Jacques Levrat, R. Butté, T. Christian, M. Glauser, E. Feltin, J.-F. Carlin, N. Grandjean,

1. PINNING AND DEPINNING OF THE POLARIZATION OF EXCITON-POLARITON CONDENSATES AT ROOM TEMPERATURE Jacques Levrat, R. Butté, T. Christian, M. Glauser, E. Feltin, J.-F. Carlin, N.Grandjean, Institute of Quantum Electronics and Photonics, Ecole Polytechnique Fédérale de Lausanne (Switzerland) D. Read, A. V. Kavokin School or Physics and Astronomy, University of Southampton (UK) Y. G. Rubo Centro de Investigaticion en Energia, Universidad Nacional Autonoma de México (Mexico) 1

2. Outlines • Introduction • Motivation – Which material ? • Detuning and temperature dependence of polariton condensation threshold of GaN-based microcavities (MCs) • Emission properties of a GaN-based MC at threshold • Linear polarization behavior - Experiments • Experimental setup • Pinning of the linear polarization • Power dependence • Linear polarization behavior - Theory • Effect of magnetic field on the pseudospin evolution • Model • Stochastic evolution of the order parameter • Model vs experimental data • Detuning dependence of the linear polarization degree • Conclusion and perspectives 2

3. Outlines • Introduction • Motivation – Which material ? • Detuning and temperature dependence of polariton condensation threshold of GaN-based microcavities (MCs) • Emission properties of a GaN-based MC at threshold • Linear polarization behavior - Experiments • Experimental setup • Pinning of the linear polarization • Power dependence • Linear polarization behavior - Theory • Effect of magnetic field on the pseudospin evolution • Model • Stochastic evolution of the order parameter • Model vs experimental data • Detuning dependence of the linear polarization degree • Conclusion and perspectives 2

4. Motivation: Which materials ? WVRS ~ 56 meV WVRS ~ 16 meV WVRS ~ 26 meV T ~ 340 K T ~ 40 K T ~ 50 K J. Kasprzak et al. Nature ,443, 409 (2006) J. Kasprzak et al. PRL ,101, 146404(2008) E. Wertz et al., APL 95, 051108 (2009) G. Christmann et al., APL 93, 051102 (2008) Efficient coupling to phonons (polar material) • Efficient thermalization of hot carriers + limited bottleneck effect 3

5. Condensation phase diagram (d,T,Pthr) ELPB ELPB ELPB Kinetic regime (tpol << trel) Thermodynamic regime (tpol >> trel) Intermediate regime t tpol k// k// k// phonon phonon Excitonic fraction Phonon efficiency Pol-pol interaction trel polariton 0 - 120 d (meV) 4 The system must face two opposite constraints Kinetic regime Thermodynamic regime Thermodynamics inhibited Thermodynamics favored polariton Tesc 340 dopt(T) T (K) J. Levrat et al., Phys. Rev. B 81, 125305 (2010) 4

6. Phase diagram (d,T,Pthr) Thermodynamic regime Kinetic regime POSSIBILITY OF ROOM TEMPERATURE MEASUREMENTS Optimum detuning • Highly stable configuration • POLARIZATION • MEASUREMENTS Photonic Disorder minimized |X0|2 ~ 20% d ~-40 meV R. Butté et al., Phys. Rev. B 80, 233301 (2009) J. Levrat et al., Phys. Rev. B 81, 125305 (2010) 5

7. UV - Fourier spectroscopy LASER UV-enhancedCCD f2 f1 BS plate SIGNAL Objective NA = 0.55 sample Bottleneck far below threshold Emission thermalized at threshold T = 300 ± 20 K J. Levrat et al., accepted for publication in Phys. Rev. Lett 6

8. Polarization measurements at RT Unpolarized emission below threshold Linearly polarized emission above threshold: polarization degree >80% X P = 1.03 Pthr P = 0.98 Pthr C Angle (degree) 5 G. Christmann et al., Appl. Phys. Lett. 93, 051102 (2008) 0 5 10 15 3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65 Energ y (eV) 7

9. Outlines • Introduction • Motivation – Which material ? • Detuning and temperature dependence of polariton condensation threshold of GaN-based microcavities (MCs) • Emission properties of a GaN-based MC at threshold • Linear polarization behavior - Experiments • Experimental setup • Pinning of the linear polarization • Power dependence • Linear polarization behavior - Theory • Effect of magnetic field on the pseudospin evolution • Model • Stochastic evolution of the order parameter • Model vs experimental data • Detuning dependence of the linear polarization degree • Conclusion and perspectives 8

10. Polarization measurements at RT Non resonant excitation @ 4.66 eV MQW MC sample LASER 45° 6° Dq = 1° k// = 0 Linear polarization averaged over 200 realizations of the condensate <rl> Tmeas.~ 25 ms 500 ps 0.12 ms 9

