Single Photons from Coupled Quantum Modes Tim Liew

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) - Single Photon Statistics - Level Diagram Comparison of different systems & Effect of dephasing

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

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. , ar. Xiv: 1003. 0131 (2010) Coupled Photonic Crystal Cavities D Gerace, et al. , Nature Phys. , 5, 281 (2009)

Theory Hamiltonian: E E 1 a F Master Equation: G a J G J=0. 5 me. V (3 um boxes, 1 um apart) E 2 a=0. 012 me. V (3 um size) [J Kasprzak, et al. , PRB, 75, 045326] G=0. 2 me. V (3. 3 ps)

Second Order Correlation Function For the same value of a, coupling to a second mode significantly decreases the value of g 2 For <N 1>=0. 02, p(n 1>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 G E a E 2 E 1 G a F a E 3

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 g 2 (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