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  1. Spatial coherence and vortices of polariton condensates Dmitriy Krizhanovskii Sheffield University, United Kingdom

  2. OUTLINE Background of semiconductor microcavities Polariton condensation. Nonequilibrium system Vortices in polariton condensates. Effect of interactions. Comparison to atom BEC Polariton condensates in acoustic lattices. Screening.

  3. Collaborators Sheffield,UK K.Guda R.Bradley D.M.Whittaker J.S.Roberts M.S.Skolnick Berlin,Germany,PDI Paulo Santos E.Cerda R.Hey Madrid, Spain Luis Vina Daniele Sanvitto

  4. A semiconductor microcavity Top DBR ( CdMnTe/CdTe) Cavity QWs (CdTe) Bottom DBR

  5. Low mass (low density of state). 104-5 times smaller than exciton mass Strong non-linearities Ideal system to study interacting BEC. Few K critical temperature A semiconductor microcavity Upper polariton Energy W Lower polariton Wavevector 0 Rabi splitting ~13-26 meV and 5-10 meV for CdTe and GaAs based microcavities, respectively

  6. signal pump idler idler emission Energy Lower polariton branch Pump signal emission Wavevector (104 cm-1) Optical parametric oscillator: resonant pumping _High enough density of excitation close to the point of inflection of LP branch may lead to polariton pair scattering _All 3 points (initial and 2 final states) can be simultaneously close to resonance with LP _Population can efficiently build-up at “signal” and “idler” modes Stevenson et al., PRL (2000) Tartakovskii et al., PRB (2000) Note: coherence of signal or Idler is not inherited from the pump

  7. Polariton condensation in CdTe: nonresonant pumping Kasprzak et al, Nature 2006

  8. Vortices of polariton condensates

  9. Vortices in polariton condensates Quantised spatial phase variation (vortex) was observed for polariton BEC (Lagoudkais et al, Nature Physics, 2008) The vortices arise from “interplay between disorder and the driven-dissipative nature of the condensate” In equilibrium condensates vortices do not form spontaneously in the limit of low temperature

  10. Creation of vortices in OPO condensate by imprinting Use of very weak probe carrying vortex M=1 resonant with the Signal Probe is 40 times weaker than signal Vortex in the signal is imprinted , phase of the signal is being locked to that of very weak probe Fork-like dislocation in signal self-interference pattern confirms quantised phase variation D.N Krizhanovskii et al, PRL (2010)

  11. Vortex core is intrinsic property of signal Vortex diameter created in the signal is not determined by the spatial profile of the probe. Interactions produce a natural size for the vortex determined by the strength of the interaction

  12. Effect of particle density and interactions on vortex size Intensity (Probe)~1/15 Intensity(Signal) Kinetic term is compensated by the interaction term, which determines the natural vortex size (healing length) x: Healing length D.N Krizhanovskii et al, PRL (2010)

  13. Vortices in atomic BEC are measured after expansion, which is a destructive technique Vortices in polariton system are measured in situ

  14. Concept of healing length Excitation spectrum of nonequilibrium condensate (Wouters, PRL 2007) Excitation spectrum of equilibrium BEC Also true for resonantly pumped polaritons (Amo, NP 2009) • Sound-like (linear) dispersion at kx~0.5-1in both cases • Healing length is inversely proportional to sound velocity cs~ x-1 • Interactions increase sound velocity.

  15. Vortex- Antivortex in signal and idler Energy Mi =1 Mp=0 Ms =-1 Wavevector (104 cm-1) OPO involve 3 coherent fields.Signal, pump, and idler Conservation of Orbital Angular Momentum in the polartion-polariton scattering 2Mp=Ms+Mi If a vortex Mi=+1 is created in idler then antivortex Ms=-1 must form

  16. Condensates in disordered potential and acoustic lattices

  17. Polariton condensation in CdTe: nonresonant pumping Boltzman distribution for higher energy polaritons. Polariton condensate is “nonequilibrium ” M. Wouters et al, PRL 2007 Emission of polariton condensate is very broad ~0.3 meV . Short coherence time ~ 6 ps => reason is noisy pump Kasprzak et al, Nature 2006

