1. Non-local exciton- polariton spin switches Laboratoire Kastler Brossel, Paris (experimental part) : C. Adrados R. Hivet J. Lefrère A.Amo E. Giacobino and A. Bramati University of Southampton : A.V. Kavokin (theoretical part) EPFL, Lausanne : T.C.H. Liew ( theoretical part ) R. Houdré (fabrication of the sample) PLMCN 10, Cuernavaca, Mexique, avril 2010

2. Outline I – Spin switch at k≠ 0 1)All optical and non local switch 2)Spin selective switch II – Spin switch at k = 0 with bistability

3. Semiconductor Microcavities in strong coupling regime : POLARITONS, mixture of excitons and photons. Excitons : High non-linearities at low thresholds due to the Coulomb interaction Photons : Propagate fast (~ 1% speed of light) Short lifetime (a few ps) All optical control : … power of the incident beam : density of polaritons … transverse direction of the incident beam : polaritons velocity … polarization of the incident beam : polaritons spin state + reduced size of the system : integrability Why the use of SC microcavities for all-optical spin switches ? High repetition rate Exciton switch with electrical control : G. Grosso et al. Nature Photonics 3, 577–580 (2009)

4. Non linear transmission (theory) : k p (μm -1 ) A A off All-optical switch Excitation power P 1 < P threshold Power dependence of the pump P threshold

5. B k p (μm -1 ) B on Renormalization of the dispersion curve Power dependence of the pump All-optical switch Excitation power P 2 > P threshold Non linear transmission (theory) : P threshold Polariton switch configuration : the amount of power P 2 -P 1 necessary to switch is added thanks to a small probe.

6. Cw pump (red) : big spot 60 μm (diameter) Cw probe (blue) : small spot 6 μm (diameter) Experimental set up (d) X Y Near field CCD  k kzkz k║k║ Microcavity sample Pump + probe superposed, with same k with incident in plane angle = 3.8° blue detuned by 0.16 meV from the LPB Laser wavelength = 836.95 nm, blue detuned by 0.16 meV from the LPB

7. Sub threshold cw pump laser, large Very localized cw probe laser renormalization Pump + probe : switch (renormalization) of the whole pump spot, induced by the probe. Pump (σ+) Probe (σ+)Pump+Probe Detection σ+ 20 µm Non local switch Polariton flow Transmitted power : 9 mW Transmitted power : 54 mW Transmitted power : 3 mW A off B on A off B on Polariton density of the σ+pump vs excitation power

8. PROBE x Energy PUMP E LPB E Laser A B t=0t=60 ps Blueshift propagation Non local switch Non-local action : The small probe switches on the pump polaritons of the arrival probe area. v polariton = hk // /m polariton = 0.94 μm/ps : propagation all over the pump beam. Model : x Polaritons Energy

9. Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right. Non local switch Polariton flow (pump and probe)

10. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

11. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

12. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

13. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

14. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

15. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

16. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

17. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

18. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

19. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

20. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

21. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

22. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

23. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

24. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

25. Non local switch Polariton flow (pump and probe) Propagation : we move the area of incidence of the probe, same k // for pump and probe, from left to right.

26. Exciton-Polariton Spin Exciton with Sz=+1 : made by a +3/2 hole and a -1/2 electron. Exciton with Sz=-1 : made by a -3/2 hole and a +1/2 electron. Exciton with Sz = ±2 (hole +3/2 and electron +1/2 or hole -3/2 and electron +1/2) don’t couple with light. In first approximation, the dominant interaction betwwen 2 excitons is the EXCHANGE INTERACTION (exchange of holes and electrons). When dressed with light (Sz=±1) it results that : Ref : P.Renucci et al, PRB 72, 075317 (2005); C.Ciuti et al, PRB 58 p7926-7933 (1998); M.Wouters, PRB 76, 045319 (2007); M.Vladimirova et al, PRB 79, 115325 (2009); M.Combescot, PRB 74, 125316 (2006). for Interaction constant between polaritons with parallel spins g↑↑ Interaction constant between polaritons with antiparallel spins g↑↓ |g↑↑| >> |g↑↓|

27. Exciton-Polariton Spin Strong EXCHANGE INTERACTION (exchange of holes and electrons) between 2 excitons (Sz=±1) dressed with light Ref : P.Renucci et al, PRB 72, 075317 (2005); C.Ciuti et al, PRB 58 p7926-7933 (1998); M.Wouters, PRB 76, 045319 (2007); M.Vladimirova et al, PRB 79, 115325 (2009); M.Combescot, PRB 74, 125316 (2006). |g↑↑| >> |g↑↓| With Interaction constant between polaritons with parallel spins g↑↑ Interaction constant between polaritons with antiparallel spins g↑↓

28. 25 μm pump σ + (no probe)probe σ + (no pump) pump σ + + probe σ + pump σ + + probe σ - FLOW 1 0 EXPERIMENT pump σ + + probe σ + pump σ + + probe σ - THEORY 1 0 A B on off Spin selectivity Pump σ+ Polariton density of the σ+pump vs excitation power >> Solution of the Gross-Pitaevskii equation

29. Pump σ+ Only on the pump (zone without probe) Ellipticity of the probe σ+σ+ σ-σ- σ+σ+ Pump σ+ and probe σ+ * Gain x6 * Propagation and spin dependence Spin selectivity pump σ + + probe σ + pump σ + + probe σ - 1 0 Threshold in the ellipticity of the probe : minimum amount of σ + required to switch on the σ + pump.

