Transcript Polarization selective scattering of polaritons in wire

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
Fundamental concepts / technical results
 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
Optical Parametric Oscillation
Oscillation Paramétrique Optique (OPO)
 Parametric conversion (for photons):
wpump
widler
wsignal
c(2)
c(3)
ws
wp
wi
wi
2(wpump,kpump)
2wp
(wsignal,ksignal) + (widler,kidler)
ws
0
 In a cavity: oscillation above a threshold (gain = cavity losses)
cavity
- Simple cavities, double (DROPO), triple (TROPO)
wp
pump
wi
ws
NL Crystal (BBO)
- Applications : - generation of new frequencies
- quantum optics (cryptography, etc).
OPO : the phase-matching problem
 Problem : phase matching !!
wP = wS + wI
r
r r
kP = kS + kI
n(wP).wP = n(ws).wS + n(wI).wI
 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
Photon confinement : semiconductor microcavity
1,0
Fabry-Pérot cavity
 meV
0,5
Miroir de
Bragg
Cavité 
Miroir de
Bragg
Cavity Mode
0,0
1,6
Energy (eV)
- Planar F.P. cavity, monolithic
- Finesse  103 , 104
1,8
Photon confinement : mode dispersion
Without confinement (3D)
Microcavity
Strong and Weak Coupling Regime
Quantum Well:
kc
n
Energie
axe de
croissance
photons
exciton
2
 k
2Mexc
exciton k// =photon k//
kz free photon
0
Fabry-Pérot Microcavity:
exciton
Selection of a photon kz
exciton k// =photon k//
kz quantified
cavité
polariton
Eexc
Energie

k //
Ecav
c
x
0
2
//
k //
A brief story of microcavities (a)
- In the weak coupling regime:
Vertical cavity lasers (VCSELs, Soda et al. Tokyo, 1979)
- Isotropic emission
- Low threshold
- Parallelisation fabrication / test
- 1979 : low T°, optical pumping
- 1988 : CW, room T°
- 2005 : Ethernet, Fiber Channel etc.
A brief story of microcavities (b)
- Strong Coupling, Microcavity-Polaritons :
C. Weisbuch et al. PRL 69 (1992).
laser
X
exciton
A brief story of microcavities (c)
- 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
OPO with polaritons in a microcavity (a)
Idler
Signal 0°
pump
idler
Dk//
DE
DE
90°
Pump : 17°
Dk//
signal
P.G. Savvidis et al. PRL 84 1547 (2000)
• OPO in a nanostructure !
• OPO with mixt light-matter excitations !
OPO with polaritons in a microcavity (b)
Strong resonant c(3)
polaritonique
nonlinearity
Low OPO threshold
R. M. Stevenson et al. PRL 85 3680 (2000)
Theory :
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)
Motivations: m-OPO
 Source of twin photons ?
quantum optics (quantum cryptography)
i
Gisin et al, Quantum cryptography, REV. MOD. PHYS. 74 (2002)
p
s
DRAWBACKS:
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
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)
Z growth axis
DBR GaAs/AlAs
-GaAs cavity 1
In0.07GaAs QW
Coupling DBR 1
-GaAs cavity 2
In0.07GaAs QW
Coupling DBR 2
-GaAs cavity 3
In0.07GaAs QW
DBR GaAs/AlAs
Substrate
 8mm
Optical modes (transfer matrices simulation)
Uncoupled cavities | Coupled cavities
 Cavity degeneracy lifted
0.9
0.8
0.7
0.6
Energy (eV)
0.5
0.4
0.3
Condition for 2 coupled cavities :
4R
Rc 
1 + R 2
 Photonics modes delocalized
throughout the whole structure
0.2
0.1
Angle (degree)
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
Inclusion of QWs / Weak and Strong coupling regime
Strong exciton-photon regime
Cavity-mode degeneracy lifted
Six polariton modes
Three coupled photonic modes
Strong Coupling
Weak Coupling
0.9
0.8
Energy (eV)
