In a homogeneous two-dimensional system at non-zero temperature, although there can be no ordering of infinite range, an ordered superfluid phase is expected to occur for a Bose liquid. Theory predicts that, in this phase, the correlation function decays with distance as a power law, and quantum vortices are bound to antivortices to form molecular-like pairs. We have studied the relevance of this theory to microcavity exciton-polaritons.
We have employed a Michelson interferometer setup to measure the first order spatial correlation function of a large condensate . The Gaussian form of the short-distance decay allows us to define an effective thermal de Broglie wavelength, although the system is not in thermal equilibrium. The long-distance decay is measured to be a power law with an exponent in the range 0.9-1.2, larger than is possible in equilibrium. Our non-equilibrium theory suggests that this can be attributed to laser pumping noise.
We have also observed a single vortex-antivortex pair in a condensate of the appropriate size . Pairs are generated due to pumping noise, and are formed sequentially at the same point due to the inhomogeneous pumping spot pro le. They are revealed in the time-integrated phase maps acquired using Michelson interferometry. Our results suggest that vortex-antivortex pairs can be created in a two-dimensional condensate without rotation or stirring. The observed correlated motion of a vortex and antivortex implies that vortex-antivortex pairs do not dissociate, which is consistent with the measured power law decay of the spatial correlation function.
These two experiments uniquely describe the phase fluctuations of the condensate order parameter and provide stringent tests to theories of non-equilibrium condensation. They also highlight the exciton polariton condensate as a very well characterized system showing mesoscopic coherence and deepen our understanding of fundamental two-dimensional bosonic physics.
Figure 1. Measured Michelson interferograms of exciton-polaritons at (a) small and (b) large densities. The first-order correlation function g(1)(x,-x) is quantified at (c) small and (d) large densities. Blue circles are experimental data, red continuous lines are fits to the short-distance gaussian decay, magenta line in (d) is a fit to the long-distance power-law decay.
Figure 2. (a) Predicted interferogram and (b) corresponding correlation function g(1)(x,y;-x,y) for a condensate with one pair. (c) Measured interferogram and (d) correlation function g(1)(x,y;-x,y).
BEC-BCS crossover has been theoretically studied in exciton field for a long time. However, it has not been experimentally achieved since even the formation of exciton BEC was not succeeded. On the contrary, success of polariton BEC due to the light effective mass of polariton for these years has opened the possibility of polariton BEC-BCS crossover. At first several theoretical works has investigated and defined polariton BCS phase, where clear experimental evidence has not been expected yet. Later our group has predicted one distinctive feature of polariton BCS phase lying between polariton BEC and photon BEC phase. The latter case we believe cannot be distinguished from a conventional photon laser, while BCS phase should show Mollow triplet like PL spectrum. Now experimental investigation of such a feature is being done.
 G. Roumpos, M. Lohse, J. Keeling, M. H. Szymańska, P. B. Littlewood, A. Löffler, S. Höffling, L. Worschech, A. Forchel, & Y. Yamamoto, “Spatial correlation function of a large exciton polariton condensate”, Phys. Rev. Lett., submitted (2010).
 G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel & Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate”, Nature Phys., published online DOI:10.1038/NPHYS1841 (2010).
 T. Byrnes, T. Horikiri, N. Ishida & Y. Yamamoto, “BCS Wave-Function Approach to the BEC-BCS Crossover of Exciton-Polariton Condensates”, Phys. Rev. Lett. 105, 186402 (2010).
Dr. Tomoyuki Horikiri
Prof. Yoshihisa Yamamoto
Dr. Tim Byrnes (NII, Japan)
Dr. Michael Fraser (NII, Japan)
Defense Advanced Research Projects Agency
National Science Foundation
NICT, MEXT, NII FIRST