Quantum control using diabatic and adibatic transitions

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Quantum control using diabatic and adibatic
transitions
Diego A. Wisniacki
University of Buenos Aires
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Colaboradores-Referencias
Colaborators

• Gustavo Murgida (UBA)
• Pablo Tamborenea (UBA)

• Short version ---gt PRL 07, cond-mat/0703192
• APS ICCMSE

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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

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Introduction
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Introduction
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Introduction
Desired state
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Introduction
Desired state
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Introduction

• Main idea of our work

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Introduction

• Main idea of our work

To travel in the spectra of eigenenergies
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Introduction

• Main idea of our work

To travel in the spectra of eigenenergies
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Introduction

• Main idea of our work

To travel in the spectra of eigenenergies
Control parameter
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Introduction

• Main idea of our work

To travel in the spectra of eigenenergies
Control parameter
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Introduction

• Main idea of our work

To travel in the spectra of eigenenergies
Control parameter
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Introduction

• Main idea of our work

To travel in the spectra of eigenenergies
Control parameter
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Introduction

• Main idea of our work

To travel in the spectra of eigenenergies
Control parameter
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Introduction

• To navigate the spectra

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Introduction

• To navigate the spectra

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Introduction

• To navigate the spectra

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Introduction

• To navigate the spectra

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The system
Quasi-one-dimensional quantum dot
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The system
Quasi-one-dimensional quantum dot
Confining potential doble quantum well
filled with 2 e
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The system
Quasi-one-dimensional quantum dot
Confining potential doble quantum well
filled with 2 e
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The system
Quasi-one-dimensional quantum dot
Confining potential doble quantum well
filled with 2 e
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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
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The system
Interaction induce chaos
PRE 01 Fendrik, Sanchez,Tamborenea
System 1 well, 2 e
Nearest neighbor spacing distribution
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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)

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The system
Spectra
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The system
Spectra

• lines

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The system
Spectra

• lines

• Avoided crossings

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Colaboradores-Referencias
The system
Cero slope delocalized
Negative slope e in the left dot
Positive slope e in the right dot
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Landau-Zener transitions in our model
LZ model
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Landau-Zener transitions in our model
LZ model
Linear functions
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Landau-Zener transitions in our model
LZ model
hyperbolas
Linear functions
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Landau-Zener transitions in our model
LZ model
if
Probability to remain in the state 1
Probability to jump to the state 2
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Landau-Zener transitions in our model
LZ model
Adibatic transitions
Diabatic transitions
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Colaboradores-Referencias
Landau-Zener transitions in our model
We study the prob. transition in several ac. For
example
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Colaboradores-Referencias
Landau-Zener transitions in our model
We study the prob. transition in several ac. For
example
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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)
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Colaboradores-Referencias
Landau-Zener transitions in our model
We study the prob. transition in several ac. For
example
2 level system
Full system
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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

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Results

• First example localization of the e in the
  left dot

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Results

• First example localization of the e in the
  left dot

EPL 01 Tamborenea, Metiu (sudden switch method)
LL
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Results

• First example localization of the e in the
  left dot

EPL 01 Tamborenea, Metiu (sudden switch method)
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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Second example complex path

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Colaboradores-Referencias
Results

• Third example more complex path

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Results
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Colaboradores-Referencias
Results

• Forth example target state a coherent
  superposition

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Colaboradores-Referencias
Results

• Forth example target state a coherent
  superposition

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Colaboradores-Referencias
Results

• Forth example target state a coherent
  superposition

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Colaboradores-Referencias
Results

• Forth example target state a coherent
  superposition

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Colaboradores-Referencias
Results

• Forth example target state a coherent
  superposition

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Colaboradores-Referencias
Results

• Forth example target state a coherent
  superposition

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Colaboradores-Referencias
Results

• Forth example target state a coherent
  superposition

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Colaboradores-Referencias
Results

• Forth example target state a coherent
  superposition

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Colaboradores-Referencias
The method questions

• Is our method generic?

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Colaboradores-Referencias
The method questions

• Is our method generic?

We need well defined avoided crossings
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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
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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?

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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).

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Colaboradores-Referencias
Final Remarks

• We can also obtain a combination of adiabatic
  states

• Control of chaotic systems

• Decoherence??? Next step???.