Presentation on theme: "Spatial coherence and vortices of polariton condensates"— Presentation transcript:
1 Spatial coherence and vortices of polariton condensates Dmitriy KrizhanovskiiSheffield University, United Kingdom
2 OUTLINE Background of semiconductor microcavities Polariton condensation. Nonequilibrium systemVortices in polariton condensates. Effect of interactions.Comparison to atom BECPolariton condensates in acoustic lattices. Screening.
4 A semiconductor microcavity Top DBR( CdMnTe/CdTe)CavityQWs (CdTe)Bottom DBR
5 A semiconductor microcavity Upper polaritonEnergyWLower polaritonWavevectorLow mass (low density of state) times smaller than exciton massIdeal system to study interacting BEC. Few K critical temperatureStrong non-linearitiesRabi splitting ~13-26 meV and 5-10 meV forCdTe and GaAs based microcavities, respectively
6 Atom BEC (3D)Polariton condensate (2D)Mass105 me4*10-5 meDensity~1014 cm -3~109 –1010cm -2Interactions ~ kN10-7 meVmeVTemperature~nKUp to 300 K
7 Optical parametric oscillator: resonant pumping signalidler_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” modesPumpsignal emissionidler emissionLower polaritonbranchWavevector (104 cm-1)EnergyStevenson et al., PRL (2000)Tartakovskii et al., PRB (2000)Note: coherence of signal orIdler is not inherited from the pump7
8 Polariton condensation in CdTe: nonresonant pumping Kasprzak et al, Nature 2006
10 Vortices in polariton condensates Quantised spatial phase variation(vortex) was observed forpolariton BEC(Lagoudkais et al, Nature Physics, 2008)The vortices arise from “interplay between disorder and the driven-dissipative nature ofthe condensate”In equilibrium condensates vortices do not form spontaneously in the limit of low temperature10
11 Creation of vortices in OPO condensate by imprinting Use of very weak probe carryingvortex M=1 resonant with theSignalProbe is 40 times weaker than signalVortex in the signal is imprinted , phase of the signalis being locked to that of very weak probeFork-like dislocation in signal self-interference patternconfirms quantised phase variationD.N Krizhanovskii et al, PRL (2010)11
12 Vortex core is intrinsic property of signal Vortex diameter created in the signal isnot determined by the spatial profile of theprobe.Interactions produce a natural size for the vortexdetermined by the strength of the interaction
13 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 lengthD.N Krizhanovskii et al, PRL (2010)
14 Vortices in atomic BEC are measured after expansion, which is Atom BEC (3D)Polariton condensate (2D)Mass105 me4*10-5 meDensity~1014 cm -3~109 –1010cm -2Interactions ~ kN10-7 meVmeVHealing length0.1 um10 umVortices in atomic BEC are measured after expansion, which isa destructive techniqueVortices in polariton system are measured in situ
15 Concept of healing length Excitation spectrumof equilibrium BECAlso true for resonantlypumped polaritons (Amo, NP 2009)Excitation spectrum ofnonequilibrium condensate (Wouters, PRL 2007)Sound-like (linear) dispersion at kx~0.5-1 in both casesHealing length is inversely proportional to sound velocity cs~ x-1Interactions increase sound velocity.
16 Vortex- Antivortex in signal and idler EnergyMi =1Mp=0Ms =-1Wavevector (104 cm-1)OPO involve 3 coherent fields.Signal, pump, and idlerConservation of Orbital Angular Momentum in thepolartion-polariton scattering 2Mp=Ms+MiIf a vortex Mi=+1 is created in idler then antivortex Ms=-1 must form
17 Condensates in disordered potential and acoustic lattices
18 Polariton condensation in CdTe: nonresonant pumping Kasprzak et al, Nature 2006Boltzman distribution for higher energy polaritons.Polariton condensate is “nonequilibrium ”M. Wouters et al, PRL 2007Emission of polariton condensate is very broad ~0.3 meV . Short coherence time ~ 6 ps=> reason is noisy pump18
19 Polariton condensation using pump with reduced noise 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 physicsMomentum (mm-1)A.P. D. Love, D. N. Krizhanovskii, et all Phys. Rev. Lett. 101, (2008) D.N. Krizhanovskii et al, PRB (2009)
20 Generalised GP approach (theory by Michiel Wouters) Gross-Pitaevskii equation 1 coupled to kinetic equation 2for exciton reservoirCoupling to reservoirExternal potentialInteractionsKinetic equation for exciton reservoirD.N. Krizhanovskii et al, PRB (2009)
21 GP approach (theory by Michiel Wouters) Experimental disorder potentialWithout disorder there is only one solution.With disorder multiple condensates observed=>result of nonequilibrium. Agreement with experimentA.P. D. Love, D. N. Krizhanovskii, et all Phys. Rev. Lett. 101, (2008); D.N. Krizhanovskii et al, PRB (2009)
22 Control of spatial coherence of condensates by SAW. Surface acoustic wavecreates periodical potential (l ~ 8 mm)SAWx||z||rfMicrocavity+QWsFormation of Brillouin ZonesEnergy gap ~ meVPolariton confinement in real space.Tool to manipulate condensates
23 Optical parametric oscillator: resonant pumping signalidlerPumpsignal emissionidler emissionLower polaritonbranchWavevector (104 cm-1)EnergyStevenson et al., PRL (2000)Tartakovskii et al., PRB (2000)23
24 OPO in periodical potential SAW 5.2 dbmSAW OFF: condensation at k=0SAW ON: condensation at the maxima of the 1st BZ at k=+q/2 and k=-q/2q- is the momentum of SAWEnergy (eV)Momentum along SAW direction (mm-1)SAWx||z||rfMicrocavity+QWsf=0f=p
25 Control of spatial coherence First order spatial correlation function g1(-r,+r) vs SAW potentialSAW 1.2 dbmSAW OFFSAW 7.2 dbmSAW directionSuppression 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.
30 Mechanism of screening Both pump and signal are modulatedPump population exhibits bistabilityAbove threshold there is more pumppolaritons in SAW minimaPump –signal interactions screen SAW potential
31 Polariton condensates (BEC) under incoherent excitation in SAW potential EnergyP-stateS-stateMomentumIn case of non-resonant pumping condensation into minima of 1st and 2nd BZs is observedNarrow S and P states are observedC. W. Lai et al., Nature 449, 529 (2007).
32 BEC: control of spatial coherence Coherence of S-state (condensationinto minima of 1st BZ)High power of SAW:Tunnelling between minima issuppressedCoherence of S-state is reduced from10 mm down to 5 mm at high powerof SAWCoherence of P-state is about mmat high power of SAW, longer thanthat for S-stateP-state has energy above periodicpotential and hence long rangespatial coherence is establishedCoherence of P-state (condensationinto minima of 2nd BZ)
33 ConclusionPolariton condensate is a nonequilibrium, strongly interacting systemControl 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 length4) Screening of SAW potnetial by strong interactions5) Vortex can be imprinted onto condensate using very weak probe6) Vortex core is determined by the interactions and decreases with population7) Vortex and antivortex states are formed due to parametric scattering