Single Photonsfrom Coupled Quantum Modes

Tim Liew & Vincenzo SavonaInstitute of Theoretical Physics, Ecole Polytechnique Federale de Lausanne

(EPFL), Switzerland

Single Mode Polariton BlockadeTwo 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

A Verger, C Ciuti & I Carusotto, PRB, 73, 193306 (2006)

Single Mode Polariton BlockadeOptical Limiter

Need confinement in an area 200nm x 200nm

E (meV)

k|| (mm-1) P

n

Planar Cavity

Two Mode System

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)

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 Photonic Crystal Cavities D Gerace, et al., Nature Phys., 5, 281 (2009)

E

E1E2

TheoryHamiltonian:

Master Equation:

J

F

=0.012 meV (3um size) [J Kasprzak, et al., PRB, 75, 045326]

J=0.5 meV (3um boxes, 1um apart)

=0.2 meV (3.3 ps)

Second Order Correlation Function

For the same value of , 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

F

E

E1

E2

E3

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