Generation of twin photons in Triple Microcavities

Jérôme TIGNON

C. Diederichs, D. Taj, T. Lecomte, C. Ciuti, Ph. Roussignol,

C. Delalande

Laboratoire Pierre Aigrain (LPA),

École Normale Supérieure, Paris, France

A. Lemaître, J. Bloch, O. Mauguin, L. Largeau

Laboratoire Photonique et Nanostructures (LPN),

CNRS, Marcoussis, France

C. Leyder, A. Bramati, E. Giacobino

Laboratoire Kastler Brossel (LKB)Ecole Normale Supérieure, Paris, France

Motivations

Fundamental

Better understanding and control of light-matter interaction in semicond. nanostructures

Practical

Generating quantum correlated photons is the basis for quantum optics applications such as quantum cryptography.

Working systems rely on large and complex optical sources

Possibility to develop an integrated micro-generator of twin photons ?

Outline

Non-linear optics

Parametric conversion Phase matching OPOs

Light-matter interaction in semiconductors

Semiconductor microcavities Weak and Strong coupling regime OPO in single microcavities A triply resonant OPO in a VCSEL-like structure

Quantum optics

Noise measurements Quantum correlated photon pairs

Fundamental concepts / technical results

Optical Parametric Oscillation

2(pump,kpump) (signal,ksignal) + (idler,kidler)

Oscillation Paramétrique Optique (OPO)

Parametric conversion (for photons):

0

p i

s

p s

i

(2) (3)

pump

signal

idler

In a cavity: oscillation above a threshold (gain = cavity losses)

p

s

i

pump

NL Crystal (BBO)

cavity- Simple cavities, double (DROPO), triple (TROPO)

- Applications : - generation of new frequencies

- quantum optics (cryptography, etc).

OPO : the phase-matching problem

ISP

ISP

kkk

Problem : phase matching !!

IISsPP nnn ).().().(

Solutions : (1) birefringence

- pbm : GaAs isotropic

Solutions : (2) quasi-phase matching

- ex : PPLN

- reduction of the size of OPO (10 cm)

- complex fabrication / alignement

Light-matter interaction in

semiconductor microcavities

1,6 1,80,0

0,5

1,0

Energy (eV)

Miroir deBragg

Miroir de Bragg

Cavité Cavity Mode

Fabry-Pérot cavity

meV

Photon confinement : semiconductor microcavity

- Planar F.P. cavity, monolithic

- Finesse 103 , 104

Without confinement (3D)

Microcavity

Photon confinement : mode dispersion

x c

axe de croissance

Quantum Well:

exciton k// =photon k//

kz free photon

Fabry-Pérot Microcavity:

Selection of a photon kz

exciton k// =photon k//

kz quantified

Eexc

Ecav

En

erg

iek

//

exciton cavité

polariton

exciton

photons

k//

Ene

rgie

excMk

2

2//

2nkc

0

0

Strong and Weak Coupling Regime

A brief story of microcavities (a)

- In the weak coupling regime:Vertical cavity lasers (VCSELs, Soda et al. Tokyo, 1979)

- 1979 : low T°, optical pumping

- 1988 : CW, room T°

- 2005 : Ethernet, Fiber Channel etc.

- Isotropic emission

- Low threshold

- Parallelisation fabrication / test

- Strong Coupling, Microcavity-Polaritons :C. Weisbuch et al. PRL 69 (1992).

exciton

cavit

yX

laser

A brief story of microcavities (b)

- First studies :

cw spectroscopy (Rabi splitting, dispersion, T° etc).

population dynamics (ps, time-resolved PL)

- Today:

Coherent and non-linear dynamics (fs, P/p, FWM)

Stimulated emission, parametric scattering

A brief story of microcavities (c)

OPO with polaritons in a microcavity (a)

P.G. Savvidis et al. PRL 84 1547 (2000)

signal

idler

k//k//

EE

pump

Pump : 17°

Idler Signal 0°

• OPO in a nanostructure !

• OPO with mixt light-matter excitations !

