ifuap-buap mini-curso en nanoestructuras · ifuap-buap mini-curso en nanoestructuras parte ii....

IFUAP-BUAP Mini-curso en Nanoestructuras

Parte II. Sergio E. Ulloa – Ohio University

Department of Physics and Astronomy, CMSSCMSS,and Nanoscale and Quantum Phenomena InstituteNanoscale and Quantum Phenomena Institute

Ohio University, Athens, OH

Supported by US DOE & NSF NIRT

¿Preguntas? ¿Más info?

[email protected]

www.phy.ohiou.edu/~ulloa/

nano.gov

mailto:[email protected]

mailto:[email protected]

http://www.phy.ohiou.edu/~ulloa/

Resumen/Outline• Quantum dots – confinement vs interactions

– How to make / study them

• Coulomb blockade & assorted IV characteristics

• Optical effects – excitons: selection rules, field effects

• Transport in complex molecules: the case of DNA

Quantum Dots: L ~ λgood things come in small packages

Confinement: KE~ k2 ~ L-2

Interactions: PE ~ q2/L

For L~100nm, PE ~ 1meVwhile KE ~ 0.5meV (in GaAs)

For L~5nm, PE ~ 20meV ; KE ~ 200meV

Total energy

E = KE + PE

Quantum dot fabrication

Lithographically

Kouwenhoven et al, U Delft Weis et al, MPI Stuttgart

Ensslin et al, ETH Zurich


Self-assembly· Stranski – Krastanow islands· MBE· in-plane densities

~ 1010 - 1011 cm-2

· size variations < 10%· sharp photoluminescence

features, frequency ∝ size

AlAs and GaAs “antidots” in InAs

Tenne et al, PRB May 2000


Colloidal dots

• Chemical synthesis• CdSe, CdS, InP, etc• Size ~ 5nm diameter• Uses for biotags

Quantum Dot Corp.

excessexcessNaBHNaBH44

solublesolublemetal saltmetal salt(AgNO(AgNO33))

colloidal METAL dots in dendrimers0.6

0.5

0.4

0.3

0.2

0.1

0.0

Abs

orba

nce

800600400Wavelength (nm)

428 nm481 nm

-H2O

• Au or Ag ~3-5nm dots

• pH or hydration changesinterdot separation aggregation changesinteractions & color

G. Van Patten, Ohio University

QD w/tunable size and e- number~ artificial atomsElectronic transport -

Low bias: ground state – Coulomb blockadeHigh bias: excited states – selection rules(!)Rings, phases & resonances

I

ωIncident/outgoing photons -

Visible/optical: excitonFar infrared: internal multi-electron excitationsRaman: excitons/confined phononsω

Capacitance -Ground state vs B-fieldCombination w/optics & in-plane transportB

Coulomb blockade

I

B field effects

QD molecules

Ramirez et al, PRB 1999

Blick et al Science 2002

future?multidotsfor quantumcomputing

in seriesin parallel

Kondo effectGoldhaber-Gordon et al Nature 1998

Kondo primer

zero-bias feature

Kouwenhoven & Glazman, Phys World 2001

Aharonov-Bohm effect22 1

2 2

ˆ;

p eH p Am m c

B A A Bρϕ

= → −

= ∇× =Φ

B

ρ

Phases, dots, “rings” and resonances

1. Phase in experiments AB interferometer

2. Phase of a resonance (single particle)

3. CB in QD ~ SP resonance?

4. What’s the Fano effect / lineshape?

5. Fano as probe of coherence in QD?

6. QD in Kondo regime phases in expts?

7. Fano+Kondo to probe coherence in QDK?

Phase in experiments AB interferometerSchuster et al, Nature 1997

Yacoby/Heiblum PRL 1995

~ CB peaks

AB oscill’s

|tQD| eiθ

weaker AB signal whenQPC is on

Nature 1998

2 i 2CE QD dir

2 2QD dir QD di Q dirr

0

D

G ~| t | | t e t |

G ~| t | | t | 2 | t | cos(|

/

| t

2

)

ϕ

ϕ

θ θ

π

ϕ

∆= +

∆ = Φ Φ

− − ∆+ +

AB interferometer: “phase measurer”QD

dir

e-

If θdir is indep of Vgate θQD can be measured

QDiQD QD

n

1 nQD C

i / 2t C | t | eE E i / 2

2(E E )tan

θ

θ θ −

Γ= =

− + Γ−

= +Γ

A “pure” resonance has the Breit-Wigner form:

∆θQD/π

BW “SP” resonances OK….coherent propagation through QDCB charging ~ not important

but….

sequence of BW resonanceswould be expected to accumulate while phase “resets” to 0 as tQD ~ 0 !!?

overlapping resonances … BW??

e-e interactions?

