QDs and optical microcavities: tailoring spontaneous emissionnanoparticles.org/pdf/Gerard.pdf ·...

LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES

QDs and optical microcavities:tailoring spontaneous emission

Jean-Michel GERARD

Equipe mixte CEA-CNRS-UJF « Nanophysique et Semiconducteurs »[email protected]

Grateful thanks to B. Gayral (CEA) as well as to

B. Sermage, A. Lemaître, I. Robert, E. Moreau, I. Abram, V. Thierry-Mieg, L. Ferlazzo from CNRS/LPN Marcoussis

Spontaneous emission control : why? (as of ~1982)


laser diode

Current I

Out

put p

ower

Is

Spontaneousemission Stimulated

emission

I

I

250n

m

Only a tiny fraction ofspontaneous emission is useful!

β ~ 10-5

100000 times decrease of Isexpected for β ~ 1 !


Two strategies toward improved SE control

Energy

Densityof photon modes

quantumwell

emission

Energy

Energyquantum dots

optical microcavity

kT

Optical microcavity = photon confinement on the wavelength scalediscrete photon modes

If the emitter is coupled to a single mode, β=1


β=1 « Thresholdless »-laser

Ideal conversion of electrical signals into optical signals. 1 e- -> 1 photon into the (single) mode. Linear input/output characteristic curve. No additional noise. High cut-off frequency

<n>=1

spontaneousemission

Stimulatedemission

Pout

Proposal :

Kobayashi et al, 1982

Yokoyama, Science 256, 62 (1992)

Björk et al, IEEE-JQE 27, 2386 (91)Pin


CQED with QDs : historical background

CQED (80->...)

SE can actually be tailored to a large extent for atoms in electromagnetic

cavities

optical microcavities (90->...)

it is possible to confine opticalphotons on the wavelength scale

in 2D, 1D, 0D

self-assembled QDs (~94->...)

single QD optical spectroscopyreveals atom-like behavior CQED with QDs

(96->...)


Outline

1) Some basic microcavity effects2) QDs as probes of photonic microstructures 3) CQED effects on QDs4) Some application prospects :

single-mode photon sourcesmicrolasers

For a recent review see: Solid state CQED with self-assembled QDs, in Topics in Applied Physics 30, 269 (2003), P. Michler ed. Springer


SE angular redistribution in planar microcavities

R

R

R

R

λ/2

emitterin free-space

A. Kastler, Appl. Optics 1,17 (1962)

Application to light emitting diodes : directional emission + high efficiency η~25%(Blondelle et al, Electron. Lett 31, 1286, 1995)

η~2% air

GaAs


Tailoring the spontaneous emission rateE

Free space modes

atom

Fermi golden rule: exponential decayeunit volumper modes ofdensity 1 ∝τ

One can tailor spontaneous emission dynamics

. Dimensionality, refractive index...

. Coupling to a single mode (0D cavity, or optical selection rule)

e.g. : strong coupling for QWs in planar cavities (Weisbuch et al, PRL 69, 3314, 1992)


Ex: Brorson et al, IEEE JQE 26, 1492 (1990)Emitter in a planar microcavity

ideal metallic mirrorsL

usual case forQWs and QDs

Thickness of the cavity layer nL/λ

Both SE rate enhancement and inhibition expected


InAs QD array in a planar microcavity

Very weak effect on QD spontaneousemission dynamics !

Solomon et al, PRL 86, 3903 (2001)

This is expected since the effective cavity length is around 4 λ/n

λ/n


Strong and weak coupling regimes in 0D cavities

Ω (V)Cavity damping (Q)

SE into other modes

Perfect cavity=> reversible spontaneous emission

hΩ = |d . Ε(r)|

Emitter dipole field per photon

time

Rabi oscillationP(t)1

=>Entangled eigenstates

2hΩ

Energy

|g, 1> |e, 0>


Strong coupling for a single cesium atom in an optical microcavity

Hood et al, PRL 98

Strong coupling first observed for atoms in the microwave spectral range (superconductors are IDEAL mirrors!)

