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New Journal of Physics

Coherence properties of exciton polariton OPO condensates in one and two dimensions

R Spano, Jorge Cuadra, G. Tosi, C. Antón, C A Lingg, D. Sanvitto, María Dolores Martín, L. Viña, P. R. Eastham, M. van der Poel, J. M. Hvam

Published Jul 20, 2012• 21 citations

Abstract

We give an overview of the coherence properties of exciton-polariton condensates generated by optical parametric scattering.Different aspects of the first-order coherence (g (1) ) have been investigated.The spatial coherence extension of a two-dimensional (2D) polariton system, below and at the parametric threshold, demonstrates the development of a constant phase coherence over the entire condensate, once the condensate phase transition takes place.The effect on coherence of the photonic versus excitonic nature of the condensates is also examined.The coherence of a quasi-1D trap, composed of a line defect, is studied, showing the detrimental effect of reduced dimensionality on the establishment of the long range order.In addition, the temporal coherence decay, g (1) (τ ), reveals a fast decay in contrast with the 2D case.The situation of a quasi-1D condensate coexisting with a 2D one is also presented.

DOI: 10.1088/1367-2630/14/7/075018

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•Jan 1, 2014•0 citations

We give an overview of the coherence properties of exciton-polariton condensates generated by optical parametric scattering.Different aspects of the first-order coherence (g (1) ) have been investigated.The spatial coherence extension of a two-dimensional (2D) polariton system, below and at the parametric threshold, demonstrates the development of a constant phase coherence over the entire condensate, once the condensate phase transition takes place.The effect on coherence of the photonic versus excitonic nature of the condensates is also examined.The coherence of a quasi-1D trap, composed of a line defect, is studied, showing the detrimental effect of reduced dimensionality on the establishment of the long range order.In addition, the temporal coherence decay, g (1) (τ ), reveals a fast decay in contrast with the 2D case.The situation of a quasi-1D condensate coexisting with a 2D one is also presented.

We report an experimental study of the spontaneous spatial and temporal coherence of polariton condensates generated in the optical parametric oscillator configuration, below and at the parametric threshold, and as a function of condensate area. Above the threshold we obtain very long coherence times (up to 3 ns) and a spatial coherence extending over the entire condensate (40 μm). The very long coherence time and its dependence on condensate area and pump power reflect the suppression of polariton-polariton interactions by an effect equivalent to motional narrowing.

A full quantum theory beyond the mean-field regime is developed for an exciton-polariton condensate, for a complete understanding of quantum fluctuations. We find an analytical solution for the polariton density matrix, showing the nonlinearity causing fast relaxation correlated with the pump so as to yield the quantum condensation above threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of the lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian, and towards a nonclassical distribution; the latter two possess off-diagonal long-range order but the last one is beyond. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning, and temperature.

We report on time-resolved measurements of the first order spatial coherence in an exciton-polariton Bose-Einstein condensate. Long-range spatial coherence is found to set in right at the onset of stimulated scattering, on a picosecond time scale. The coherence reaches its maximum value after the population and decays slowly, staying up to a few hundred picoseconds. This behavior can be qualitatively reproduced, using a stochastic classical field model describing interaction between the polariton condensate and the exciton reservoir within a disordered potential.

The Berezinskii-Kosterlitz-Thouless (BKT) theorem predicts that two-dimensional bosonic condensates exhibit quasi-long-range order which is characterized by a slow decay of the spatial coherence. However previous measurements on exciton-polariton condensates revealed that their spatial coherence can decay faster than allowed under the BKT theory, and different theoretical explanations have already been proposed. Through theoretical and experimental study of exciton-polariton condensates, we show that the fast decay of the coherence can be explained through the simultaneous presence of multiple modes in the condensate.

The second- and third-order coherence functions

{g}^{(n)}(0)

(

n=2

and 3) of an exciton-polariton condensate are measured and compared to the theory. Contrary to an ideal photon laser, deviation from unity in the second- and third-order coherence functions is observed, thus showing a bunching effect, but not the characteristics of a standard thermal state with

{g}^{(n)}(0)=n!

. The increase in bunching with the order of the coherence function,

{g}^{(3)}(0)>{g}^{(2)}(0)>1

, indicates that the polariton condensate is different from a coherent state, a number state, or a thermal state. The measurement of third-order coherence has the advantage, compared to the second-order one, that the difference between a thermal state and a coherent state is more pronounced. The experimental results are in agreement with the theoretical model where polariton-polariton and polariton-phonon interactions are responsible for the loss of temporal coherence.

A second-order coherence function of an exciton-polariton condensate is calculated in the time domain by the quantum Monte-Carlo wavefunction method.We fully consider polariton-polariton interactions within the five lowest quantized exciton-polariton branch in a one-dimensional model.Our calculated second-order coherence function qualitatively agrees with the experimental results obtained by H. Deng et.al, 1) and it approaches to one at well above threshold like an ideal photon laser.However, the polariton number distribution is broad compared with Poissonian distribution, which indicates that the polariton condensate is different from a coherent state.