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Spin Density and Entanglement Calculation for Many-Electron States of Nitrogen-Vacancy Centers in Diamond

Babamoradi, Mohsen | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42431 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Vesaghi, Mohammad Ali; Heidari Saani, Mehdi
  7. Abstract:
  8. Nitrogen-Vacancy (NV) consists of a substitutional nitrogen located at a lattice site adjacent to a carbon vacancy. It has attracted much attention due to its application in solid state quantum information processing. Its long coherence time and ability to be used in ambient temperature made it a major candidate for quantum bit (Qbit). Due to its importance, a lot of theoretical studies for the NV’s properties based on the DFT and other single particle approaches have been done, while many-body approaches are not expanded so. For the first time, a generalized Hubbard Hamiltonian was used as a many-body approach to study NV defects. The obtained wavefunctions and states result to good agreement with experiment. By utilizing these wavefunctions the spin density or unpaired electron probability density on the vacancy’s neighboring sites nitrogen and three carbons were calculated. The spin density is an important quantity measured by EPR experiment. Our calculated spin density on the nitrogen site for the ground state of NV- is zero which is in good agreement with experimental results that show its value is less than 2%. For the excited state other theoretical studies suggest either 0% or 100% spin density on the N site, while is in controversial with the 6% experimental value. Our result improves this value as 19%. Furthermore, for the other excited states of NV- and NV0, we predict spin density that might be verified by EPR. Also the results of calculated spin density on the three neighboring carbon’s sites show that for the spatial degenerate states, the three carbons are not the same, and have different spin density. This is another indication for the Jahn-Teller effect and explains why the ground state of NV0 and other spatial degenerate excited states of NV- and NV0 are not detectable by the EPR experiment. Another issue for NV defects is the relaxation of atoms around vacancy; therefore we study the effect of relaxation of neighboring atoms from -20% to +20% with C3v symmetry on the spin density. Any relaxation of the vacancy’s neighboring atoms does not change the spin density on the nitrogen for the ground state of NV-. While for the excited state with relaxation of vacancy’s neighboring atoms from inward to outward the spin density migrate considerably from nitrogen to three carbons site which is in agreement with other theoretical results and experimental values. For the ground state of NV0, more than 10% inward relaxation causes significant spin density on the nitrogen, which predicts considerable spin density on the nitrogen at equilibrium distance from vacancy. Also for the first excited state of NV0, moving from inward relaxation to outward relaxation shows migration of spin density from nitrogen site to the three carbons site, same as the case for excited state of NV-
  9. Keywords:
  10. Generalized Hubbard Model ; Entanglement ; Spin Relaxation ; Spin Density Waves ; Nitrogen-Vacancy Complex ; Cosmological Black Hole

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