More recently observed in the optical spectral range


Strong and weak coupling regimes in 0D cavities

time

dampedRabi oscillation

P(t) 1

Ω (V)Cavity damping (Q)

SE into other modes

Ω >> 1/τdecoherence =>

τ ∼ 2 τdecoh

time

P(t) 1

Ω < 1/τdecoherence => exponential decay« weak coupling regime »

τ ∼ f(Q,V,…)


Two important figures of merit

Ability to confine the e.m. field spatially:

effeff Vn

V 20

max 2:

εωε h

= dd

Actual cavity Equivalent cavityvolume Veff

Ability to store the e.m. energy:

ephoton

e

QQmodmod

1:ω

τωω

∆=↔

∆=

Around 1 eV, Q=1000 <-> τphoton =0.6 ps


The « Purcell effect »

Decoherence mostly due to photon escape (low Q) => ∆ωmode >> ∆ωem

ρ(ω)

~1/Q

~ Q

weakcouplingregime

( )2

.1 fdi εωρτ

rr∝

free space

Purcell (1946)Fp=

magnitude for an ideal emitter

.quasi-monochromatic

.spatial matching

.spectral matching

( )V

nQ

cav

free3

243 λπτ

τ=

Fp


Spontaneous emission rate for a « non-ideal » emitter

2

22

2

max2

mod2

mod

2mod

)(

).()()(4 drE

drE

ErEF

eeme

ep

cav

freerr

rrr

ωωωω

ττ

∆+−∆

=

Spectral detuning spatial detuning dipole misorientation

If the emitter linewidth is not negligible,

( ) ( )

out washediseffect Purcell theand emitter broad afor

)(

em

em

QQ

dL

→

→ ∫ ωωωρωρω

« natural » emitter line


How to confine light in all 3 dimensions with dielectrics ?

metallic mirrors are too lossy at optical frequencies!

distributed Bragg reflection total internal reflection(DBR, photonic crystal) (e.g. optical fibers)


Some 0D solid-state microcavities1 µm

2 µm 3 µm

V < (λ/n)3V=6 (λ/n)3

V=5 (λ/n)3

3D confined modesbut not perfect « photonic dots » (leaky modes)!

Q ?


Probing cavity modes with QDs

1.346 1.348 1.350 1.352 1.354

theory:

x10

PL

inte

nsity

(arb

. uni

ts)

Energy (eV)

Systematic probing of cavity modes (no selection rule)J.M. Gérard et al, Appl. Phys. Lett. 61, 459 (1996)

QD internal light source widely used to study microdisks orPC cavities see e.g. D. Labilloy et al, APL 73, 1314 (1998)

diam=4 µm1 µm

GaAs/AlAsmicropillar


E. Moreau et al,

APL 79, 2865 (2001)Probing cavity modes with one (few) QDs

1.250 1.255 1.260 1.265

10K1 µm

1 µW 200 µW

PL

Inte

nsity

(lin

. uni

ts.)

energy (eV)

cavitymode

Very strong homogeneous broadening of the single QD emission underhigh excitation conditions => broadband light source!


Probing cavity modes with QDs (2)

0.0 0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40: theory

∆E

(meV

)

Pillar Radius (µm)

neff<n

Resonance condition:

planar: L= λ / npillar : L= λ/ neff

L

Appl. Phys. Lett. 61, 459 (1996)


Large diameter micropillars (d>4λ/n)

Same profile for guided mode in GaAs and AlAs layers

⇒No mode coupling at interfaces⇒Fundamental pillar mode built using

neff (GaAs) = neff (AlAs)n (GaAs) n(AlAs)

=> the structure is still a « λ-cavity » for the novelresonant wavelength λ = L . neff (GaAs)

=> Cavity Q unchanged

L


Probing cavity Q’s

High Q’s can be achieved (Q=5000, τ~3ps)

Q drops at small sizes : intrinsic or extrinsic effect ?

0 2 4 6 8

1 000Q

diameter (µm)

Qplanar

Very weak absorption of the QD array => we probe the « empty » cavity Q (as long as Q<~10000)


Numerical study of the intrinsic Q of GaAs/AlAs micropillarsP. Lalanne et al, APL june 2004

0.2 0.4 0.6 0.8 1 1.2 1.4200

400

600

800

1000

1200

1400

1600

0.4 0.43

diameter (µm)

Q

Strong oscillations in the small diameter limit !


