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 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 Desired state

Introduction Main idea of our work To travel in the spectra of eigenenergies 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

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

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

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)

The system Spectra lines Avoided crossings

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

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

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

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

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)

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

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

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

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

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Second example: complex path

Colaboradores-Referencias Results Third example: more complex path

Results

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

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

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

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

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

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

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

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

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?

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).

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