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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 Desired state

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

  6. Introduction • To navigate the spectra

  7. Introduction • To navigate the spectra

  8. Introduction • To navigate the spectra

  9. Introduction • To navigate the spectra

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

  11. 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

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

  13. 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)

  14. The system Spectra • lines • Avoided crossings

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

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

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

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

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

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

  21. The method: navigating the spectrum • 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 • We use adiabatic and rapid transitions to travel in the spectra • If it is posible try to make slow variations of the parameter

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  36. Results

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

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

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

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

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

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

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

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

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

  46. 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).

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

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