G(B)=G(-B) not valid here (open device ∆θ ≠ 0,π)Why? … N theory papers …

nice disc: Aharony et al cond-mat/0205268

Fano effect / lineshapeinterference of discrete “autoionized” statewith a continuum asymmetric peaks in atomic excitation spectra

In QD; expt: Göres PRB 2000th: Clerk PRL 2001 …Ugo Fano, PR 1961

In AB interf + QD;expt: Kobayashi PRL 2002

Fano … ψE

mixVE

E'E E 'E '

a bϕ ψΨ = +∑&ϕ

21 E

2

E 'E

E

'

'

E

'

E

E| V |(E) tanE E F(E

; ')

| V |; F(E

1a s V sin (E

) shift of resonance due to continuumE E '

in ( )b cos (E) (E EV E E

E

)

)V '

ϕ

π

δππ

− = =−

∆ = −−

∆= − ∆ −

−= ∆

− ∑

“excitation” of ΨE via an operator T from an initial state I yields:

E ' E '

E

E E

'

*E

V modified state due to mixE E '

sin| T | I | T | I | T | I cosVψϕ

ψπ

Φ = + →−

∆Ψ = Φ − ∆

∑

Fano lineshape2

E*E E

2 2E

2 2E

| | T | I | (q )| |

E E F|

T | I | 1 transition prob via "autoionize

T | Iq ; cot ; 2 | V |

V | T | I / 2

d" state

ϕε

εψ ε

ππ ψ

− −Φ=

Ψ=

= − ∆ =

+=

+

Γ =Γ

Is G ~ |tQD + tdir|2 a Fano line?

idir d QD

zt e G ; ti

β

ε= =

+

2

d 2

| q |G G1

εε+

=+

withi

d

zq i eG

β−= +

Clerk PRL 2001Notice prob can vanishdue to interference

Fano as probe (proof?) of coherence in QD (CB)

Kobayashi PRL 2002

direct paths “through” QD?

how is QD “intrinsic” width affected by ring?

decoherence?1 vs N passes?

QD in Kondo regime phases in expts?

peaks deform

AB osc’s clear

phase lapses in CBbutplateaus in K valley~ π

Ji, Heiblum, Science 2000

phases in Kondo regime

phase evolves from plateaus ~ πto

lapses to 0 as Γ decreases

th: Gerland PRL 2000

K res phase shift ~ π/2(NRG)

phases in Kondo regime

w/temperature w/DC bias

Fano+Kondo to probe coherence in QDK?

Hofstetter PRL 2001(~Bulka PRL 2001) r 1

dotG ( ) [ ( )]ω ω ε ω −= − − Σ

AB phase/flux

direct ~ W

and for

dot

2R

2

2

b

2

b

L b

2

(e q) sing T "generalized Fano fo

e 2[ (0

rm"

)] /

4 / ; q (1e 1 e

T ) / T cos1

ε

α

ϕα

α ϕ

= +ℜΣ Γ

= Γ

+= +

+Γ Γ = − −

+

references on phases/Kondo/resonances

• Yacoby, PRL 74, 4047 (1995)

• Schuster, Nature 385, 417 (1997)

• Aharony, cond-mat/0205268

• Fano, PR 124, 1866 (1961)

• Clerk, PRL 86, 4636 (2001)

• Kobayashi, PRL 88, 256806 (2002)

• Ji, Science 290, 779 (2000)

• Gerland, PRL 84, 3710 (2000)

• Bulka, PRL 86, 5128 (2001)

• Hofstetter, PRL 87, 156803 (2001)

IFUAP–BUAP – Minicurso en NanoestructurasTarea # 1 — Entrega: 22 Julio 2003

1. [40pts] (a) Calcule el espectro para una partıcula de masa m confinada en una caja “rectan-gular” en 3D y 2D de radio R. Suponga que la caja tiene paredes infinitamente duras.(b) Describa como varıa la energıa de confinamiento con respecto a R.(c) Escriba la forma completa de los eigenstados en 3D/2D.(d) ¿Cual es el valor de la energıa (en eV) para los dos primeros estados en 2/3D si la masa dela partıcula es 0.067m0 (con m0 la masa del electron libre), y el radio es R = 5, 50, 100nm?Hint: funciones de Bessel.