0.7
0.6
0.5
0.4
0.3
Angle (degree)
Experimental setup
QW1
QW2
QW3
Optical
fiber
q
CW Ti:sa
850 nm
90°
Bragg mirrors
Triple microcavity
 8mm
Sample Growth: LPN
Tuning of the photon modes
Single cavities
Triple cavity
Y
X
X
 Spacer wedge along X by
interruption of the rotation at 0°
Ecav
 Cavity 1 : interruption at 0° (X)
 Cavity 2 : no interruption
 Cavity 3 : interruption at 90° (Y)
Ecav
X
X
OPO (a)
C. Diederichs et al, NATURE 440 (2006)
1.475
 all beams @ 0°
x 200
Energy (eV)
1.470
1.465
 energy conservation
idler
pump
8E5
4.562E5
2.751E4
1.460
signal
1659
100.0
-30 -25 -20 -15 -10
-5
0
5
Angle (degree)
10
15
20
25
30
T=6K
OPO (b)
C. Diederichs et al, NATURE 440 (2006)
1.475
 idler: negative dispersion
x 200
Energy (eV)
1.470
1.465
 momentum conservation
idler
pump
8E5
4.562E5
2.751E4
1.460
signal
1659
100.0
-30 -25 -20 -15 -10
-5
0
5
Angle (degree)
10
15
20
25
30
T=6K
Properties of the OPO
Pump
5
Signal
5000
 Below threshold : 2 kW/cm2
4
 Above threshold : 3.2 kW/cm2
 gain of 4800
3
 narrowing of the signal and idler from
1 meV to below 200 meV
Idler
3000
2000
2
x 1000
Intensity (a.u.)
4000
 high conversion efficiency under
cw excitation = 10-2
1000
1
0
0
1.460
1.465
Energy (eV)
1.470
15
5
Idler intensity (a.u.)
Signal intensity (a.u.)
Phase-matching dependence
10
5
0
-1 0
0
1
2
3
4
x = 2Ep-Es-Ei (meV)
5
-1 0
1
2
3
4
5
x = 2Ep-Es-Ei (meV)
 x : “phase-matching” parameter
 Strong non-linear emission of the signal and idler states only for x=0, i.e.
for DE=0, Dk=0 (phase-matching).
10
4
10
2
10
0
10
 OPO threshold : 2.4 kW/cm2
signal
idler
OPO
Normalized intensity (a.u.)
Power dependence (a)
-2
10
3
10
2
4
Pump Power (W/cm )
10
2
10
0
10
signal
idler
Laser
-2
10
3
LASER
10
4
Out of phase-matching
OPO
Normalized intensity (a.u.)
Power dependence (b)
 Lasing at 6 kW/cm2
 Low OPO threshold
10
2
4
Pump Power (W/cm )
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
Réciprocal space imaging
qy
qx
f’
p
s
i
Fourier Plane
“Horizontal” Parametric Scattering
s
qy
p
p
s
i
i
qx
Horizontal Parametric Scattering (c)
Large Negative detuning
a)
Rayleigh
Scattering
Intensity (a.u.)
1
~P
0,1
0,01
1E-3
10
100
1000
Power (mW)
Detuning close to zero
b)
OPO
Intensity (a.u.)
100
~P
10
1
2
~P
0,1
10
100
Power (mW)
1000
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)
• 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 !!
z
Quantum correlated
signal and idler beams
Twin beams from Optical Parametric Oscillators
signal
pump
c(2)
Parametric conversion :
Production of a photon pair,
correlation in space and time
idler
Parametric oscillation:
production of twin beams,
correlated in intensity
c(2)
+/--
Spectrum
Analyzer
Beam Noise
+ iwt
iwt
ˆ
ˆ
ˆ
E(t ) =  (aw e + aw e ) =  ( Xˆ cos(wt ) + Yˆ sin(wt ))
Spectrum
Analyzer
+
ˆ
X = aˆw + aˆw
is the amplitude quadrature
+
ˆ
I = aˆw (aˆw + aˆw ) = aˆw Xˆ
2
2
ˆ
ˆ
I () = I DX ()
Noise spectral density at the frequency Ω
Amplitude fluctuations
Vacuum Noise, Beam noise, Squeezing
Y
X
- 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
I1
I1± I2
μTROPO
+/--
Spectrum
Analyzer
I2
Noise of the difference / Vacuum noise < 1
Quantum correlations !
Experiment. (a) Dispersion (b) Fourier Plane
E
qy
S
pump
I
q
qx
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 : m-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
Prospects
 Electrical injection
 Operating temperature