Date post: | 30-May-2018 |
Category: |
Documents |
Upload: | hossienhossieni |
View: | 219 times |
Download: | 0 times |
of 29
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
1/29
inQuantum
Dots
By:Hossien Hossieni
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
2/29
Additionspin
of
2electron
For2electronadditionofspinsyields1,0
Spin1istrip et s=1,m=1,0,1
= = ,
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
3/29
QuantumDot
Quantumdots,alsocalledartificialatoms,are
smallregions(from1toabout100nm;1nm)
ofonesemiconductormaterialburiedin
energygap E.Theyaremadeupbyroughly1
millionatoms
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
4/29
TwoQuantum
Dot
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
5/29
ConfinementPotentialModelsinQuantumDots
bythefollowingsimpleforms:
2 Parabolic(harmonicoscillator)potential 3 Gaussianpotentialwell
4 Powerex onential otentialwell
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
6/29
RectangularPotentialWell
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
7/29
ParabolicPotentialWell
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
8/29
GaussianPotential
Well
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
9/29
PowerExponentialPotentialWell
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
10/29
PowerExponentialPotentialinCoupledQuantum
Dots
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
11/29
TheHamiltonianofthesystem
Coulombpotential(betweentwoelectron)
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
12/29
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
13/29
GroundStateEnergy
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
14/29
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
15/29
Bychoosing
Weget
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
16/29
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
17/29
Groundstateeigen valueenergyE0vs.confinementpotentialrangeRfor
,
=
,
=
=
.
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
18/29
GroundstateenergyE0vs.confinementpotentialrangeRfordifferent
,
=
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
19/29
Coulomb
interaction
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
20/29
LinearEntropyandEntanglementMeasure
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
21/29
Groundstateeigen valueenergyE0,CoulombenergyCandLinearEntropy
LofthereduceddensitymatrixfortwoelectronsconfinedincoupledQDstructures
versusvaryingconfinementpotentialrangeRfordifferentvaluesofp.
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
22/29
TimeDependenceinQuantumMechanics
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
23/29
SuddenChangeintheHamiltonian
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
24/29
TimeDependentPerturbationTheory
Inthatcase,theSchrdingerequationfortheHamiltonian
isequiva enttot eseto coup e equations
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
25/29
TransitionAmplitudesandProbabilities
Thesetofcoupledequations
isnoteasiertosolvewemultiply
theperturbationV(t)bytheunphysicalparameter (0 1)andexpand
theam litudes
Thetermslinearin yield
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
26/29
Electronlocalizationandentanglementinatwoelectron
uantum
dot
ThelastterminEq.istheZeemaninteractionwithgbeingtheeffectivegfactor, B the
Bohrmagneton,andsthespinofanindividualelectron.
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
27/29
Entanglemententropyofexcitedstates
consideringtheXYspinchainoflengthNwith
Hamiltonianisgivenby
.isthetransversemagneticeld and theanisotro arameter.
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
28/29
QuantumEntanglementandSymmetry
Bipartitesymmetricstates
8/14/2019 Study Entanglement Between Two Electrons StudyEntanglementBetweenTwoElectrons
29/29
1DanielR.Bes,QuantumMechanicsAModernandConciseIntroductoryCourse 2ShirwanMuhamad Abdullah,EffectofConfinementPotentialGeometryonEntanglement
BetweenTwoElectronsinQuantumDotsMSc.Thesis 3DavidJ.Griffiths IntroductiontoQuantumMechanics
,
twoelectronquantumdot
5VincenzoAlbaetal,Entanglemententropyofexcitedstates
6DariuszChruscinski etal,QuantumEntanglementandSymmetry