Quantised Vortices in an ExcitonQuantised Vortices in an Exciton--Polariton CondensatePolariton Condensate

Konstantinos G. LagoudakisKonstantinos G. Lagoudakis11, Michiel Wouters, Michiel Wouters22,,Maxime RichardMaxime Richard11, Augustin Baas, Augustin Baas11, Iacopo Carusotto, Iacopo Carusotto33,,Regis AndreRegis Andre44, Le Si Dang, Le Si Dang44, Benoit Deveaud, Benoit Deveaud--PledranPledran11

1IPEQ, Ecole Polytechnique Fédérale de Lausanne(EPFL), Station 3, 1015 Lausanne, Switzerland. 2ITP, Ecole Polytechnique Fédérale de Lausanne(EPFL), Station 3, 1015 Lausanne, Switzerland.

3Institut Néel, CNRS, 25 Avenue des Martyrs, 38042 Grenoble, France. 4INFM-CNR BEC and Dipartimento di Fisica, Universita di Trento, via Sommarive 14 38050 Trento, Italy

44thth International Conference on Spontaneous Coherence in International Conference on Spontaneous Coherence in Excitonic SystemsExcitonic Systems

OutlineOutlineVortices in classical and quantum fluids Vortices in classical and quantum fluids Vortex observation methods in atomic Vortex observation methods in atomic BECsBECsAchieving a polariton quantum fluidAchieving a polariton quantum fluidVortices in a coherent polariton fluidVortices in a coherent polariton fluidPhase and density analysisPhase and density analysisBrief theoretical modelBrief theoretical modelSummarySummary

Vortices in classical fluidsVortices in classical fluidsA vortex is a spinning, often turbulent, flow of fluid.A vortex is a spinning, often turbulent, flow of fluid.Any spiral motion with closed streamlines is vortex flow.Any spiral motion with closed streamlines is vortex flow.Many examples of vortices in nature (tornados, whirlpools etc.)Many examples of vortices in nature (tornados, whirlpools etc.)

Physical properties are determined Physical properties are determined by classical statistical mechanicsby classical statistical mechanics

The angular momentum is not The angular momentum is not quantisedquantised

Lack of fluid at vortex coreLack of fluid at vortex core

Vortices in quantum fluidsVortices in quantum fluids

Described by quantum mechanicsDescribed by quantum mechanicsQuantisation of angular momentumQuantisation of angular momentum

Observable CharacteristicsObservable CharacteristicsThe phase: multiple integers of 2The phase: multiple integers of 2ππ around the corearound the coreThe density: fluid density at core vanishesThe density: fluid density at core vanishes

Access to the coherence of the fluid is essentialAccess to the coherence of the fluid is essentialSource: E. L. Bolda et al. Detection of Vorticity in Bose-Einstein Condensed Gases by Matter-Wave Interference

Phys.Rev.Lett. 81, 5477 (1998).

Observation of vortices in quantum Observation of vortices in quantum fluidsfluids

Various species can be found : Free vortices thermally activated (e.g. Helium II, atom condensates [1])Vortex lattices appearing in a rotating superfluid (Helium II, atom condensates [2])Static Vortices pinned by disorder (superconductors [3])

[1] Z. Hadzibabic et al. Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas, Nature 441,1118 (2006)[2] J. R. Abo-Shaeer et al.Observation of Vortex Lattices in Bose-Einstein Condensates, Science 292, 476 (2001)[3] K. Harada et al. Direct Observation of Vortex Dynamics in Superconducting Films with Regular Arrays of Defects

Science 274, 1167 (1996)[4] Inouye S. et al.Observation of Vortex Phase Singularities in Bose-Einstein Condensates, Phys. Rev. Lett. 87, 080402 (2001). [5] Matthews M. R. et al. Vortices in a Bose-Einstein Condensate, Phys. Rev. Lett. 83, 2498 (1999).

[4] [5] [3]

Vortices in Semiconductor Vortices in Semiconductor microcavities??microcavities??

Microcavities are good candidates since :Microcavities are good candidates since :Polaritons are very light: mass 10Polaritons are very light: mass 10--55mmee

Low condensation critical density Low condensation critical density High condensation critical temperatureHigh condensation critical temperature

In semiconductor MCs, condensationIn semiconductor MCs, condensationof polaritons has been demonstratedof polaritons has been demonstrated

J. Kasprzak “Bose–Einstein condensation of exciton polaritons” Nature 443, 409-414, (2006) Balili, R. et al. “Bose–Einstein condensation of microcavity polaritons in a trap” Science 316,1007–1010 (2007).Christopoulos, S. et al. “Room-temperature polariton lasing in semiconductor microcavities” Phys.Rev. Lett. 98, 126405 (2007).

Condensation of exciton polaritons in Condensation of exciton polaritons in CdTe microcavitiesCdTe microcavities

From extracavity field we can accessFrom extracavity field we can access::CoherenceCoherenceNoiseNoisePolarisation Polarisation Energy Energy MomentumMomentum

4 x 4QWs

2λ spacerDBR DBR

V. Savona et al. Optical Properties of Microcavity Polaritons. Phase Transitions 68 169-279 (1999) and V. Savona et al. Quantum-Well Excitons in Semiconductor Microcavities - Unified Treatment of Weak and Strong Coupling

Regimes. Sol. St. Com. 93 733-739 (1995)

CharacteristicsCharacteristics::Solid state systemSolid state systemDisordered environmentDisordered environmentNonNon--equilibriumequilibriumSteady state Steady state →→incoming and incoming and outgoing flow of particlesoutgoing flow of particles kz

k//k

Measurement of spatial coherenceMeasurement of spatial coherence

Setup:Setup:

