quantum control using diabatic and adibatic transitions
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Quantum control using diabatic and adibatic
transitions
Diego A. Wisniacki
University of Buenos Aires
Colaboradores-ReferenciasColaborators
Gustavo Murgida (UBA)
Pablo Tamborenea (UBA)
Short version ---> PRL 07, cond-mat/0703192
APS ICCMSE
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
Introduction
∣ initial⟩ ∣ final ⟩
∣ final ⟩≈∣ target ⟩ Desired state
t0
tf
Introduction
H
iE
i
Main idea of our work
To travel in the spectra of eigenenergies
Ei
Control parameter
Introduction
To navigate the spectra
Introduction
To navigate the spectra
Introduction
To navigate the spectra
Introduction
To navigate the spectra
The system
Quasi-one-dimensional quantum dot:
Confining potential: doble quantum well filled with 2 e
Lz
Lz≫L
x yLy
Lx
Colaboradores-ReferenciasThe system
H=−ℏ2
2 m ∂
2
∂ z1
2 ∂2
∂ z2
2V z
1V z
2V
C∣z1− z
2∣−e z1 z
2E t
Time dependent electric field
Coulombian interaction
The Hamiltonian of the system:
Note: no spin term-we assume total spin wavefunction: singlet
The system
PRE 01 Fendrik, Sanchez,Tamborenea
Interaction induce chaos
Nearest neighbor spacing distribution
System: 1 well, 2 e
Colaboradores-ReferenciasThe system
We solve numerically the time independent Schroeringer eq.
Electric field is considered as a parameter
Characteristics of the spectrum (eigenfunctions and eigenvalues)
The system
Spectra lines
Avoided crossings
Colaboradores-ReferenciasThe systemCero slopedelocalized
Positive slope e¯ in the right dot
Negative slope e¯ in the left dot
Landau-Zener transitions in our model
LZ model
∣1 ⟩ ,∣2 ⟩
H =1
2
1=E
0
1
2=E
0
2
Linear functions
hyperbolas
Landau-Zener transitions in our model
LZ model
∣ t−∞ ⟩=∣1 ⟩
P1t∞=exp−2 2 / ℏ v 1− 2Probability to remain in the state 1
P2 t∞=1−exp−2 2 / ℏ v 1− 2
Probability to jump to the state 2
t =v tif
Landau-Zener transitions in our model
LZ model
2 / ℏ v 1−2≫1Adibatic transitions
Diabatic transitions 2 / ℏ v 1−2≪1
v≪2 / ℏ1−2
v≫2 / ℏ1−2
Colaboradores-ReferenciasLandau-Zener transitions in our model
E(t)
We study the prob. transition in several ac. For example:
Full system 2 level systemLZ prediction
P1
E=0.07, 0.27, 0.53,1.07, 4.27kV
cm ps∣1⟩
∣2 ⟩ ∣1⟩
∣2 ⟩
Colaboradores-ReferenciasLandau-Zener transitions in our model
We study the prob. transition in several ac. For example:
Full system 2 level system
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
Results
First example: localization of the e¯ in the left dot EPL 01 Tamborenea, Metiu
(sudden switch method)
PRRt =∫R dz1∫R dz 2∣ z1, z2, t ∣
2
LL
Results
First example: localization of the e¯ in the left dot
EPL 01 Tamborenea, Metiu (sudden switch method)
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults Second example: complex path
Colaboradores-ReferenciasResults
Third example: more complex path
Results
∣⟨target∣ T
f⟩∣=0.91
Colaboradores-ReferenciasResults
Forth example: target state a coherent superposition
∣ target ⟩= a1∣R R ⟩ a
2∣L L ⟩a
3∣R L ⟩ ∣a 1∣
2=∣a2∣
2=∣a 3∣
2=1 /3
Colaboradores-ReferenciasResults
Forth example: target state a coherent superposition
∣target⟩= 1
3[∣R R ⟩∣L L ⟩∣R L ⟩ ] ∣a 1∣
2=∣a2∣
2=∣a 3∣
2=1 /3
Colaboradores-ReferenciasResults
Forth example: target state a coherent superposition
∣target⟩= 1
3[∣R R ⟩∣L L ⟩∣R L ⟩ ] ∣a 1∣
2=∣a2∣
2=∣a 3∣
2=1 /3
Colaboradores-ReferenciasResults
Forth example: target state a coherent superposition
∣target⟩= 1
3[∣R R ⟩∣L L ⟩∣R L ⟩ ] ∣a 1∣
2=∣a2∣
2=∣a 3∣
2=1 /3
Colaboradores-ReferenciasResults
Forth example: target state a coherent superposition
∣target⟩= 1
3[∣R R ⟩∣L L ⟩∣R L ⟩ ] ∣a 1∣
2=∣a2∣
2=∣a 3∣
2=1 /3
Colaboradores-ReferenciasResults
Forth example: target state a coherent superposition
∣target⟩= 1
3[∣R R ⟩∣L L ⟩∣R L ⟩ ] ∣a 1∣
2=∣a2∣
2=∣a 3∣
2=1 /3
Colaboradores-ReferenciasResults
Forth example: target state a coherent superposition
∣target⟩= 1
3[∣R R ⟩∣L L ⟩∣R L ⟩ ] ∣a 1∣
2=∣a2∣
2=∣a 3∣
2=1 /3
Colaboradores-ReferenciasResults
Forth example: target state a coherent superposition
∣target⟩= 1
3[∣R R ⟩∣L L ⟩∣R L ⟩ ]
∣a 1∣2=∣a2∣
2=∣a 3∣
2=1 /3
Colaboradores-ReferenciasThe 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
Colaboradores-ReferenciasFinal Remarks
We found a method to control quantum systems
Our method works well: ∣⟨target∣ T
f⟩∣≈0.9
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).
Colaboradores-ReferenciasFinal Remarks
We can also obtain a combination of adiabatic states
Control of chaotic systems
Decoherence??? Next step???.