Molecular Physics*, vol. 106, no. 14, pp. 1777-1786. https://doi.org/10.1080/00268970802290313

}

TY - JOUR

T1 - Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot

AU - Sadiek, Gehad

AU - Huang, Zhen

AU - Aldossary, Omar

AU - Kais, Sabre

PY - 2008/7/1

Y1 - 2008/7/1

N2 - We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction Jz is different from the lateral one Jl. We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = Jl - Jz between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.

AB - We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction Jz is different from the lateral one Jl. We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = Jl - Jz between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.

KW - Decoherence

KW - Entanglement

KW - Quantum computing

UR - http://www.scopus.com/inward/record.url?scp=53449086631&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=53449086631&partnerID=8YFLogxK

U2 - 10.1080/00268970802290313

DO - 10.1080/00268970802290313

M3 - Article

AN - SCOPUS:53449086631

VL - 106

SP - 1777

EP - 1786

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 14

ER -