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

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: Confining potential: doble quantum well filled with 2 e

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

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

20. 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

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

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 right dot e¯ in the left 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 Linear functions hyperbolas

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

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

32. 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

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 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

36. 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

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

51. Results

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

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

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

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

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

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 The method: questions We need well defined avoided crossings  a/R Stadium billiard Is our method generic? Is our method experimentally possible?

61. 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).

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