30. Polarization control A B on off >> Linearly polarized pump Spin dependent interaction Final polarization: that of the probe σ+σ+

31. Polarization control Linearly polarized pump Spin dependent interaction Final polarization: that of the probe A B on off pump TE + probe σ + 25 μm FLOW pump TE + probe σ + det σ++σ -σ++σ - 1 0 EXPERIMENT THEORY σ+σ+ >>

32. Polarization control Linearly polarized pump Spin dependent interaction Final polarization: that of the probe A B on off >> σ -σ -

33. Polarization control Linearly polarized pump Spin dependent interaction Final polarization: that of the probe A B on off 25 μm FLOW det σ++σ -σ++σ - 1 0 EXPERIMENT THEORY σ -σ - pump TE + probe σ - >>

34. Pump TE (linear) Polarization control Detected Ellipticity

35. ● Interaction between parallel spins >> interaction between opposed spins Pump purely circular + probe : EXCLUSIVE SWITCH Pump linearly polarized + probe : polarization CONTROL ● Non local action ● Low threshold : strong non-linearities and 5 ps polariton lifetime we need low energy densities to induce the switch : 1-2 fJ/μm 2, 2 orders of magnitude less than the state-of-the-art all optical spin switch. ● High potential repetition rate (for a 60 μm spot and a 3.8° incident angle) : about 10 GHz CONCLUSION spin switch at k≠0 Amo et al., Nature Photonics (DOI : 10.1038/NPHOTON.2010.79 )

36. Bistability at k // = 0 At normal incidence, we can observe a hysteresis cycle (ref : A.Baas, PRB 70, 161307(R), 2004)

37. + Switch off the probe COPOLARIZED probe pump pump + probe : ON Pump only : ON Spin switch at k // = 0 with bistability 736 10800

38. ● Exclusive switch : when the pump and the probe are crosspolarized, no switch. ● Propagation mecanism : diffusion of the polaritons (probe and pump) thanks to their Δk (around k=0). To check in real time. Spin switch at k // = 0 with bistability

39. Constructive interferences Destructive interferences Excitation power ● How to switch off the pump thanks to the probe only ? By dephasing the probe with respect to the pump. Probe and Pump must have the SAME SIZE. Spin switch at k // = 0 with bistability Pump OFF state Pump + probe : ON Pump only : ON state Switch off the probe Add a probe (same size as pump) in phase with pump Pump + probe out of phase Ref : I.A.Shelykh et al, PRL 100, 116401 (2008)

40. ● How to switch off the pump thanks to the probe only ? by dephasing the probe with respect to the pump and making destructive interferences. For that we need a pump and a probe with THE SAME SIZE. Spin switch at k // = 0 with bistability Pump σ + + probe σ + : pump has been switched on by the probe. Probe has been dephased : extinction of the pump Pump σ + only : the pump stays in the ON state (hysteresis).

41. CONCLUSION spin switch at k=0 ● We have one bit : we can go from 1 state to the other by tuning an external probe (perturbation), and the bit keeps the memory of the perturbation. ● Also here, we have a high speed of switch : when pump and probe with the same size, it is given by the polariton lifetime (ps range), repetition rate of about 1 THz. ● Very low thresholds (strong non-linearities thanks to the excitonic part of the polaritons)

42. Spin bistability (k=0) : spin rings Power dependence for an elliptical excitation (mainly spin up) Signature of the interaction between spin up and spin down Ref Yvan, Gippius

43. ρ c =-1 : σ - ρ c =+1 : σ + Spin rings (still k=0) Colors : degree of circular polarization ρ c Real space (x,y) Ref Yvan, Gippius

44. ρ c =-1 : σ - ρ c =+1 : σ + Spin rings (still k=0) Colors : degree of circular polarization ρ c Real space (x,y) Ref Yvan, Gippius

45. ρ c =-1 : σ - ρ c =+1 : σ + Spin rings (still k=0) SPIN RING : both spin up and spin down are renormalized at the center of the GAUSSIAN spot (ρ c ≈0). Colors : degree of circular polarization ρ c Real space (x,y) Ref Yvan, Gippius

46. ρ c =-1 : σ - ρ c =+1 : σ + Spin rings (still k=0) Colors : degree of circular polarization ρ c Real space (x,y) Ref Yvan, Gippius

47. ρ c =-1 : σ - ρ c =+1 : σ + Spin rings (still k=0) Colors : degree of circular polarization ρ c Real space (x,y) Ref Yvan, Gippius