90°

Strong resonant (3)

polaritonique nonlinearity

Low OPO threshold

R. M. Stevenson et al. PRL 85 3680 (2000)

OPO with polaritons in a microcavity (b)

o C. Ciuti et al., Phys. Rev. B 62, 4825 (2000)(théorie quantique)

o D. M. Whittaker et al., Phys. Rev. B 63, 193305 (2001)(théorie semi-classique)

Theory :

Gisin et al, Quantum cryptography, REV. MOD. PHYS. 74 (2002)

Motivations: -OPO

Source of twin photons ? quantum optics (quantum cryptography)

o Strong coupling regime required Low temperature (max 50 K)

o Idler emitted at very large angle + weakly coupled to outside

Inefficient collection for twin photons applications

o Pump injection at large angle No electrical injection with an integrated system

DRAWBACKS:

sp

i

What we want!

o Phase-matching without the strong coupling exciton / photon

Increase the temperature

o High idler intensity (at a smaller emission angle)

Efficient collection for twin photons applications

o Pump injection at 0°

Electrical injection possible

Micro-OPO in triple microcavities

New Design: a Triple Microcavity

C. Diederichs and J. Tignon, APL 87 (2005)

Coupling DBR 1

DBR GaAs/AlAs

-GaAs cavity 1

Substrate

-GaAs cavity 2

-GaAs cavity 3

DBR GaAs/AlAs

Coupling DBR 2

In0.07GaAs QW

Z growth axis

8m

In0.07GaAs QW

In0.07GaAs QW

Angle (degree)

Ene

rgy

(eV

)

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Optical modes (transfer matrices simulation)

Cavity degeneracy lifted

For dual-cavities : see e.g. Stanley et al., APL 65 (1994) : strong coupling between 2 cavities Pellandini et al., APL 71 (1997) : dual- laser emission

Armitage et al., PRB 57 (1998) : polariton dispersion

Uncoupled cavities |Coupled cavities

21

4

R

RRc

Condition for 2 coupled cavities :

Photonics modes delocalized throughout the whole structure

Inclusion of QWs / Weak and Strong coupling regime

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Angle (degree)

Ene

rgy

(eV

)

Strong Coupling Weak Coupling

Strong exciton-photon regime

Six polariton modes

Cavity-mode degeneracy lifted

Three coupled photonic modes

Experimental setup

Triple microcavity 8m

90°

CW Ti:sa

850 nm

Bragg mirrors

subs

trate

Optical fiber

QW1 QW2 QW3

Sample Growth: LPN

Tuning of the photon modes

Single cavities

X

Spacer wedge along X by interruption of the rotation at 0°

X

Ecav

Triple cavity

Cavity 1 : interruption at 0° (X) Cavity 2 : no interruption Cavity 3 : interruption at 90° (Y)

X

Y

Ecav

X

C. Diederichs et al, NATURE 440 (2006)

OPO (a)

all beams @ 0°

energy conservation

-30 -25 -20 -15 -10 -5 0

1.460

1.465

1.470

1.475

signal

pump

idler

Ene

rgy

(eV

)

Angle (degree)

0 5 10 15 20 25 30

x 200

100.0

1659

2.751E4

4.562E58E5

T = 6 K

OPO (b)

idler: negative dispersion

momentum conservation

-30 -25 -20 -15 -10 -5 0

1.460

1.465

1.470

1.475

signal

pump

idler

Ene

rgy

(eV

)

Angle (degree)

0 5 10 15 20 25 30

x 200

100.0

1659

2.751E4

4.562E58E5

T = 6 K

C. Diederichs et al, NATURE 440 (2006)

1.460 1.465 1.470

0

1000

2000

3000

4000

5000

0

1

2

3

4

5

Inte

nsity

(a.

u.)

Idle

r

Pum

p

Sig

nal

x 10

00

Energy (eV)

Properties of the OPO

Below threshold : 2 kW/cm2

Above threshold : 3.2 kW/cm2

gain of 4800

narrowing of the signal and idler from 1 meV to below 200 eV

high conversion efficiency under cw excitation = 10-2

Phase-matching dependence

-1 0 1 2 3 4 5

0

5

x = 2Ep-E

s-E

i (meV)

Id

ler

inte

nsi

ty (

a.u

.)