Principle:Principle:

Use of retroreflector has many Use of retroreflector has many advantages

Stabilized Michelson interferometer

BS

RRM

Sample on cold finger of cryostat

BSL

L

Quasi-CW non-resonant

excitation

CCD

Mirror Mirror armarm

RetroreflectorRetroreflectorarmarm

““InterferogramInterferogram””

advantages

Vortices in the condensed state of Vortices in the condensed state of polaritonspolaritons

Experimental realisation:Experimental realisation:Mirror armMirror arm Retroreflector armRetroreflector arm InterferogramInterferogram

Disorder in sampleDisorder in sampleDifferent positions will give different Different positions will give different interferogramsinterferogramsSome give Some give interferogramsinterferograms with forklike dislocationswith forklike dislocations

→→Possible existence of pinned vorticesPossible existence of pinned vortices

Vortices in the condensed state of Vortices in the condensed state of polaritonspolaritons

22ππ phase shift is verified by monitoring dislocation while phase shift is verified by monitoring dislocation while changing the orientation of fringeschanging the orientation of fringesA forklike dislocation is seen for all fringe orientationsA forklike dislocation is seen for all fringe orientations

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Extraction of phase from interferogramExtraction of phase from interferogram

Application of fringes: key feature for extraction of the phaseApplication of fringes: key feature for extraction of the phaseThe dislocation indeed gives a 2The dislocation indeed gives a 2ππ winding of the phasewinding of the phase

Density requirements??Density requirements??

The phase shifts around vortex by 2The phase shifts around vortex by 2ππ..What happens with the density?What happens with the density?

Looking real space luminescence is not enoughLooking real space luminescence is not enoughLuminescence seen Luminescence seen →→ condensed polaritons + thermal condensed polaritons + thermal polariton gaspolariton gasWe only want the density of polaritons at the We only want the density of polaritons at the condensed statecondensed stateCondensate state is at one energy Condensate state is at one energy

Spectrally resolved real space imagingSpectrally resolved real space imaging

Real space luminescence is sent to monochromator slits Real space luminescence is sent to monochromator slits Multiple acquisitions of real space linesMultiple acquisitions of real space linesReconstruction of real space image from these linesReconstruction of real space image from these lines

CC

DM

Sample in cold finger cryostat

Quasi CW excitation

BSL

Double monochromator L

Experimental Setup

Real space spectrally resolved imagingReal space spectrally resolved imagingReal space luminescence is cut into Real space luminescence is cut into ‘‘slicesslices’’Each slice Each slice →→ real space line VS energyreal space line VS energySlices are stack together to recreate real spaceSlices are stack together to recreate real spaceCubes of data: each plane is a real space image at specific enerCubes of data: each plane is a real space image at specific energygy

x

y

Energy

y

x

Similarity of reconstructed image with Similarity of reconstructed image with real spacereal space

By averaging over all energies we should be able to By averaging over all energies we should be able to reconstruct real space imagereconstruct real space image

1210

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0R

eal s

pace

y (µ

m)

121086420real space x (µm)

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eal s

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vortex vortex

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At the energy of the condensateAt the energy of the condensatevortex is located at a region of reduced densityvortex is located at a region of reduced densitylooking in both x and y directions there is a local minimumlooking in both x and y directions there is a local minimum

Vortices are hence identified in a polariton condensate:Vortices are hence identified in a polariton condensate:Both characteristics are demonstratedBoth characteristics are demonstrated

5.5

5.0

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real

spac

e y

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)

6.56.05.55.04.5real space x (µm)

4.6x103

4.4

4.2

4.0

3.8

Intensity (arb. un.)

Additional features of the vorticesAdditional features of the vortices

We studied:We studied:excitation power dependence of excitation power dependence of vortexvortex

excitation excitation spotsizespotsize effect on effect on vortexvortex

Vortices demonstrated experimentallyVortices demonstrated experimentally

reproduction by theory?reproduction by theory?

Theoretical description:Theoretical description:Gross Pitaevskii equation with pumping and Gross Pitaevskii equation with pumping and dissipation termsdissipation termsNeed equation for the excitonic reservoir dynamicsNeed equation for the excitonic reservoir dynamics

This model gives a good description of the effectsThis model gives a good description of the effects

See next talk by Michiel WoutersSee next talk by Michiel Wouters

Theory behind the vortex appearanceTheory behind the vortex appearanceFor given disorder potentials vortices appear as For given disorder potentials vortices appear as solutions of the system solutions of the system Phase winding and zero density are reproducedPhase winding and zero density are reproduced

86

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nsity

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)

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e (π

)

Understanding gainedUnderstanding gained

Origin of Pinning : due to disorder Origin of Pinning : due to disorder ‘‘shapeshape’’Vortices are created due to:Vortices are created due to:

Shape of disorder potentialShape of disorder potentialIncoming and outgoing flow of polaritons (Non Incoming and outgoing flow of polaritons (Non equilibrium)equilibrium)

From theoryFrom theory

From experimentFrom experimentPinning of vortices at specific positionsPinning of vortices at specific positionsPinning of the sign Pinning of the sign

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SummarySummary

Quantised vortices are observed experimentallyQuantised vortices are observed experimentallyDensity local minimum at vortex coreDensity local minimum at vortex corePhase shift around vortex is 2Phase shift around vortex is 2ππTheory can describe the system Theory can describe the system behaviourbehaviour wellwellGives an insight to origin and pinning of vorticesGives an insight to origin and pinning of vortices

Thank you for your attentionThank you for your attention

K. G. Lagoudakis, M. Wouters et. al. “Quantized Vortices in an Exciton-Polariton Condensate” Nature Phys. 4, 706-710 (2008)