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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
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
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
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
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)
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 !!
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 !
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
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