2. [60pts] (a) Estime el efecto de la interaccion de Coulomb entre electrones en un punto cuanticode radio R, utilizando U = e2/Rε, donde ε es la constante dielectrica del material (≈ 12 paramaterials tıpicos), si el radio del punto es 5 o 100nm. Compare esta estimacion con la diferenciaentre los dos primeros niveles en un punto como se modelo en 1 arriba, ∆ = E2 − E1. ¿Paraque radio R son estas dos cantidades iguales (U = ∆)? Haga la estimacion tanto en 2D comoen 3D.(b) Use teorıa de perturbaciones para hacer la estimacion mas confiable:

〈Ψn(1)Ψm(2)|V (1 − 2)|Ψk(1)Ψl(2)〉,

en donde V (1 − 2) = e2/ε|r1 − r2| es la interaccion de Coulomb entre dos partıculas, y lasvarias Ψj son las funciones de onda (modeladas/escritas en 1(c) arriba). Use cualquier metodode integracion, numerica incluso, para evaluar (o al menos estimar) la integral en el caso quelos dos electrones estan en el estado base (y diferente spin, por supuesto) en un punto en 3D.Compare con (a) y comente.Hint (aunque no esencial):

1

|r|=

∫ 4π

q2e−iq·rd3q


Parte II. – Toma 2Sergio E. Ulloa – Ohio University





Self-assembly· Stranski – Krastanow islands· MBE· in-plane densities

~ 1010 - 1011 cm-2

· size variations < 10%· sharp photoluminescence

features, frequency ∝ size

laser power

Findeis et al, Sol. State Comm, 2000

•Excitons•Excited excitons (s- and p-shell)•Biexcitons, X-, X--, etc.

Photoluminescence in SINGLE QD

Excitons and dot shapes• Dot asymmetries reflected in exciton properties:

– Binding energy vs dot size– Oscillator strength / optical response– Influence of magnetic field

• Raman differential cross section and intensity ---experiments and phonon mode confinement:– Selection rules– Carrier masses– Scanning experiments

• Quantum rings: excitonic Aharonov-Bohm effect for neutral/polarizable entity

see part I

Trallero & Ulloa PRB 1999

Simple geometry: Parabolic confinementV(x,y)

Lx

wx

wy

Ly

B

Eg

Vez Vhz

x

y

z

Lz

( )2

2 2 2 2

2

1 1p A ( )2 2

| r r |

e h eh

j j j j x j y j jj

ehe h

H H H H

eH m x y V zm c

eH

ω ω

ε

= + +

= ± + + +

= −−

COM rel cH H H H= + +

Harmonic Oscillator in

2D

Song& SU; Pereyra & SU PRB 2000

effective confinement increases with B field

0

1

/ /

1 (circular limit)

Bx y x y

B

η ω ω η ω ω

η

=

>>

= → =

→

off-diagonal Coulomb interaction

exact expression: Song & SU PRB 1995

off-diagonal one-particle elements

Coulomb interactions in harmonic oscillator basis

exciton size

binding energy

Lx/Ly = 1:1 ◊ 2:1 + 3:1

binding energy = Eexc – E0 = Eb

Eb ~ 1/L

saturates to 2D value for L>>aB & all shapes

exciton “shrinks” as L 0, rS Lbut

rs aB as L>> aB

χ = linear optical susceptibility ~ PLE signal ~ optical response

COM gnd state & replicas

excitedexcited states of internal degrees states of internal degrees of freedomof freedom

area of dots = 5x5 nm2

Magnetic field effects

diamagnetic shift

orbital “Zeeman” splitting

binding energy exciton size

η=1η=1.25 suppression of

Zeeman orbital splitting

asymmetry of structure

SAQD RINGS!!

80nm

smallest COHERENTring potential for electronsand/or holes

Lorke et al PRL 1999

J Garcia 1999

Is there AB effect for excitons?

A le edc c

φ∆ = = Φ∫flux lines

v 0→

v exciton charge = ZERO→ no ABE?

