1. Indistinguishability of emitted photons from a semiconductor quantum dot in a micropillar cavity S. Varoutsis LPN Marcoussis S. Laurent, E. Viasnoff, P. Kramper & M. Gallard L. Le Gratiet, C. Mériadec, L. Ferlazzo I. Sagnes, A. Lemaître, I. Robert-Philip, I. Abram

2. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Motivation Production of indistinguishable single photons  Toolbox for quantum optics experiments  Linear optics quantum computation Photon-based two-qubit gates

3. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Single quantum dots InAs GaAs 3 nm

4. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Spectroscopy of single quantum dots Sharp spectral lines at low temperature (< 30  eV) Dephasing mechanisms (phonon, electrostatic) “Artificial”atoms InAs Pumping on an excited state of the exciton : one e-h pair Spectral filtering of the X line Emission of single photons GaAs InAs E GaAs Wetting layer Dot 900910920930940950960 200 400 600 800 1000 1200 1400 Intensity (arb. units) Wavelength (nm) 0 Laser at 888nm T ~4K

5. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Generation of single photons 1 photon Start Detector Stop Detector 50/50 Beamsplitter T ~ 12.2 ns 2T 3T TT Start Stop 0 T 2T 3T 4T Nb of coincidences Delay t 1 2 3 -20-1001020 0,0 0,2 0,4 0,6 0,8 1,0 g (2) (t) Delay t (ns)

6. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons Characteristics  Same polarization mode  Same spatial mode  Same spectral-temporal mode Purest state of light Pump pulse time Negligible jitter (  relax ~10 ps) compared with pulse duration No phase diffusion (T 2 ) during the pulse duration

7. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Key parameters : Indistinguishable Photons For indistinguishable photons : T2 = 2 T1 t T 1 ~ 1.2 ns Lifetime : T 1 Coherence time :T 2 Dephasing (phonons, electrostatic...) Pure dephasing time T 2 * T 2 = 1/T 2 * + 1/2T 1 1 ~ 300 ps

8. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons - T 1 shortening Cavity effects (Purcell) Cavity Quantum Electrodynamics (CQED) We use an isolated emitter X transition of a single QD We modify the EM environment EM modes of a microcavity Control of the interaction

9. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons - T 1 shortening Cavity effects (Purcell) F = = +  3 Q 0 3    0 4  2 V n 3  0 Enhanced spontaneous emission into the cavity mode Leakage spontaneous emission into free space 0 20 40 60 80 100 120 10 10 2 10 3 10 4 01234567890123456789 Q F Diameter (  m)

10. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons │1 1 > │1 2 > t 2 │1 3 > │1 4 > - r 2 │1 3 > │1 4 > + rt │2 3 > │0 4 > - rt │0 3 > │2 4 > │1 1 > │0 2 >r │1 3 > │0 4 > + t │0 3 > │1 4 > │0 1 > │1 2 >t │1 3 > │0 4 > - r │0 3 > │1 4 > A single photon on a beamsplitter A single photon on each input arm of a beamsplitter Both photons go the same way : «coalescence» into a two-photon state 1 2 3 4

11. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons Experimental set-up Time-interval counter Spectro- -meter Sample Stop Start 2 ns Spectro- -meter 2 ns

12. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons Experimental set-up Photon 2 Photon 1 4 ns Photon 1 Photon 2 2 ns Photon 2 Photon 1 Peak at  t=0 (Long-Short) Peak at  t=4 ns (Short-Long) Peak at  t=2 ns (Long-Long or Short-Short) 0 24 -2 -4  t (ns) Number of events

13. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons Experimental set-up For indistinguishable photons + 0 24 -2 -4  t (ns) Number of events Photon 1 Photon 2 Peak at  t=0 (Long-Short)

14. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons Number of events Strongly reduced probability (ideally 0) of simultaneous detection of two photons (i.e. one on each output arm) The photons coalesce two-photon state -20-1001020 0 100 200 300 400 500 600 Photon separation  t (ns)

15. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Direct measurement of T1 and T2 -4004080120160 0,0 0,2 0,4 0,6 0,8 Visibility Time (ps) 1,0 T2 ~ 100ps -2000200400600800 0 1000 2000 3000 4000 5000 6000 Intensity (arb. units) Time (ps) T1 ~ 90ps

16. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons Mandel dip T1 ~ 90ps T2 ~ 100ps and T2* ~ 225ps F ~15 & Coalescence efficiency ~ 55%  Photon 2 Photon 1 J. Bylander, I. Robert-Philip, and I. Abram, Eur. Phys. J. D 22, (2003) 295-301 -300-200-1000100200300 0,0 0,2 0,4 0,6 0,8 1,0 g (2) () Time delay  (ps) Theoretical prediction for: T1 = 90ps and T2 = 100ps Experimental Data

17. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Indistinguishable Photons Mandel dip T1 ~ 60 - 110 psT 2 * ~ 200 - 660 ps F ~15-25 Best coalescence efficiency ~ 76% -400-2000200400 0,0 0,2 0,4 0,6 0,8 1,0 Delay  (ps) g (2) (  )

18. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Resonant condition of Purcell effect 02 60 80 100 120 140 -4-2024 0 4 8 12 16 20 24 Lifetime (ps) Purcell Factor Detuning (Angstroms)

19. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Temperature dependence 3.3 2.9 2.8 0-2.2 Detuning ( Å) g (2) (0) 0.0 0.2 0.4 0.6 0.8 1.0 01020304050 0 100 200 300 400 500 Characteristic T 2 * T 1 g (2) (0) 0.0 0.2 0.4 0.6 0.8 1.0 01020304050 0 100 200 300 400 500 Characteristic times (ps) Temperature (K) T 2 * T 1

20. LABORATOIRE DE PHOTONIQUE ET DE NANOSTRUCTURES Conclusions Generation of indistinguishable single photons  Toolbox for quantum optics experiments  Engineering of nanosources for photon-based quantum information processing Future prospect :  Generation of entangled photons to implement more sophisticated functionalities of quantum information processing (teleportation, quantum logic...)