Small diameter micropillars (d>4λ/n)

(Slightly) different mode profile in GaAs andAlAs layers

⇒ inter-mode coupling at interfaces

⇒ fundamental pillar mode built usingand

L


refle

ctiv

ity

neff<nEnergy

Blue shift of the DBR stopband as a result for the lateral confinement


Energy of the fundamentalpillar mode

refle

ctiv

ity

Energy

Resonant cavity mode = α + β with |α|>>|β|

The component propagates freely through the DBRs

=> interferences and oscillations on Q !


Numerical study of the intrinsic Q of GaAs/AlAs micropillarsP. Lalanne et al, APL june 2004

0.2 0.4 0.6 0.8 1 1.2 1.4200

400

600

800

1000

1200

1400

1600

0.4 0.43

diameter (µm)

Q

Behavior well understood in a two-mode transfer matrix model

( + )


Probing cavity Q’s

0 2 4 6 8

1 000Q

diameter (µm)

Q2D

see e.g.T.Rivera et al,APL 74, 911 (1999)

High Q’s can be achieved (Q=5000, τ~3ps)

Q drops at small sizes : scattering by sidewall roughness

Fp = 32 achieved for d=1 µm !


Some 0D solid-state microcavities1 µm

2 µm 3 µm

V=6 (λ/n)3, Q=12000Fp =150

V=1.2(λ/n)3, Q=13000Fp=810 (Caltech 04)

V=5 (λ/n)3, Q=2100Fp=32

High Q, low volume, 3D confined modes


Some solid-state CQED experiments

performed with QDs


CQED : strong coupling for single QDs?

|ground, 1 photon>

Ωrabi

|excited, 0 photon>

2hΩ

Energy

|g, 1> |e, 0>

InAs QD in solid-state cavity : huge vacuum field (105 V/cm)

large dipole (0.6 e.nm)

hΩ = |d . εmax|

Sizeable vacuum Rabi splitting expected : 2hΩ ~ 50 µeV for V~ 10 (λ/n)3

∆EemitterVRS observable 2hΩ > ∆Ecavity

Here, negligible emitter linewidth⇒the relevant criteria for strong coupling is : 4 hΩ > ∆Ecavity

Andreani et al, PRB 60, 13276 (1999)


Strong coupling for single QDs ? Gérard et al, Physica E9, 131 (2001)


Strong coupling for single QDs ? Gérard et al, Physica E9, 131 (2001)Andreani et al, PRB 60, 13276 (1999)


Fresh news !

The strong coupling regime has been observed by tworesearch groups :

. micropillars + big InGaAs QDs displaying a « giant »oscillator strength (Forchel et al, Würzburg)

. InAs QD in high Q photonic crystal microcavity(Scherer et al, Caltech)

(still unpublished)


Purcell effect on InAs QDs

1946: Purcell’s paper1983: Observation for atoms in cavities (x 500! Haroche et al, ENS Paris)

1997: First observation of the Purcell effect in a solid-state microcavity !

QD array in micropillar x 5 J.M. Gérard et al, PRL 81, 1110 (1998)QD array in microdisk x 18 B. Gayral et al, Physica E7, 641(2000)

x 12 B. Gayral et al, APL 78, 2828 (2001)QD array in PC cavity x 12 T. Happ et al, PRB 66, R041303 (2002)

single QD in microdisk x 6 A. Kiraz et al, APL 78, 3932 (2001)single QD in micropillar > x 3 E. Moreau et al, APL 79, 2865 (2001)

x 4 G. Solomon et al, PRL 86, 3903 (2001)x 5 J. Vuckovic et al, APL 82, 3596 (2003)


Purcell effect for a collection of QDs (d=1 µm, Fp=32)

0 1000 2000

QBs out of resonance QBs in resonance

τ ~ 0.25 ns

τ = 1.05 ns

PL

inte

nsity

(lin

. uni

ts)

time (ps)

1.346 1.348

PL

inte

nsity

(arb

. uni

ts)

PL decay faster only for on-resonance QDs : intrinsic effectSE rate enhancement (x5) much smaller than Fp

PRL 81, 1110 (1998)


How to understand the magnitude of the Purcell effect

M o d e d ens ityd

E nergy

Random distribution of QDs=> spatial + spectral averaging


Fp : the relevant figure of merit

0 5 10 15 20 25 30 350

1

2

3

4

5

6 experiment model for 2D dipole

Q=2000d=1.3 µm

Q=960d=1 µm

Q=1600d=0.9 µm

Q=2250d=1 µm

Q=5200d=4.2 µm

τ 0 / τ do

n

Purcell factor FP

+random distribution

Enhancement factordepends as expectedon Fp , not d or Q

Good agreement with theory

PRL 81, 1110 (1998)