AB is the nonadiabatic version of Berry phase in a flux

M. Berry, Proc. R. Soc. Lond. A 392, 45 (1984)

Ground state of 1D excitons (Romer & Raikh 2000): BUT...

Results for microscopic calculationSong & SU PRB 2001

soft/parab walls

hard wall

NO AB oscillations!!binding energy

AB oscillations seen if ring is narrower ~ 1D likewidth = 10nm

Hu et al PRB 2001

heavyhole

lighthole

BUT excitons are polarizable!

flux lines

e-

∆R

80 nm

e-h+

v 0→

v e-

Φe

flux lines

h+∆Φ

( )e h e hec

φ φ∆ − ∆ = Φ − Φ

net flux is nonzero!

*0 0( ) / 2e hR R R a= +strong Coulomb interaction limit:

22

1200

,2excE L EMR

∆Φ= + + Φ

2 2( ) .e hR R Bπ∆Φ = −

correlated motion*

0 0R aweak interaction limit:

2 22 2

2 20 0

,2 2

e hexc e h

e e h hE L L

m R m R Φ Φ

= + + − Φ Φ

2( ) ( ) ,e h e hR BπΦ = e hL L L= +

independent motion

weak interaction limit

optical emission stronglyoptical emission stronglysuppressed in B field suppressed in B field

windows windows

dark window Ltot non zero

bright window Ltot = 0

Govorov et al PRB 2002

strong interaction limit

optical emission stronglyoptical emission stronglysuppressed after critical suppressed after critical

B field B field

effective persistent currentassociated with Berry´s phase

and angular momentum inground state

Optical emission from a charge tunable quantum ring Warburton et al Nature 2000

Optical detection of the AB effect in a charged particleBayer et al PRL 2003

lithographic ring

~90nm

~30nm

PL

no oscillations in X0

only diamagnetic shift

experiments calculations

reasonable agreement w/calculations interactionsdo not change period and only slightly the amplitude

Science 2000

IFUAP–BUAP – Minicurso en Nanoestructuras Tarea # 2

Efecto Aharonov-Bohm en un anillo conductor. (a) En la figura debajo se muestra la conductancia experimental de un anillo

construido en un gas de electrones de dos dimensiones en un semiconductor. Estime de la gráfica el período de éstas oscilaciones de Aharonov-Bohm. El eje horizontal es campo magnético en milésimas de Tesla. ¿Por cierto, porqué se esperaría que la conductancia G fuera simétrica al invertir B, tal y como aparece en la figura?

(b) Suponiendo que éstas oscilaciones son producidas por el efecto AB, la conductancia G se puede aproximar por:

G ≈ G0 |1+ exp(iΦ/Φ0)|2 ,

en done Φ=BA es el flujo a través del anillo de area A, y Φ0=h/e es el cuanto de flujo magnético. Deduzca entonces el diámetro del anillo. (c) Suponga que el anillo fuera “ancho” y que entonces tuviera mas de un canal

transversal. Si el anillo es de 1 micra de radio interno y 2 micras de radio externo, estime el numero de canales permitidos para una longitud de Fermi de 50nm. De este número, estime que rango de períodos de oscilaciones AB se podrían ver en el experimento. ¿Se esperaría que las oscilaciones sobrevivieran? Explique brevemente su respuesta.


Parte II. – Toma 3Sergio E. Ulloa – Ohio University




Photons, excitons, spins, energy transfer & entaglement – all in QDs

• Gammon/Steel – optical control of quantum dot state

• Imamoglou – single photon source from quantum dots

• Klimov – Förster coupling between quantum dots

• Zrenner – coherent control of quantum dot photodiode

Gammon/Steel – optical control of quantum dot state

Gammon/Steel – optical control of quantum dot stateBonadeo et al PRL 1998

Naturally Formed GaAs QDs

42 Å GaAs layer500 Å Ga0.3 Al0.7As

250 Å Ga0.3 Al0.7As

500 Å GaAs cap layerAl mask with apertures

42 Å STM image showing the island

formation and elongation.

