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Spin-orbit effects on the full dynamics of double quantum dot qubit states

APS March Meeting , Boston, MA, 29 February 2012. Spin-orbit effects on the full dynamics of double quantum dot qubit states. E. Cota Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México , Ensenada, MEXICO S. E. Ulloa, J.E. Rolón

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Spin-orbit effects on the full dynamics of double quantum dot qubit states

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  1. APS March Meeting , Boston, MA, 29 February 2012 Spin-orbit effects on the full dynamics of double quantum dot qubit states E. Cota Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México , Ensenada, MEXICO S. E. Ulloa, J.E. Rolón Department of Physics and Astronomy, Ohio University, USA G. Platero Instituto de Ciencia de Materiales de Madrid – CSIC, Madrid, SPAIN

  2. Combining rotations around two axes Petta et al (2005)

  3. Model Electron spin Hamiltonian for a single QD: Double dot: J.M. Taylor et al. PRB 76, 035315 (2007)

  4. Energy levels for finite external magnetic field (in ) Triplet: Singlet :

  5. Spin-orbit interaction introduces non-spin conserving tunneling matrix elements (Danon & Nazarov, PRB 80, 0413019 (R) (2009)) Tunneling Hamiltonian: spin indices Defining one can write, in basis

  6. Total Hamiltonian in basis HFI couples and triplet states SOI couples and triplet states Let

  7. Bloch-Feshbach Projection Method Construct effective operators acting within relevant subspace Let be the relevant subspace onto which we want to constrain the dynamics of the system : projection operator onto ; projected Green’s function onto level-shift operator The poles of give the eigenvalues of

  8. Summary • We calculate numerically the probability of measurement of in double quantum dot system, including hyperfine and spin-orbit interactions, using the complete basis. • When probabilities show oscillations, depending on the value of , corresponding to new frequencies due to coupling mainly to • Frequency of oscillations of strongly dependent on values of and detuning • Feshbach projection method allows determination of (through identification of the frequency of )

  9. P(Z)

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