Dependence of SE rate enhancement on the spectral detuning

fromSolomon et al, PRL 86, 3903 (2001)

see alsoGraham et al, APL 74, 3408 (1999)

Experiment in good agreement withthe expected spectral dependence


SE inhibition in metal-coated micropillars

No inhibition in standrad micropillars, due to leaky modes => gold-coated pillars

M. Bayer et al,

PRL 86, 3168 (2001)

Efficient reduction of the density

of non-resonant modes by the

metallic coating

=> strong SE inhibition (/10)

for out-of-resonance QDs

cavitym

ode energy


Purcell effect for QDs in microdisks

200 400 600 800 1000 1200 1400 1600 1800

2 µm

Off-resonance

Q=7000

Q=10000

Inte

nsity

(lin

. sca

le)

Time (ps)

Up to x 12 SE rate enhancement

B. Gayral et alAPL 78, 2828 (2001)


Purcell effect in microdisks

0 200 400 600 800

experimentmodels:

Fp+spectral/spatial averaging

+ "jitter" due to relaxation time

Inte

nsity

PL

(lin.

sca

le)

Time (ps)

(30 ps)

B. Gayral et al, APL 78, 2828 (2001)


Purcell effect in a c.w. experiment

1E-4 1E-3 0.01 0.1 1

100

1000

10000

100000

1000000

1E7

out-of-resonance QDs

in-resonance QDs8KP

L in

tens

ity (l

og)

excitation power (log)

PL

B. Gayral et alPhysica E7, 641 (2001)

Saturation due to filling of fundamental QD statesPurcell effect (x18 here!)=> saturation occurs for higher pumping power

Same behavior observed for QDs in PC cavities (Happ et al, PRB 2002)


Few QDs in a micropillar

1.250 1.255 1.260 1.265

10K1 µm

1 µW 200 µW

PL

Inte

nsity

(lin

. uni

ts.)

energy (eV)

cavitymode


Purcell effect on isolated QDs in a micropillar(Q2D=1000, Q=500, Fp=7)

1E-3

0,01

0,1

Rel

ativ

e In

tens

ity τ ~ 400 ps

τ ~ 1.1 ns

τ ~ 1.3 ns

0 2 4 6 8 10Delay (ns)

SE enhancement > x 3

Cavity Mode

QD1QD3

10 µW100 nW

λ (nm)970 980 990

QD2

Moreau et al,APL 79, 2865 (2001)


Beware !

Unlike experiments on large collections of QDs, quantitative modelling not possible

since the QD location (and τfree) are not precisely known !(see e.g. Gayral et al, PRL 90, 229701, 2003)

Coupling the QD in/out of resonance is a good way to highlight the Purcell effect andto estimate its magnitude


Purcell effect for a single QD in a microdisk

0 2 4 6 8 10 12 14 16 18 20

0.1

1

T=4K1.75nsec

T=48K1.75nsec

T=31K850psec (resonance)

Inte

nsity

(a.u

.)Time (ns)

Kiraz et al, APL 78, 3932 (2001)UCSB

F>2


Applications of the Purcell effect


(Nearly) single-mode spontaneous emission

ω

ρ(ω)

QD

Purcell effect=

selective enhancement of SE into the resonant mode

F/τfree

γ/τfree(γ∼1) 1≈

+=

γβ

FF J.M. Gérard et al

PRL 81, 1110 (1998)

Very interesting for single photon sources and microlasers !


What is a single photon source ?What is a single photon source ?

clicclic

Source able to emit single photons pulses on demand

N.B. : Non-classical state of light⇒Impossible to generate it using a thermal source or a laser

Applications : quantum cryptography, metrology...


