1. from Coupled Quantum Modes Tim Liew & Vincenzo Savona
Single Photons
from Coupled Quantum Modes
Tim Liew & Vincenzo Savona
Institute of Theoretical Physics, Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland
Single Mode Polariton Blockade
Two coupled modes (polariton boxes)
- Master Equation for the density matrix
- Single Photon Statistics
- Linear Fluctuation Theory
Three couple modes (parametric scattering)
- Level Diagram
Comparison of different systems & Effect of dephasing

2. Need confinement in an area 200nm x 200nm
Single Mode Polariton Blockade
A Verger, C Ciuti & I Carusotto, PRB, 73, (2006)
Optical Limiter n
E (meV)
Need confinement in an area 200nm x 200nm
k|| (mm-1) P
Planar Cavity

3. Two Mode System Metal surface pattern
C W Lai, et al., Nature, 450, 529 (2007)
S Utsunomiya, et. al., Nature Phys., 4, 700 (2008)
C Symonds, et al., APL, 95, (2009)
M Kaliteevski, et al., APL, 95, (2009)
Pattern Cavity Thickness
R Idrissi Kaitouni, et al., PRB, 74, (2006)
R Cerna, et al., PRB, 80, (2009)
Apply Stress
R Balili, et al., Science, 316, 1007 (2007)
Coupled Micropillar Cavities
D Bajoni, et al., APL, 90, (2007)
D Bajoni, et al., PRL, 100, (2008)
Optical Excitation
A Amo, et al., arXiv: (2010)
Coupled Photonic Crystal Cavities
D Gerace, et al., Nature Phys., 5, 281 (2009)

4. Theory Hamiltonian: J=0.5 meV E (3um boxes, 1um apart) G a J E2 E1
a=0.012 meV (3um size)
[J Kasprzak, et al., PRB, 75, ] F
G=0.2 meV (3.3 ps)
Master Equation:

5. Second Order Correlation Function
For the same value of a, coupling to a second mode significantly decreases the value of g2
For <N1>=0.02, p(n1>1)=0.18% (five times better than the failure rate of devices based on spontaneous parametric down conversion)

6. Linear Fluctuation Theory

7. Parametrically Coupled ModesG E E1 E2 E3 a F

8. Level Diagram Diagonalize the Hamiltonian
This state can only be reached via decay from an n=3 state

9. Comparison of different schemes
Pure dephasing term (exciton-phonon scattering):
D F Walls & G J Milburn, PRA, 31, 2403 (1985)

10. Summary
Noise correlations between coupled quantum modes can deliver better single photon statistics than a single isolated mode.
The enhancement is such that with the nonlinearity available in today’s samples, one can find a low value of g2 (despite dephasing).
One can also consider using parametrically coupled modes to improve single photon statistics.
T C H Liew & V Savona, PRL, to be published April 2010