Stability and spatial coherence of nonresonantly pumped exciton-polariton condensates Nataliya Bobrovska 1 , Elena A. Ostrovskaya 2 , Michał Matuszewski 1 1 Institute of Physics, Polish Academy of Sciences, Warsaw 2 Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, The Australian National University, Canberra
EXCITON-POLARITON CONDESATE ● Low effective mass (10 5 times smaller than exciton mass) ● Strong interparticle interactions
THE MODEL EXCITON-POLARITON CONDESATE Polariton condensates are the nonequlibrium systems where continuous pumping is necessary to maintain the condensate population Resonant pumping Nonresonant pumping Kasprzak et al., Nature 2006
HOMOGENEOUS PUMPING OUTLINE Model system (open-dissipative Gross-Pitaevskii equation) Stability and coherence of exciton-polariton condensate under homogeneous pumping Stability and coherence of exciton-polariton condensate under inhomogeneous pumping
INHOMOGENEOUS PUMPING THE MODEL Wouters & Carusotto, PRL 2007
INHOMOGENEOUS PUMPING OPEN-DISSIPATIVE GROSS-PITAEVSKII MODEL Rate equation for the reservoir density Open-dissipative Gross-Pitaevskii equation Wouters & Carusotto, PRL 2007
METHODS One-dimensional exciton-polariton condensate ● Bogoliubov-de Gennes method ● Direct numerical integration Dimensionless units ℏ= m = 1 Bobrovska et al., PRB 2014
INHOMOGENEOUS PUMPING HOMOGENEOUS PUMPING ● P = const ODGP model Threshold pumping: Below threshold Above threshold No condensate! Condesate!
INHOMOGENEOUS PUMPING HOMOGENEOUS PUMPING Density evolution of the condensate stability limit The analytical condition for condensate stability Periodic boundary conditions Smirnov et al., PRB 2014 Bobrovska et al., PRB 2014
INHOMOGENEOUS PUMPING HOMOGENEOUS PUMPING Density evolution of the condensate First-order correlation function First-order correlation TWA – truncated Wigner Approximation Bobrovska et al., PRB 2014
INHOMOGENEOUS PUMPING HOMOGENEOUS PUMPING Uniform flow waves Bobrovska et al., PRB 2014
INHOMOGENEOUS PUMPING HOMOGENEOUS PUMPING Effect of polariton energy relaxation Tanese et al, Nat. Commun 2013 Relaxation term Bobrovska et al., PRB 2014
INHOMOGENEOUS PUMPING INHOMOGENEOUS PUMPING Gaussian profile ● Narrow (W = 15.8) ● Wider (W = 44.7) Large spot Small spot Bobrovska et al., PRB 2014
INHOMOGENEOUS PUMPING HOMOGENEOUS PUMPING Experimental evidence of influence of the pumping profile on the stability and condensate coherence in 2D are recently shown in the organic condensates. experiment Numerical simulations 2D simulations Kena-Cohen et al., Nat. Phot, 2010 Courtesy of S. Kena-Cohen Daskalakis et al. ArXiv:1503.01373v
CONCLUSIONS Homogeneous pumping ● Instability in steady state leads to a significant reduction of the condensate coherence ● The polariton energy relaxation has a little effect on the condensate stability Inhomogeneous pumping ● Pumping profile has significant effect on the condensate stability and changes the condensate coherence length
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