  18. Polariton condensation using pump with reduced noise A.P. D. Love, D. N. Krizhanovskii, et allPhys. Rev. Lett. 101, 067404 (2008)D.N. Krizhanovskii et al, PRB (2009) • Multiple condensates near the bottom of LP branch • ~5-10μeV linewidth with CW noise free diode laser (at 1.81eV) • ~0.3meV previously reported for multimode laser excitation (Kasprzak et al, Nature (2006), 0.55meV Balili, Snoke Science 2007) • ~2 orders of magnitude reduction in linewidth reveals new physics Momentum (mm-1)

  19. Generalised GP approach (theory by Michiel Wouters) Gross-Pitaevskii equation 1 coupled to kinetic equation 2 for exciton reservoir Coupling to reservoir External potential Interactions Kinetic equation for exciton reservoir D.N. Krizhanovskii et al, PRB (2009)

  20. GP approach (theory by Michiel Wouters) Experimental disorder potential Without disorder there is only one solution. With disorder multiple condensates observed=>result of nonequilibrium. Agreement with experiment A.P. D. Love, D. N. Krizhanovskii, et allPhys. Rev. Lett. 101, 067404 (2008); D.N. Krizhanovskii et al, PRB (2009)

  21. rf SAW z||[001] Microcavity+QWs x||[100] Control of spatial coherence of condensates by SAW. Surface acoustic wave creates periodical potential (l ~ 8 mm) Formation of Brillouin Zones Energy gap ~0.1-0.2 meV Polariton confinement in real space. Tool to manipulate condensates

  22. signal pump idler idler emission Energy Lower polariton branch Pump signal emission Wavevector (104 cm-1) Optical parametric oscillator: resonant pumping Stevenson et al., PRL (2000) Tartakovskii et al., PRB (2000)

  23. OPO in periodical potential rf SAW z||[001] Microcavity+QWs x||[100] SAW 5.2 dbm SAW OFF: condensation at k=0 SAW ON: condensation at the maxima of the 1st BZ at k=+q/2 and k=-q/2 q- is the momentum of SAW Energy (eV) Momentum along SAW direction (mm-1) f=0 f=p

  24. Control of spatial coherence First order spatial correlation function g1(-r,+r) vs SAW potential SAW 1.2 dbm SAW 7.2 dbm SAW direction SAW OFF Suppression of polariton tunneling; Reduction of coherence length along SAW when tunneling time becomes comparable to coherence time (200 ps, D.Krizhanovskii et al, PRL 2006) Coherence length along SAW wire L ~10 microns. Higher noise in 1D system.

  25. Screening of SAW potential

  26. Screening of SAW potential

  27. Screening of SAW potential

  28. Screening of SAW potential

  29. Mechanism of screening Both pump and signal are modulated Pump population exhibits bistability Above threshold there is more pump polaritons in SAW minima Pump –signal interactions screen SAW potential

  30. Polariton condensates (BEC) under incoherent excitation in SAW potential Energy P-state S-state Momentum In case of non-resonant pumping condensation into minima of 1st and 2nd BZs is observed Narrow S and P states are observed C. W. Lai et al., Nature 449, 529 (2007).

  31. BEC: control of spatial coherence Coherence of S-state (condensation into minima of 1st BZ) High power of SAW: Tunnelling between minima is suppressed Coherence of S-state is reduced from 10 mm down to 5 mm at high power of SAW Coherence of P-state is about 10-12 mm at high power of SAW, longer than that for S-state P-state has energy above periodic potential and hence long range spatial coherence is established Coherence of P-state (condensation into minima of 2nd BZ)

  32. Conclusion • Polariton condensate is a nonequilibrium, strongly interacting system • Control of spatial coherence of by periodical potential created by Surface of Acoustic Wave. • Transition from a single condensate with a long range spatial coherence into fragmented condensed state with reduced coherence length • 4) Screening of SAW potnetial by strong interactions • 5) Vortex can be imprinted onto condensate using very weak probe • 6) Vortex core is determined by the interactions and decreases with population • 7) Vortex and antivortex states are formed due to parametric scattering