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

Need confinement in an area 200nm x 200nm Single Mode Polariton Blockade A Verger, C Ciuti & I Carusotto, PRB, 73, 193306 (2006) Optical Limiter n E (meV) Need confinement in an area 200nm x 200nm k|| (mm-1) P Planar Cavity

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, 151114 (2009) M Kaliteevski, et al., APL, 95, 251108 (2009) Pattern Cavity Thickness R Idrissi Kaitouni, et al., PRB, 74, 155311 (2006) R Cerna, et al., PRB, 80, 121309 (2009) Apply Stress R Balili, et al., Science, 316, 1007 (2007) Coupled Micropillar Cavities D Bajoni, et al., APL, 90, 051107 (2007) D Bajoni, et al., PRL, 100, 047401 (2008) Optical Excitation A Amo, et al., arXiv:1003.0131 (2010) Coupled Photonic Crystal Cavities D Gerace, et al., Nature Phys., 5, 281 (2009)

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, 045326] F G=0.2 meV (3.3 ps) Master Equation:

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)

Linear Fluctuation Theory

Parametrically Coupled Modes G E E1 E2 E3 a F

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

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

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