4 th International Conference on Spontaneous Coherence in Excitonic Systems Quantised Vortices in an Exciton- Polariton Condensate Konstantinos G. Lagoudakis 1, Michiel Wouters 2, Maxime Richard 1, Augustin Baas 1, Iacopo Carusotto 3, Regis Andre 4, Le Si Dang 4, Benoit Deveaud-Pledran 1 1 IPEQ, Ecole Polytechnique Fédérale de Lausanne(EPFL), Station 3, 1015 Lausanne, Switzerland. 2 ITP, Ecole Polytechnique Fédérale de Lausanne(EPFL), Station 3, 1015 Lausanne, Switzerland. 3 Institut Néel, CNRS, 25 Avenue des Martyrs, 38042 Grenoble, France. 4 INFM-CNR BEC and Dipartimento di Fisica, Universita di Trento, via Sommarive 14 38050 Trento, Italy
Outline Vortices in classical and quantum fluids Vortex observation methods in atomic BECs Achieving a polariton quantum fluid Vortices in a coherent polariton fluid Phase and density analysis Brief theoretical model Summary
Vortices in classical fluids A vortex is a spinning, often turbulent, flow of fluid. Any spiral motion with closed streamlines is vortex flow. Many examples of vortices in nature (tornados, whirlpools etc.) Physical properties are determined by classical statistical mechanics The angular momentum is not quantised Lack of fluid at vortex core
Vortices in quantum fluids Described by quantum mechanics Quantisation of angular momentum Observable Characteristics The phase: multiple integers of 2π2 around the core The density: fluid density at core vanishes Access Access to the coherence of the fluid is essential Source: 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 fluids 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]) [4] [5] [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).
Vortices in Semiconductor microcavities?? Microcavities are good candidates since : Polaritons are very light: mass 10-5 m e Low condensation critical density High condensation critical temperature In semiconductor MCs, condensation of polaritons has been demonstrated. Kasprzak Bose Einstein condensation of exciton polaritons Nature 443, 409-414, (2006) alili, R. et al. Bose Einstein condensation of microcavity polaritons in a trap Science 316,1007 1010 (2007). hristopoulos, S. et al. Room-temperature polariton lasing in semiconductor microcavities Phys.Rev. Lett. 98, 126405 (2007).
Condensation of exciton polaritons in Characteristics: CdTe microcavities Solid state system Disordered environment DBR 2λ spacer DBR Non-equilibrium Steady state incoming and outgoing flow of particles k z From extracavity field we can access: k k // Coherence Noise Polarisation Energy Momentum 4 x 4QWs 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)
Measurement of spatial coherence Quasi-CW non-resonant excitation BS L Sample on cold finger of cryostat Setup: CCD L BS RR Stabilized Michelson interferometer M Principle: Mirror arm Retroreflector arm Interferogram Use of retroreflector has many advantages
Vortices in the condensed state of polaritons Experimental realisation: Mirror arm Retroreflector arm Interferogram Disorder in sample Different positions will give different interferograms Some give interferograms with forklike dislocations Possible existence of pinned vortices
Vortices in the condensed state of polaritons 2π phase shift is verified by monitoring dislocation while changing the orientation of fringes A forklike dislocation is seen for all fringe orientations 10
Extraction of phase from interferogram Application of fringes: key feature for extraction of the phase The dislocation indeed gives a 2π2 winding of the phase
Density requirements?? The phase shifts around vortex by 2π. 2 What happens with the density? Looking real space luminescence is not enough Luminescence seen condensed polaritons + thermal polariton gas We only want the density of polaritons at the condensed state Condensate state is at one energy
Spectrally resolved real space imaging Real space luminescence is sent to monochromator slits Multiple acquisitions of real space lines Reconstruction of real space image from these lines Experimental Setup Quasi CW excitation BS L Sample in cold finger cryostat Double monochromator CCD L M
Real space spectrally resolved imaging Real space luminescence is cut into slices Each slice real space line VS energy Slices are stack together to recreate real space Cubes of data: each plane is a real space image at specific energy y y Energy x x
Similarity of reconstructed image with real space By averaging over all energies we should be able to reconstruct real space image 0 2 real space x (µm) 4 6 8 10 12 0 2 real space x (µm) 4 6 8 10 12 2 0 2 0 Real space y (µm) 6 8 4 Real space y (µm) 6 8 4 10 10 12 12 vortex vortex 15
At the energy of the condensate vortex is located at a region of reduced density looking in both x and y directions there is a local minimum 5.5 4.6x10 3 5.0 4.4 real space y (µm) 4.5 4.0 4.2 4.0 Intensity (arb. un.) 3.5 4.5 5.0 5.5 6.0 6.5 real space x (µm) Vortices are hence identified in a polariton condensate: Both characteristics are demonstrated 3.8
Additional features of the vortices We studied: excitation power dependence of vortex excitation spotsize effect on vortex
Vortices demonstrated experimentally reproduction by theory? Theoretical description: Gross Pitaevskii equation with pumping and dissipation terms Need equation for the excitonic reservoir dynamics This model gives a good description of the effects See next talk by Michiel Wouters
Theory behind the vortex appearance For given disorder potentials vortices appear as solutions of the system Phase winding and zero density are reproduced 8-4 real space x (µm) -2 0 2 4 6 real space y (µm) 2 4 0 60 40 20-2 8-4 -2 real space x (µm) 0 2 4 2.0 6 real space y (µm) 0 2 4 1.5 1.0 0.5 intensity (arb. un.) -2 phase (π) 0.0 0
Understanding gained From experiment Pinning of vortices at specific positions Pinning of the sign From theory Origin of Pinning : due to disorder shape Vortices are created due to: Shape of disorder potential Incoming and outgoing flow of polaritons (Non equilibrium) 20
Summary Quantised vortices are observed experimentally Density local minimum at vortex core Phase shift around vortex is 2π2 Theory can describe the system behaviour well Gives an insight to origin and pinning of vortices Thank you for your attention K. G. Lagoudakis, M. Wouters et. al. Quantized Vortices in an Exciton-Polariton Condensate Nature Phys. 4, 706-710 (2008)