For over a decade, we have been engaging in research on the properties and novel phenomena of microcavity exciton-polariton systems such as stimulated scattering, parametric amplification, lasing without electronic population inversion, and quantum phase transition at temperatures from 4 K up to room temperature.
A phase transition from a classical thermal mixed state to a quantum mechanical pure state of exciton-plaritons is observed in a GaAs 12-quantum well microcavity structure. Figure 1 captures such phase transition vividly by increasing the injected polariton population. The parabolic energy dispersion for the thermal state becomes the one condensate state accompanying with the momentum and energy narrowing. This phase transition is evidenced with the observation of a nonlinear threshold behavior in the pump-intensity dependence of the emission, a decrease of the relaxation time into the lower polariton state and the spatial and temporal coherence.
Figure 1. Power-dependent energy dispersion of lower polariton at cryogenic temperature, ~7K. The phase transition from thermal state to the condensate state occurs above quantum degeneracy point. X-axis is the in-plane wave number and y-axis is the energy. The energy blue shift for the condensate state is manifestation of the polariton-polariton interaction.
Despite polariton condensation is often specified as BEC, the resulting polariton condensate does not show all order temporal coherence (Fig. 2). It contradicts usual BEC picture where condensate takes a coherent state which must be all order coherent. Although the bunching effect (g(n)(0)>1) in experiments due to the incoherence of polariton condensate was not explained enough, recent theoretical studies in this field have revealed that such higher-order incoherence is a resultant of quantum depletion of condensate due to polariton-polariton scattering on ground state. The quantum depletion mechanism makes the population of ground state polariton decrease so much. Then, the coherent state is broken after the depletion of condensate polaritons. However, there are several uncertainties, for example, the depletion mechanism is basically a non-resonant scattering (non energy conserving process), hence, there is room for controversy that the process can contribute to the incoherence enough. And in high excitation regime, the condensate spectrum is broadened due to self interactions, which leads to the deviation from LP dispersion, while theoretical studies on LP dispersion also far above threshold are in progress. Further investigation will be done experimentally and theoretically to clarify the physics.
Figure 2. Second and third order coherence function taken in experiments (square, red) are compared with the theoretical prediction (blue, green lines).
H. Deng, G. Weihs, C. Santori, J. Bloch and Y. Yamamoto, "Condensation of Semiconductor Microcavity Exciton-Polaritons," Science 298, 199 (2002).
C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa and Y. Yamamoto, "Coherent zero-state and π-state in an exciton-polariton condensate array," Nature 450, 529 (2007).
S. Utsunomiya, L. Tian, G. Roumpos, C. W. Lai, N. Kumada, T. Fujisawa, M. Kuwata-Gonokami, A. Löffler, S. Höfling, A. Forchel and Y. Yamamoto, "Observation of Bogoliubov excitations in exciton-polariton condensates," Nature Physics 4, 700 (2008).
T. Horikiri, P. Schwendimann, A. Quattropani, S. Höfling, A. Forchel and Y. Yamamoto, "Higher order coherence of exciton-polariton condensates," Phys. Rev. B 81, 033307 (2010).
Dr. Na Young Kim
Dr. Tomoyuki Horikiri
Wolfgang H. Nitsche
Crystal C. Bray
Prof. Yoshihisa Yamamoto
Defense Advanced Research Projects Agency
National Science Foundation
NICT, MEXT, NII FIRST