Gammon et al., Phys. Rev. Lett.76,3005 (1996)40nm

Samples are provided by D.S. Katzer, D. Park, and E. S. Snow, NRL

1623 1623.5 1624 1624.5 1625 1625.5 1626

Photoluminescence of a Single Exciton

Energy (meV)

0.000 T

0.430 T

0.860 T

1.290 T

2.150 T

3.010 T

3.870 T

4.730 T

QD Magneto-excitons * * -- g factorg factorB0

Weak field limit:

* First reported by S. W. Brown et al.,Phys. Rev. B 54, R17 339 (1996)

Hint = g*exµBB0Sz + αB0

2

g*ex = g*

e + g*hh

g*hh = 6κ + 27q/2

0

0.2

0.4

0.6

0.8

0 1 2 3 4 5

splittingshift

Magnetic Field (Tesla)

Zeeman splitting

laser power

Findeis et al, Sol. State Comm, 2000

•Excitons•Excited excitons (s- and p-shell)•Biexcitons, X-, X--, etc.

Photoluminescence in SINGLE QD

• Linear Spectroscopy: PhotoluminescenceIndirect probe of exciton resonancesRequires spectral diffusion of excited carriers

• Coherent Nonlinear Spectroscopy:CW differential transmissionResonant excitationProbe coherent interaction in the system

Experimental Techniques

Lock-in Am

plifierR

F Electronics

Epump

EprobeENL

AOM ƒ~100MHz

Detector

Reference

Imaging

CW FrequencyStabilized Dye

Lasers

5 K

Eprobe

ENL (ε) ~ χ(3) (ε) Epump E*pump Eprobe

Isignal = Re ( ENLE*probe )

D Steel et al U Michigan

NonNon--degenerate Nonlineardegenerate NonlinearSpectroscopy: AdvantagesSpectroscopy: Advantages

• Probe single excitonic state decay dynamics

Measure both T1 and T2 *

• Probe coupling between different excitonic states

Probe inter-dot energy transfer and dot-dot coupling

Study excited states of excitons

Probe multi-exciton correlation effects ;

Study the coherent interaction between exciton doublet .

* Nicolas H. Bonadeo et al., PRL, 81, 2759 (1998)

hhhh ExcitonicExcitonic Level DiagramLevel Diagram

σ+2

1−2

1+

23+

σ−

23−

Non-degenerate experiments can excite both σ+ and σ- excitons by varying the frequency and the polarization of the excitation beams (pump and probe beam).

21−

23+

23−

23+

23−

21+

21−

21+ Two-exciton state

Bound state of multi-excitons

σ+ stateσ- state

Ground state:0-exciton state

∆E

Scattering states

B0 = 0 B0 ≠ 0

c

v

Exciting Two ElectronsExciting Two Electrons

c

Two contributions:1. Incoherent:

Ground state depletion

2. Coherent:

Zeeman coherence

between σ- and σ+ state

21−

23+

23−

23+

23−

21+

σ+ stateσ- state

Ground state

Pumpσ−

Probeσ+

σ+2

1−2

1+

23+

23−

Resonant and coherent

excitation of two electronsσ−

v

3-level diagram in 2-electron basis

Optically Entangling Two Systems: the Importance of Coupling

Optically Entangling Two Systems: the Importance of Coupling

couplingcouplingcoupling

H0 + H´ H0 + H´Htotal=

• Without coupling → Product state of the two subsystems.• A strong coupling allows one system to see the excitation of the other.

Coulomb interaction between charged particles: trapped ionsMagnetic dipole interaction: NMR systemsExciton-exciton Coulomb coupling: excitons

• Mutual coherence between E and E´ is essential .

Coulomb Correlation*:Coulomb Correlation*:Coulomb interaction between electronCoulomb interaction between electron--hole pairs within single QDhole pairs within single QD

Two electrons are involved

within a single QD.Pumpσ−

Probeσ+

21−

23+

23−

23+

23−

21+

21−

21+ Two-exciton state

Bound state of multi-excitons

σ+ stateσ- state

Ground state:0-exciton state

∆E

Scattering states

Coulomb interaction between the two

excitons is important.

Two-exciton state cancels the signal due

to the symmetry in the level diagram.

But

21−

23−2

3+

21+

σ+σ-

* Kner et al Phys. Rev. Lett. 78, 1319 (1997)Ostreich et al Phys. Rev. Lett. 74, 4698 (1995)

Turn Turn offoff the Coulombthe CoulombCorrelation

Turn Turn onon the Coulomb Correlationthe Coulomb CorrelationCorrelation

Pumpσ−

+-Probe

σ+g Pumpσ−

- +Probe

σ+g

4 5 6 7 8 9-2 -1 0 1 2 3

σ− σ+

Pump: σ−

1==== −+−+ γγγγ No Signal !!