-1 0 1 2 3 4 5

0

5

10

15

x = 2Ep-E

s-E

i (meV)

Sig

nal i

nten

sity

(a.

u.)

x : “phase-matching” parameter Strong non-linear emission of the signal and idler states only for x=0, i.e. for E=0, k=0 (phase-matching).

103 10410-2

100

102

104

OP

O

N

orm

aliz

ed in

tensi

ty (

a.u

.)

Pump Power (W/cm2)

signal idler

Power dependence (a)

OPO threshold : 2.4 kW/cm2

103 10410-2

100

102

104

LA

SE

R

OP

O

N

orm

aliz

ed in

tensi

ty (

a.u

.)

Pump Power (W/cm2)

signal idler Laser

Power dependence (b)

Lasing at 6 kW/cm2

Low OPO threshold

Out of phase-matching

Comments / saturation of the idler

- Idler at higher energy is degenerate with QW absorption continuum

- Idler (and not Signal) is subject to multiple parametric scattering

- Signal / Idler ratio important ?

- yes for quantum-noise measurements applications

- no if one counts coincidences (it just lowers the overal coincidence counting rate)

“Horizontal” Parametric Scattering

s i

p

Fourier Plane

f ’

x

y

Réciprocal space imaging

“Horizontal” Parametric Scattering

s i

p

i

p

x

y

s

Large Negative detuning

Detuning close to zero

Horizontal Parametric Scattering (c)

10 100 10000,1

1

10

100

10 100 10001E-3

0,01

0,1

1

Inte

nsity

(a.

u.)

Power (mW)

~ P2

~ P

~ P

b)

a)

Inte

nsity

(a.

u.)

Power (mW)

Rayleigh

Scattering

OPO

What determines the angles ?

• Stereographic projection of the crystal

• Easy defect propagation

along some directions

The experimental configuration,

with an excitation along a high

symmetry direction allows probing these axis.

X ray diffraction (L. Largeau, LPN)

z

• Characterization by X-ray diffraction

• No dislocation

• Mosaicity

• elastic deformation due to AlAs / GaAs mismatch

• correlation length 400 nm with underlying crystal symmetry => photonic disorder

• common effect in all microcavities !!

Quantum correlated

signal and idler beams

pump

idler

signal Parametric conversion :

Production of a photon pair, correlation in space and time

+/--SpectrumAnalyzer

Parametric oscillation: production of twin beams,

correlated in intensity

(2)

(2)

Twin beams from Optical Parametric Oscillators

Beam Noise

SpectrumAnalyzer

))sin(ˆ)cos(ˆ()ˆˆ()(ˆ tYtXeaeatE titi

aaX ˆˆˆ is the amplitude quadrature

XaaaaI ˆˆ)ˆˆ(ˆˆ

)(ˆ)(ˆ 22 XII

Noise spectral density at the frequency Noise spectral density at the frequency ΩΩAmplitude fluctuationsAmplitude fluctuations

X

Y

Vacuum Noise, Beam noise, Squeezing

- Fluctuations limited by Heisenberg

- Vaccum noise (shot-noise, standard quantum limit)

- Beam noise for a coherent state

- Squeezing : non-classical state, quantum optics applications

Quantum correlations measurement: noise measurements

SpectrumAnalyzer

+/--

II11

II22

II11± ± II22μTROPO

Noise of the difference / Vacuum noise < 1 Quantum correlations !

S

I

pump

E

x

y

Experiment. (a) Dispersion (b) Fourier Plane

Quantum correlations measurement: noise measurements

Submitted to publication

Noise of the difference is below the Shot Noise

Detuning dependence

Summary / Outlook

Realization of a triply resonant OPO in a VCSEL-like structure : -VTROPO

cw operation with low threshold

Operation up to at least 150 K (compare with 50 K)

Generation of photon pairs in various configurations

Generation of quantum correlated twin photon pairs

Electrical injection

Operating temperature

Prospects