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/
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:
Confining potential: doble quantum well
filled with 2 e

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
Colaboradores-Referencias
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
Colaboradores-Referencias
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
Colaboradores-Referencias
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)

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Results
Second example: complex path

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Results
Second example: complex path

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Results
Second example: complex path

27. Colaboradores-Referencias
Results
Second example: complex path

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Results
Second example: complex path

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Results
Second example: complex path

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Results
Second example: complex path

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Results
Second example: complex path

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Results
Second example: complex path

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Results
Second example: complex path

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Results
Second example: complex path

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Results
Third example: more complex path

36. Results

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Results
Forth example: target state a coherent superposition

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Results
Forth example: target state a coherent superposition

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Results
Forth example: target state a coherent superposition

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Results
Forth example: target state a coherent superposition

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

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Results
Forth example: target state a coherent superposition

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Results
Forth example: target state a coherent superposition

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