4 5 6 7 8 9-2 -1 0 1 2 3Probe ( γ )

Ground-state

Depletion

ZeemanCoherence

Total Signal

Probe ( γ )

1632.3 1632.4 1632.5 1632.6Energy (meV)

Degenerate and Non-degenerate Coherent Nonliear Response

σ− σ+

pump

probe

Degenerate

Non-degenerate

1.3 Tesla5K

σ−

σ+

Evidence for Zeeman Coherence in Single QDs

Experiment : Coulomb Correlation and Experiment : Coulomb Correlation and ZeemanZeeman CoherenceCoherence

4 5 6 7 8 9

Ground state

depletion

ZeemanCoherence

Total Signal

-2 -1 0 1 2 3

σ+ σ−

Pump: σ−

1==== −+−+ γγγγ

Probe ( γ )

Creation of two-electron entanglement

Ultimate Goal

• Combine:Optical control of individual QDsLong spin lifetimesQD nanostructure engineering

• To produce:Qubit register of QD spins

Coherence of a single QD can be controlled – Gammon et al have demonstrated this for excitons [Stievator et al., PRL (2001)]

Next: QNOT and other quantum gates

Spins have long coherence times: dephasing times T2* = 5ns-300ns[Dzhioev et al., PRL (2002)]

Next: explore in single QDs; optical read-out and initialization schemes

Science 2001

Imamoglou – single photon source from QDs

Imamoglou – single photon source from QDsMichler et al., Science 290, 2282 (2000)

• It is difficult to isolate a single photon, or fix the number of photons in a pulse

• Fluctuations in photon number mask the quantum features of light

• A stable train of laser pulses have Poissonian (photon number) statistics

It is desirable to have single photon sources:

single photon turnstile

Complete regulation of photon generation

Single Photon SourcesQuantum Cryptography: secure key distribution by single photon pulses

Quantum Computation: single photons + linear optical elementsE. Knill, R. Laflamme, and G.J. Milburn, Nature 409, 46 (2001)

Available sources:

• Highly attenuated laser pulse ⇒ Poisson fluctuations

• Parametric down conversion ⇒ Random generation of single photons

Possible solution: Deterministic (triggered) single photon emission:Single Photon Turnstile DeviceA. Imamoglu, Y. Yamamoto, Phys. Rev. Lett. 72, 210 (1994)

Experiments:

Coulomb blockade of electron/hole tunneling in a mesoscopic pn-junction:

J. Kim et al. Nature 397, 500 (1999)

Single Molecule at room temperature:

B. Lounis and W.E. Moerner, Nature 407, 491 (2000)

Single InAs Quantum Dot in a microcavity:

P. Michler et al., Science 290, 2282 (2000)

Signature of a triggered single-photon source

2)2(

)(:)()(:

)(tItItI

gτ

τ+

=• Intensity (photon) correlation function:

1

0 τ

g(2)(τ)• Single quantum emitter (I.e. an atom) driven by a cw laser field exhibits photon antibunching.

g(2)(τ)

τ0

• Triggered single photon source: absence of a peak at τ=0 indicates that none of the pulses contain more than 1 photon.

Photon antibunching• Intensity correlation (g(2)(τ)) of light generated by a

single two-level (anharmonic) emitter.

• Assume that at τ=0 a photon is detected:- We know that the system is necessarily in theground state |g>

- Emission of another photon at τ=0+ε is impossible.⇒ Photon antibunching: g(2)(0) = 0.

• g(2)(τ) recovers its steady-state value in a timescale given by the spontaneous emission time.

pump

• If three are two or more 2-level emitters, detection of a photon at τ=0 can not ensure that the system is in the ground state (g(2)(0) >0.5).

(nonclassical light)

photon

at ωp

Single InAs Quantum Dots

Energy (eV)1.25 1.30 1.35

Inte

nsity

(a.u

.)

