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Quantum control using diabatic and adibatic transitions

Quantum control using diabatic and adibatic transitions. Diego A. Wisniacki. University of Buenos Aires. Colaboradores-Referencias. Colaborators. Gustavo Murgida (UBA) Pablo Tamborenea (UBA). Short version ---> PRL 07, cond-mat/0703192 APS ICCMSE. Outline. Introduction

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Quantum control using diabatic and adibatic transitions

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  1. Quantum control using diabatic and adibatic transitions Diego A. Wisniacki University of Buenos Aires

  2. Colaboradores-Referencias Colaborators • Gustavo Murgida (UBA) • Pablo Tamborenea (UBA) • Short version ---> PRL 07, cond-mat/0703192 • APS ICCMSE

  3. Outline • Introduction • The system:quasi-one-dimensional quantum dot with 2 e inside • Landau- Zener transitions in our system • The method: traveling in the spectra • Results • Final Remarks

  4. Introduction

  5. Introduction

  6. Introduction Desired state

  7. Introduction Desired state

  8. Introduction • Main idea of our work

  9. Introduction • Main idea of our work To travel in the spectra of eigenenergies

  10. Introduction • Main idea of our work To travel in the spectra of eigenenergies

  11. Introduction • Main idea of our work To travel in the spectra of eigenenergies

  12. Introduction • Main idea of our work To travel in the spectra of eigenenergies

  13. Introduction • To navigate the spectra

  14. Introduction • To navigate the spectra

  15. Introduction • To navigate the spectra

  16. The system Quasi-one-dimensional quantum dot:

  17. The system Quasi-one-dimensional quantum dot: filled with 2 e Confining potential: doble quantum well

  18. The system Quasi-one-dimensional quantum dot: filled with 2 e Confining potential: doble quantum well

  19. The system Quasi-one-dimensional quantum dot: filled with 2 e Confining potential: doble quantum well

  20. Colaboradores-Referencias The system The Hamiltonian of the system: Time dependent electric field Coulombian interaction Note: no spin term-we assume total spin wavefunction: singlet

  21. The system Interaction induce chaos PRE 01 Fendrik, Sanchez,Tamborenea System: 1 well, 2 e Nearest neighbor spacing distribution

  22. Colaboradores-Referencias The system • We solve numerically the time independent Schroeringer eq. • Electric field is considered as a parameter • Characteristics of the spectrum (eigenfunctions and eigenvalues)

  23. The system Spectra

  24. The system Spectra • lines

  25. The system Spectra • lines • Avoided crossings

  26. Colaboradores-Referencias The system delocalized e¯ in the left dot e¯ in the right dot

  27. Landau-Zener transitions in our model LZ model

  28. Landau-Zener transitions in our model LZ model Linear functions

  29. Landau-Zener transitions in our model LZ model hyperbolas Linear functions

  30. Landau-Zener transitions in our model LZ model if Probability to remain in the state 1 Probability to jump to the state 2

  31. Landau-Zener transitions in our model LZ model Slow transitions Fast transitions

  32. Colaboradores-Referencias Landau-Zener transitions in our model We study the prob. transition in several ac. For example: LZ prediction Full system 2 level system E(t)

  33. The method: navigating the spectrum • Choose the initial state and the desired final state in the spectra

  34. The method: navigating the spectrum • Choose the initial state and the desired final state in the spectra • Find a path in the spectra

  35. The method: navigating the spectrum • Choose the initial state and the desired final state in the spectra • Find a path in the spectra • We use adiabatic and rapid transitions to travel in the spectra

  36. The method: navigating the spectrum • Choose the initial state and the desired final state in the spectra • Find a path in the spectra • We use adiabatic and rapid transitions to travel in the spectra • Avoid adiabatic transitions in very small avoided crossings • If it is posible try to make slow variations of the parameter

  37. Results • First example: localization of the e¯ in the left dot EPL 01 Tamborenea, Metiu (sudden switch method)

  38. Results • First example: localization of the e¯ in the left dot EPL 01 Tamborenea, Metiu

  39. Colaboradores-Referencias Results • Second example: complex path

  40. Colaboradores-Referencias Results • Second example: complex path

  41. Colaboradores-Referencias Results • Second example: complex path

  42. Colaboradores-Referencias Results • Second example: complex path

  43. Colaboradores-Referencias Results • Second example: complex path

  44. Colaboradores-Referencias Results • Second example: complex path

  45. Colaboradores-Referencias Results • Second example: complex path

  46. Colaboradores-Referencias Results • Second example: complex path

  47. Colaboradores-Referencias Results • Second example: complex path

  48. Colaboradores-Referencias Results • Second example: complex path

  49. Colaboradores-Referencias Results • Second example: complex path

  50. Colaboradores-Referencias Results • Third example:more complex path

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