48. Polarization control A B on off 1 0 pump TE + probe σ + pump TE + probe σ - 25 μm FLOW EXPERIMENT pump TE + probe σ + pump TE + probe σ - THEORY 1 0 det σ++σ -σ++σ - Amo et al., Nature Photonics (DOI : 10.1038/NPHOTON.2010.79 ) >> Linearly polarized pump Spin dependent interaction Final polarization: that of the probe

49. Conclusion spin rings at k=0 measure (sign and value) of the ratio g parall /g oppos in our conditions (normal incidence, slightly negative cavity-exciton detuning and laser detuned from LPB by +0.124 meV) ● At normal incidence, the interaction between antiparallel spins is not negligible. ● Spin rings predicted by … Identical to the simulations. Enable the vizualisation of the gaussian beam. Interest… Ref Yvan, Gippius

51. Transmission versus excitation for different laser – LPB detunings (with E laser always larger than E LPB ) : hysteresis cycles with increasing sizes and increasing thresholds with the detuning.

52. Pump = 165 mW ; Probe = 11 mW Detection σ+ PUMP σ+ PROBE σ+ Pump (σ+) Probe (σ+)Pump+Probe Detection σ- Pump (σ+) Probe (σ+)Pump+Probe 20 µm 2009-10-14 12 reel PumpP ProbeP detM.txt 2009-10-14 12 reel PumpP ProbeP detP.txt 2009-10-14 13 reel PumpP detM.txt 2009-10-14 13 reel PumpP detP.txt 2009-10-14 14 reel ProbeP detM.txt 2009-10-14 14 reel ProbeP detP.txt Spin conditions

53. Detection σ+ PUMP σ+ PROBE σ- Pump (σ+)Probe (σ-)Pump+Probe Detection σ- Pump (σ+)Probe (σ-)Pump+Probe 20 µm 2009-10-14 13 reel PumpP detM.txt 2009-10-14 13 reel PumpP detP.txt 2009-10-14 15 reel PumpP ProbeM detM.txt 2009-10-14 15 reel PumpP ProbeM detP.txt 2009-10-14 16 reel ProbeM detM.txt 2009-10-14 16 reel ProbeM detP.txt Pump = 165 mW ; Probe = 11 mW Spin conditions

54. PUMP σ- PROBE σ+ Detection σ+ Pump (σ-)Probe (σ+) Pump+Probe Detection σ- Pump (σ-)Probe (σ+) Pump+Probe 20 µm 2009-10-14 19 reel PumpM ProbeP detM.txt 2009-10-14 19 reel PumpM ProbeP detP.txt 2009-10-14 18 reel PumpM detM.txt 2009-10-14 18 reel PumpM detP.txt 2009-10-14 14 reel ProbeP detM.txt 2009-10-14 14 reel ProbeP detP.txt Pump = 165 mW ; Probe = 11 mW Spin conditions

55. Detection σ+ PUMP σ- PROBE σ- Pump (σ-) Probe (σ-)Pump+Probe Detection σ- Pump (σ-) Probe (σ-)Pump+Probe 20 µm 2009-10-14 18 reel PumpM detM.txt 2009-10-14 18 reel PumpM detP.txt 2009-10-14 16 reel ProbeM detM.txt 2009-10-14 16 reel ProbeM detP.txt 2009-10-14 17 reel PumpM ProbeM detM.txt 2009-10-14 17 reel PumpM ProbeM detP.txt Pump = 165 mW ; Probe = 11 mW Spin conditions

56. Pump (Linear V)Probe (V)Pump+Probe Pump (Linear V)Probe (V)Pump+Probe 15-10-2009 15-22 Pump = 153 mW; Probe = 24 mW Detection H PUMP LINEAR V PROBE V Detection V 20 µm 2009-10-15 21 R PumpV ProbeV detV.txt 2009-10-15 21 R PumpV ProbeV detH.txt 2009-10-15 22 R ProbeV detV.txt 2009-10-15 22 R ProbeV detH.txt 2009-10-15 20 R PumpV detV.txt 2009-10-15 20 R PumpV detH.txt The absolute z-scale in slides 7-8 is kept the same

57. Pump (Linear V)Probe (H)Pump+Probe Pump (Linear V)Probe (H)Pump+Probe 15-10-2009 15-22 Pump = 153 mW; Probe = 24 mW The absolute z-scale in slides 2 thru 6 is kept the same Detection H PUMP LINEAR V PROBE H Detection V 20 µm 2009-10-15 20 R PumpV detV.txt 2009-10-15 20 R PumpV detH.txt 2009-10-15 18 R PumpV ProbeH detV.txt 2009-10-15 18 R PumpV ProbeH detH.txt 2009-10-15 19 R ProbeH detV.txt 2009-10-15 19 R ProbeH detH.txt

58. σ- polarization of detection 08-10-2009 03-09 Pump = 140 mW; Probe = 60 mW PUMP LINEAR V Polarization characterization of the pump 30 µm σ+V H absolute z-scale is the same as in the previous slides

59. Spin dependence : does not work with cross-polarized pump and probe, and with a vertically polarized pump, the polarization of the probe determines the final polarization of the transmitted beam. summary