P (W/cm2)

650

400

210

105

55

17 x5 in intensity

x2 in intensity

s-Shell

p-ShellInAs/GaAs Single QD

1X2X

T=4K

Two main wavelengths emitted from each shell

(For s-Shell)•2X recombination while there is already an e-h

pair in the s-shell (biexciton)•1X recombination while there is no other e-h pair

in the s-shell (exciton)

Due to carrier-carrier interactionTypically hν1X = hν2X + 2-3meV

Unique wavelengths for 1X and 2X transitions

Exciton linewidth measured by a scanning Fabry-Perot

Under non-resonant pulsed excitation

500 1000 15000

50

100

150

200

250

Inte

nsity

(a.u

.)

Bins

Free Spectral Range: 62 µeV

linewidth: 5.6 µeV

1.325 1.330 1.335

X2

X1

Inte

nsity

(a.u

.)

Energy (eV)

Photon antibunching from a Single Quantum Dot

(a)

(b)

(c)

-10 0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

0

20

40

60

Delay Time τ (ns)

Cor

rela

tion

Func

tion

g(2) (τ

) Coincidence C

ounts n( τ)

0.0

0.5

1.0

1.5

2.0

0

20

40

60

-10 0 10 20 30 40 50

0.0

0.5

1.0

1.5

2.0

0

20

40

60

80

0.5

0.0

-10 50

Energy (eV)1.335 1.340 1.345

Inte

nsity

(a.u

.) 1X

2X

105 W/cm2

g2(0)=0.1τ = 750 ps

55 W/cm2

g2(0)=0.0τ = 1.4 ns

15 W/cm2

g2(0)=0.0τ = 3.6 ns

proof of atom-like behavior

PL spectrumP=55W/cm2

T=4K

A single quantum dot excited with a short-pulse laser can provide single-photon pulses on demand

BUT

How about embedding quantum dots in a microcavityto increase collection efficiency and fast emission?

Microdisk Cavities

No roughness on the sidewall up to 1nm !Q>18000 for 4.5µm diameter microdiskQ=9000 for 2µm diameter microdisk

Fundamental whispering gallery modes cover a ring with width ~ λ/2n on the microdisk

Q>17000

Q=13500

Michler et al., Appl. Phys. Lett. 77, 184 (2000)

A single quantum dot in a microdisk

Energy (eV)1.315 1.320 1.325 1.330

Inte

nsity

(a.u

.)

1X

2X

WGM

Q = 6500

Larger width of the peaks due to larger lifetime of the quantum dot

P=20W/cm2

T=4K

Pump power well above saturation level

Tuning the quantum dot into resonance with a Cavity Mode

EWGM-E1X (meV)-1.5 -1.0 -0.5 0.0 0.5 1.0

WG

M In

tens

ity (a

.u.)

0

200

400

600

800

Temperature (K)0 10 20 30 40 50 60

Ener

gy (m

eV)

1318

1319

1320

1321

1322

1323

WGM1X

T=44K

• Small peak appears at τ=0:• Purcell effect: reduction of emission time

Cavity coupling can provide better collection

Klimov – Förster coupling between QDs

Klimov – Förster coupling between QDsCrooker et al PRL 2002

D* + A D + A*

Non-Radiative Energy Transfer Mechanism

Coulomb-driven interaction

Dipole-dipole interaction (Förster 1946) Higher multipoles interaction (Förster – Dexter)

Exchange-driven interaction (Dexter)

trioctylphosphine oxide (TOPO) ~11A

A acceptor: larger dot

D donor: smaller dot

NQDs have bettercharacteristics than

biological light harvesting compounds, eg LH2

(a) PL decays from a dense film of monodisperse R=12.4A/9A CdSe/ZnS NQDs at the energies specified in the inset. Inset: cw PL spectra from film (solid) and original solution (dashed).

(b) Dynamic redshift of the peak emission.Inset: PL spectra at the specified times.

Crooker et al PRL 2002

(a) Schematic of NQD energy-gradient bilayer for light harvesting—13 A dots on 20.5 A dots.

(b) ‘‘Instantaneous’’ PL spectra at 500 ps intervals (from 0 to 5 ns), showing rapid collapse of emission from 13 A dots.

