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

Abstract

We study the time evolution of entanglement of two spins in anisotropically coupled quantum dot interacting with the unpolarized nuclear spins environment. We assume that the exchange coupling strength in the z-direction $J_z$ is different from the lateral one $J_l$. 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 $J=\Vert J_l-J_z\Vert$ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behavior controlled by the competition between the exchange interaction $J$ and the external magnetic field. The entanglement shows a quasi-symmetric behavior 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 isotropically coupled quantum dot.

24 pages and 7 figures. v3: major changes

References in corpus (12)

• Single-shot read-out of an individual electron spin in a quantum dot
• Control and Detection of Singlet-Triplet Mixing in a Random Nuclear Field
• Triplet-Singlet Spin Relaxation via Nuclei in a Double Quantum Dot
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Singlet-triplet decoherence due to nuclear spins in a double quantum dot
• Nuclear spin state narrowing via gate--controlled Rabi oscillations in a double quantum dot
• Analytical Solution of Electron Spin Decoherence Through Hyperfine Interaction in a Quantum Dot
• Electron spin phase relaxation of phosphorus donors in nuclear spin enriched silicon
• Spin-spin coupling in electrostatically coupled quantum dots
• Detecting entanglement using a double quantum dot turnstile
• Non-Perturbative Bounds on Hyperfine-Induced Electron Spin Coherence Times
• Anisotropic spin relaxation in quantum dots

Cited by in corpus (2)

• Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases
• Dynamics of entanglement in a two-dimensional spin system