11. Pinning of polarization at threshold a-plane m-plane a-plane m-plane Pinning of the polarization arising from bare mode splitting at k// = 0 Cavity mode Exciton Lower symmetry of the QW interfaces Local anisotropy due to thickness fluctuations of DBR layers Polarization is pinned along crystal preferential axes (a- and m-planes) Exciton localization on islands of monolayer QW width fluctuations Local strain ( birefringence) 10

12. Evolution of <rl> vs power Below threshold: FWHM ~15 meV Opposite behavior for a SC laser Henry et al., IEEE JQE 18, 259 (1982) • <rl > rapidly decreases well before reaching nsat • Broadening increase of the modes ~ 150 µeV • Blueshift of the mode < 1 meV J. Levrat et al., accepted for publication in Phys. Rev. Lett 11

13. Outlines • Introduction • Motivation – Which material ? • Detuning and temperature dependence of polariton condensation threshold of GaN-based microcavities (MCs) • Emission properties of a GaN-based MC at threshold • Linear polarization behavior - Experiments • Experimental setup • Pinning of the linear polarization • Power dependence • Linear polarization behavior - Theory • Effect of magnetic field on the pseudospin evolution • Model • Stochastic evolution of the order parameter • Model vs experimental data • Detuning dependence of the linear polarization degree • Conclusion and perspectives 12

14. Effect of magnetic field on pseudospin Intrinsic (WLT) Self-induced Larmor precession Arises from in-plane anisotropy Wint S TE-TM splitting of photonic mode TE-TM splitting of excitonic mode leads to beats between circularly polarized components of the photoemission WLT Shelykh et al., Semicond. Sci. Technol. 25, 1 (2009) Self-induced (Wint) Arises from anisotropic polariton-polariton interaction Pseudospin (S) Accounts for both spin (z) and dipole moment (x-y plane) orientation Spin-dependent polariton-polariton interaction Population imbalance of circular polarization Pseudospin changes due to effects of magnetic field and scattering with phonons, polaritons and defects  rich and complex dynamics! leads to beats between linearly polarized components of the photoemission Shelykh et al., PSS(b) 242, 2271 (2005) 13

15. Model E 2-level system Question of interest Pinning of the order parameter of BECs: ys (t) ,s = ± 1 (2 component complex vector correlated with the Stokes vector of light emitted by polariton condensates) Incoherent reservoir Nr(t) W(t) k Condensate n(t) W(t) : income rate from reservoir Nr (t) : reservoir occupation number Gr-1: polariton lifetime in the reservoir n(t) : condensate occupation P(t) : pumping rate D. Read et al., Phys. Rev. B 80, 195309 (2009) In the simplest-case of phonon-assisted relaxation: W(t) determines the noise amplitude, responsible for the phase and polarization fluctuations in the condensate 14

16. Stochastic evolution of the order parameter Splitting between x- and y-polarizations Escape rate Gc-1 = tpol ~ 0.2 ps x Relaxation parameter << Gc Income rate y Singlet polaritons (a2 < 0) Shot noise from the income of polaritons in the condensate Triplet polaritons (a1 > 0) D. Read et al., Phys. Rev. B 80, 195309 (2009) Pseudospin components Time-integrated components Averaged components Once averaged over noise realizations: <sy> = <sz> = 0 <rl> = <sx> (fee energy minimized) 15

17. Simulations • Far below threshold  • Weak condensate occupation • Effect of disorder not pronounced • Polariton-polariton interactions negligible • At threshold  • Pinning sx = -1 highly pronounced • Polariton-polariton interaction negligible <sx> ~ 0 <sx> ~ 0.8 • Slightly above threshold • Pinning and Larmor precession compete to be the dominant effect • Far above threshold  • Larmor precession dominates any remaining asymmetry in (sx,sy) plane <sx> ~ 0.4 <sx> ~ 0.18 J. Levrat et al., accepted for publication in Phys. Rev. Lett 16

18. Model vs experimental results J. Levrat et al., accepted for publication in Phys. Rev. Lett 17

19. Detuning dependence ? Reduced averaged linear polarization degree at d ~ - 60 meV Minimum threshold power at d ~ - 60 meV No time to relax to the lowest energy state (linear polarization) Quick build-up of linear polarization fast relaxation J. Levrat et al., accepted for publication in Phys. Rev. Lett 18

20. Perspectives Room temperature polariton condensation + + Pinning of the linear polarization degree at threshold Self-induced Larmor precession Ultra-fast polarization switiching device based on polariton condensates operating at room temperature + = Control of the photonic disorder 19

21. Conclusions • Full phase diagram of polariton condensation in GaN MCs (thermodynamic vs kinetic regimes) • Pinning of the order parameter at threshold vs detuning • Depinning of the order parameter with pump power (pinning vs Larmor precession) • Possibility of RT ultrafast polarization switch 20

22. Acknowledgments Thank you for your attention 21