Our Goal

Study the excitation energy transfer in quantum-dotarrays using an appropriate model Hamiltonian

† † † † † †( ) † †, ,

N N NH T c c T d d Uc c d d U c c d de NNi j i j i i i i i i j jh

N

i j i i jV c

NNd d cs j ji ii j

= + + + +∑ ∑ ∑=

∑≠

Period of small oscillation ~ 1.3 ~1

2T Ve cProbability of each basis state as a function of time

0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0 |1100> |1001> |0110> |0011>

Vct/(2π)

0 30 600.5

1.0

1.5

2.0

10 12 14 16 18 20 22 240.5

0.6

0.7

0.8

0.9

1.0

tota

l pro

babi

lity

of e

xcito

n st

ate

Vct/(2π )

3.6

3.4

-13.7

-14.28

Period of large oscillation ~ 15 ~ 12 fV Vc

0.2

Probability of each basis as a functionof time without tunneling

Probability of each basis as a functionof time without Förster

Calculations for two dots

0 10 20 30 40 50

0.0

0.5

1.0

1.5

2.0

Vct/(2π)

|1100> |1001> |0110> |0011>

Te/Vc=0Vf/Vc=-0.04Vcnn/Vc=-0.1

0 2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

Vc/(2π)

|1100> |1001> |0110> |0011>

Probability of each basis as a function of time

Te/Vc=-0.8Vf=0Vcnn/Vc=-0.1

Time evolution of the oscillator strength of an exciton initially localized at dot 12 in a 24 dot chain

0 10 20 30 40 50 60 70 800.0

0.5

1.0

1.5

2.0

2.5

3.0

Osc

illat

or s

tren

gth

Vct/2π

1 Psec

Vc=10 mev Vc=100 mev

4Te/Vc=0.30.8 1.6

Vc,nn/Vc=0.1Vf/Vc=0.04Th=0

G. W. Bryant, Physica B 314, 15 (2002).

30 20 10 0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

Vct/2π

(12) (11) (14) (10) (15) (9) (16) (8) (17) (7) (18) (6) (19) (5) (20) (4) (21) (3) (22) (2) (23) (1) (24)

The “movie” of the 24 dots

exciton probability at each dot

0 5 10 15 20 25 300.0

0.2

0.4

0.6

0.8

1.0

Vc/(2π)

12

13

1415 16 17 18 19

2021 22

24

23

probability of exciton state in each dot

Förster rate for polymer

2 23.11 8 8Vh ctn n U U V Vc c

π π= = ≈→ +

From graph/calculation

22.2tVc

π≈

exciton probability at each dot

Vct/2π

efficient interdot transfer rate

Zrenner – coherent control of quantum dot photodiodes

Zrenner – coherent control of quantum dot photodiodesZrenner et al Nature 2002

Shadow mask

Top contact: 5nm Ti (semitransparent)

QDs InGaAs

Back contact

Laser focus

Possibles Possibles measurementmeasurementss

Photolumenescence (PL) spectrum (for τrad< τtunnel)

Photocurrent (PC) spectrum (for τrad> τtunnel)

Rabi Oscillation in a two level systemRabi Oscillation in a two level system

0ω

0 ( ) cos( )2 2z x

tH tω σ ω σΩ= +

( )( ) tt µ ε⋅Ω =

For For ω = ωω = ω0 0 and using RWAand using RWA

20 sin

2XP →Θ =

( )t dtτ

−∞

Θ = Ω∫0.0

0.5

1.0

πPulsed Area (Θ)

3π 4π2π0

Exciton Population

Time scales for the deviceTime scales for the device

rad 1 nsτ tunnel 3 ps τ → ∞ Tuned by VbTuned by Vb

PhotoluminescencePhotoluminescence τrad< τtunnel τrad< τtunnel τrad> τtunnel

NeHe laser

PhotocurrentPhotocurrent τrad> τtunnel

Ti:sapphire laser

pulse 1 psτ

pulse 82 MHzfF. Findeis et al. Appl. Phys. Lett. 78, 2958 (2001)

Artificial ion (charged exciton)Artificial ion (charged exciton)τrad< τtunnel

F. Findeis et al. Phys. Rev. B 63, 121309 (2001)

How does the Zrenner device work?How does the Zrenner device work?

τrad> τtunnel

A. Zrenner et al. Nature 418, 612 (2002)

How does the Zrenner device work?How does the Zrenner device work?

pulse 1 psτ

pulse 82 MHzf

pulseXXI e fρ=

2sin2XXρ Θ =

Mesoscopic optical spectrum analyserMesoscopic optical spectrum analyser

QCSEQCSE

Rabi Oscillation in the photocurrentRabi Oscillation in the photocurrent

pulseXXI e fρ=

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