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

6. 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 Control parameter

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

13. Introduction Main idea of our work To travel in the spectra of eigenenergies Control parameter

14. Introduction Main idea of our work To travel in the spectra of eigenenergies Control parameter

15. Introduction Main idea of our work To travel in the spectra of eigenenergies Control parameter

16. Introduction To navigate the spectra

17. Introduction To navigate the spectra

18. Introduction To navigate the spectra

19. Introduction To navigate the spectra

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

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

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

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

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

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

26. 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)

27. The system Spectra

28. The system Spectra lines

29. The system Spectra lines Avoided crossings

30. Colaboradores-Referencias The system Cero slope delocalized Positive slope e¯ in the right dot Negative slope e¯ in the left dot

31. Landau-Zener transitions in our model LZ model

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

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

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

35. Landau-Zener transitions in our model LZ model Adibatic transitions Diabatic transitions

36. Colaboradores-Referencias Landau-Zener transitions in our model We study the prob. transition in several ac. For example:

37. Colaboradores-Referencias Landau-Zener transitions in our model We study the prob. transition in several ac. For example:

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

39. Colaboradores-Referencias Landau-Zener transitions in our model We study the prob. transition in several ac. For example: Full system 2 level system

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

41. Results First example: localization of the e¯ in the left dot

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

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

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 Second example: complex path

51. Colaboradores-Referencias Results Second example: complex path

52. Colaboradores-Referencias Results Second example: complex path

53. Colaboradores-Referencias Results Second example: complex path

54. Colaboradores-Referencias Results Second example: complex path

55. Colaboradores-Referencias Results Third example: more complex path

56. Results

57. Colaboradores-Referencias Results Forth example: target state a coherent superposition

58. Colaboradores-Referencias Results Forth example: target state a coherent superposition

59. Colaboradores-Referencias Results Forth example: target state a coherent superposition

60. Colaboradores-Referencias Results Forth example: target state a coherent superposition

61. Colaboradores-Referencias Results Forth example: target state a coherent superposition

62. Colaboradores-Referencias Results Forth example: target state a coherent superposition

63. Colaboradores-Referencias Results Forth example: target state a coherent superposition

64. Colaboradores-Referencias Results Forth example: target state a coherent superposition

65. Colaboradores-Referencias The method: questions Is our method generic?

66. Colaboradores-Referencias The method: questions We need well defined avoided crossings Is our method generic?

67. Colaboradores-Referencias The method: questions We need well defined avoided crossings  a/R Stadium billiard Is our method generic? LZ transitions Sanchez, Vergini DW PRE 96

68. Colaboradores-Referencias The method: questions We need well defined avoided crossings  a/R Stadium billiard Is our method generic? Is our method experimentally possible? LZ transitions Sanchez, Vergini DW PRE 96

69. Colaboradores-Referencias Final Remarks We found a method to control quantum systems Our method works well: With our method it is posible to travel in the spectra of the system We can control several aspects of the wave function (localization of the e¯, etc).

70. Colaboradores-Referencias Final Remarks We can also obtain a combination of adiabatic states Control of chaotic systems Decoherence??? Next step???.