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PLMCN 2010, Mexica Dmitriy Krizhanovskii Sheffield University, United Kingdom Spatial coherence and vortices of polariton condensates

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PLMCN 2010, Mexica OUTLINE Background of semiconductor microcavities Vortices in polariton condensates. Effect of interactions. Comparison to atom BEC Polariton condensation. Nonequilibrium system Polariton condensates in acoustic lattices. Screening.

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PLMCN 2010, Mexica 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

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PLMCN 2010, Mexica ( CdMnTe/CdTe) Bottom DBR QWs (CdTe) A semiconductor microcavity Cavity Top DBR

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PLMCN 2010, Mexica Low mass (low density of state) times smaller than exciton mass Ideal system to study interacting BEC. Few K critical temperature Strong non-linearities A semiconductor microcavity Upper polariton Lower polariton Energy Wavevector 0 Rabi splitting ~13-26 meV and 5-10 meV for CdTe and GaAs based microcavities, respectively

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PLMCN 2010, Mexica Atom BEC (3D)Polariton condensate (2D) Mass10 5 m e 4*10 -5 m e Density~10 14 cm -3 ~10 9 –10 10 cm -2 Interactions ~ N meV meV Temperature~nKUp to 300 K

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PLMCN 2010, Mexica 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 Pump signal emission idler emission Lower polariton branch Wavevector (10 4 cm -1 ) Energy pump signal idler Stevenson et al., PRL (2000) Tartakovskii et al., PRB (2000) Note: coherence of signal or Idler is not inherited from the pump

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PLMCN 2010, Mexica Polariton condensation in CdTe: nonresonant pumping Kasprzak et al, Nature 2006 Kasprzak et al, Nature 2006

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PLMCN 2010, Mexica Vortices of polariton condensates

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PLMCN 2010, Mexica 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

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PLMCN 2010, Mexica 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)

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PLMCN 2010, Mexica 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

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

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PLMCN 2010, Mexica Atom BEC (3D)Polariton condensate (2D) Mass10 5 m e 4*10 -5 m e Density~10 14 cm -3 ~10 9 –10 10 cm -2 Interactions ~ N meV meV Healing length0.1 um10 um Vortices in atomic BEC are measured after expansion, which is a destructive technique Vortices in polariton system are measured in situ

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PLMCN 2010, Mexica Excitation spectrum of equilibrium BEC Also true for resonantly pumped polaritons (Amo, NP 2009) Excitation spectrum of nonequilibrium condensate (Wouters, PRL 2007) Sound-like (linear) dispersion at k in both cases Healing length is inversely proportional to sound velocity c s ~ Interactions increase sound velocity. Concept of healing length

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PLMCN 2010, Mexica Vortex- Antivortex in signal and idler OPO involve 3 coherent fields.Signal, pump, and idler Conservation of Orbital Angular Momentum in the polartion-polariton scattering 2M p =M s +M i If a vortex M i =+1 is created in idler then antivortex M s =-1 must form M p =0 M s =- 1 M i =1 Wavevector (10 4 cm -1 ) Energy

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PLMCN 2010, Mexica Condensates in disordered potential and acoustic lattices

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PLMCN 2010, Mexica Polariton condensation in CdTe: nonresonant pumping Kasprzak et al, Nature 2006 Kasprzak et al, Nature 2006 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

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PLMCN 2010, Mexica A.P. D. Love, D. N. Krizhanovskii, et all Phys. Rev. Lett. 101, (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 ( m -1 ) Polariton condensation using pump with reduced noise

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PLMCN 2010, Mexica Generalised GP approach (theory by Michiel Wouters) Gross-Pitaevskii equation 1 coupled to kinetic equation 2 for exciton reservoir Coupling to reservoir Interactions External potential Kinetic equation for exciton reservoir D.N. Krizhanovskii et al, PRB (2009)

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PLMCN 2010, Mexica 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 all Phys. Rev. Lett. 101, (2008); D.N. Krizhanovskii et al, PRB (2009) Experimental disorder potential GP approach (theory by Michiel Wouters)

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PLMCN 2010, Mexica Control of spatial coherence of condensates by SAW. SAW x||[100] z||[001] rf Microcavity+QWs Formation of Brillouin Zones Energy gap ~ meV Surface acoustic wave creates periodical potential ( m) Polariton confinement in real space. Tool to manipulate condensates

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PLMCN 2010, Mexica Optical parametric oscillator: resonant pumping Pump signal emission idler emission Lower polariton branch Wavevector (10 4 cm -1 ) Energy pump signal idler Stevenson et al., PRL (2000) Tartakovskii et al., PRB (2000)

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PLMCN 2010, Mexica OPO in periodical potential Momentum along SAW direction ( m -1 ) Energy (eV) SAW 5.2 dbm SAW OFF: condensation at k=0 SAW ON: condensation at the maxima of the 1 st BZ at k=+q/2 and k=-q/2 q- is the momentum of SAW SAW x||[100] z||[001] rf Microcavity+QWs

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PLMCN 2010, Mexica Control of spatial coherence First order spatial correlation function g 1 (-r,+r) vs SAW potential SAW direction 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) SAW OFF SAW 1.2 dbm SAW 7.2 dbm Coherence length along SAW wire L ~10 microns. Higher noise in 1D system.

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PLMCN 2010, Mexica Screening of SAW potential

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PLMCN 2010, Mexica Screening of SAW potential

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PLMCN 2010, Mexica Screening of SAW potential

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PLMCN 2010, Mexica Screening of SAW potential

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PLMCN 2010, Mexica 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

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PLMCN 2010, Mexica Polariton condensates (BEC) under incoherent excitation in SAW potential Energy Momentum S-state P-state In case of non-resonant pumping condensation into minima of 1st and 2 nd BZs is observed Narrow S and P states are observed C. W. Lai et al., Nature 449, 529 (2007).

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PLMCN 2010, Mexica BEC: control of spatial coherence High power of SAW: Tunnelling between minima is suppressed Coherence of S-state is reduced from 10 m down to 5 m at high power of SAW Coherence of P-state is about m 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 S-state (condensation into minima of 1st BZ) Coherence of P-state (condensation into minima of 2nd BZ)

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PLMCN 2010, Mexica 1)Polariton condensate is a nonequilibrium, strongly interacting system 2)Control of spatial coherence of by periodical potential created by Surface of Acoustic Wave. 3)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 Conclusion

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