A single-mode single-photon source

GaAs/AlAs micropillar

20 nmIsolated InAs QD

=> Single-photon emission

⇒ Efficient collection+

single-mode behaviorproposal: J.M. Gérard et B. Gayral,

J Lightwave Technol. 17, 2089 (1999)exp : E. Moreau et al, APL 79, 2865 (2001)


Some properties of this single photon source

<2% !Single photon collection efficiency

44%38%

All photons prepared in the same mode (spatial+ polarization)

~ No two-photon pulses

Key device for the practical implementationof quantum cryptography

air

GaAs

Pelton et al, PRL 89, 233602 (2002)Moreau et al, Physica E 13, 418 (2002)


SPS efficiency for GaAs/AlAs micropillarsscattering by

sidewall roughness

Q spoiling ε < β

int

int

111

QQ

QQQ scat

βε =

+=

J.M. Gérard et al, quant-ph/0207115W. Barnes et al, Eur. Phys. J. D.18, 197 (2002)

0 2 4 6 8

1 000Q

diameter (µm)

scattering by sidewall roughness !

ε < βa careful optimisation of the intrinsiclosses is necessary!

Q2D


Polarization control in single-mode micropillars

Elliptical cross section

1.4 µm

0.7 µm

1.265 1.270 1.275 1.280

PL In

tens

ity (

lin.)

Energy (eV)

x-polarized

y-polarized

Non degenerate fundamental modeGayral et al, APL 72, 1421, 1998

~ 90% linear polarisation degreeof single QD emission

Moreau et al, APL 79, 2865, 2001


Indistinguishable single photons and the issue of decoherence

Indistinguishable single photons T2 = 2 T1

Decoherence events

t

t


InAs QD SPS : photon coalescence experiment

Santori et al, Nature 419, 594 (2002)

Probability of detection on D1+D2D1 D2

InAs QD in bulk GaAs : T2 (~ 600ps) << 2 T1 (~2 ns)

Here, emission of nearly-Fourier-transform limited single photons by the InAs QD, thanks to the Purcell effect


Toward « nanolasers »

β ~0.04Ith = 36 µA

Huffaker et al,APL 71, 1449 (1997)

β ~ 10-5β ~ 0.1

Ith = 5 mA Ith = 40 µA

Fujita et al, Electron. Lett. 36, 790 (2000)

Sub µA threshold current expected in the β~1 limit !

Purcell effect at 300K ???


QDsThe smallest PC cavities exhibitV’s as low as 0.2 (λ/n)3

Best QD arrays ~ 15 meV linewidthat 300K

Assuming Qcav > Q QDs , the SE rate enhancement factor is :

( )V

nQQDs

cav

free3

243 λπτ

τ= ~ 30

and β > 0.95 !

Probably the best strategy to date for approaching the regime of« thresholdless » lasing at 300K


Conclusion

Using QDs has been the key for observing CQED effects

Solid-state CQED is a very lively domain

Still many basic effects to be observed !

Important potential applications in optoelectronics andquantum information science


What is beyond?

moderate β, huge Q

200 µW at 300Kfor InAs QDs

(ENS/LKB2003)

moderate Q, high βusing the Purcell effect

ex: QDs in 2D PCs

β∼1 in 3D PCs


Single quantum dot laser?Low temperature required !!!

cavem ωωγτβ

∆>∆⇒>

without

Purcell ef

fectwithPurcell effect

Strong couplingΩ<∆<∆ hemcav ωωIth~10 pA predictedPelton et Yamamoto,PRA 59, 2418 (1999)

Τ

emcav ωω ∆<Ω<∆ h

Weak coupling and lasing


Semiconductor microdisks2 µm

GaAs disk

GaAlAs pedestal

3D photon confinement using waveguiding + total internal reflexion(whispering gallery modes)

V~ 5 (λ/n)3 !


Probing WGMs with QDs

1.2 1.3

unprocessed QB array(weak excitation)

50 µW100 µW

2.5 mW

PL

Inte

nsity

(lin

. uni

ts)

Energy (eV)

B. Gayral et al

APL (1999)

Observation of high Q WGMsGreat sensitivity of Q on sidewall roughnessQ>10000 for wet-etched microdisks

QD internal light source also commonly used to probe PC cavities

see e.g. D. Labilloy et al, APL 73, 1314 (1998)


An ideal dielectric microcavity

E. Yablonovitch, PRL, 2238 (1991)

photonic crystal + defect

β = 1

All photons are collected/prepared in a single mode !

Rem: spontaneous emission control= main initial motivation for developping photonic crystals

3D PCs and SPSs


To be done !!

Photonic defect+

SC or diamond nanoX, molecule

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