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arXiv:1404.3535 · Physical Review Letters

Spatial Coherence Properties of One Dimensional Exciton-Polariton Condensates

Julian Fischer, Ivan G. Savenko, M. D. Fraser, Steffen Holzinger, Sebastian Brodbeck, Martin Kamp, Ivan Andreevich Shelykh, Christian Schneider, Sven Höfling

Published Nov 14, 2014• 65 citations

Abstract

In this work, we combine a systematic experimental investigation of the power- and temperature-dependent evolution of the spatial coherence function, g^{(1)}(r), in a one dimensional exciton-polariton channel with a modern microscopic numerical theory based on a stochastic master equation approach. The spatial coherence function g^{(1)}(r) is extracted via high-precision Michelson interferometry, which allows us to demonstrate that in the regime of nonresonant excitation, the dependence g^{(1)}(r) reaches a saturation value with a plateau, which is determined by the intensity of the pump and effective temperature of the crystal lattice. The theory, which was extended to allow for treating incoherent excitation in a stochastic frame, matches the experimental data with good qualitative and quantitative agreement. This allows us to verify the prediction that the decay of the off-diagonal long-range order can be almost fully suppressed in one dimensional condensate systems.

DOI: 10.1103/physrevlett.113.203902

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In this work, we combine a systematic experimental investigation of the power- and temperature-dependent evolution of the spatial coherence function, g^{(1)}(r), in a one dimensional exciton-polariton channel with a modern microscopic numerical theory based on a stochastic master equation approach. The spatial coherence function g^{(1)}(r) is extracted via high-precision Michelson interferometry, which allows us to demonstrate that in the regime of nonresonant excitation, the dependence g^{(1)}(r) reaches a saturation value with a plateau, which is determined by the intensity of the pump and effective temperature of the crystal lattice. The theory, which was extended to allow for treating incoherent excitation in a stochastic frame, matches the experimental data with good qualitative and quantitative agreement. This allows us to verify the prediction that the decay of the off-diagonal long-range order can be almost fully suppressed in one dimensional condensate systems.

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We investigate with a Boltzmann-Master equation approach the coherence properties of mi-crocavity (mc) polaritons and compare the results with corresponding experiments in GaAs mc’s. The spatial first-order coherence function is determined by the polariton population of the ground state and the excited states which are known from the solution of the Boltzmann equation. Fig. 1 shows how the spatial correlation increases with increasing pump powers. The results are in very good agreement with the double-slit experiment by Deng et al. [1] for GaAs mc’s with a cavity life time of 2ps. The results do not leave much room for depletion effects in these mc’s which have been predicted for CdTe mc’s with stronger interactions[2]. The second-order correlation function g(2) of the polariton condensate is calculated by a Master equation for the probabilty to find n particles in the ground state. The rates between the excited states and the ground state known from the solution of the Boltzmann equation are corrected by a gain saturation [3]. The resulting g(2)(P/Pth) show a smooth transition from the thermal limit (g(2) = 2) below threshold to the coherent limit (g(2) = 1) not to far above treshold. In order to explain the observed large correlations above the coherent limit which persist for a wide range of pump powers [4, 5, 6], we study the non-resonant two-polariton scattering processes introduced by [7] and also a kinetic depletion model. A fully satisfactory understanding is however up to now not reached.

We report on the measurement of first-order spatial correlations on a one-dimensional

97%

excitonic polariton condensate, excited in cooled ZnO microwires by nonresonant optical pulses. We find that, thanks to the tiny

3%

photonic fraction, a coherence length as large as 10 $\ensuremath{\mu}$m can build up, i.e., orders of magnitude larger than any reported so far for an ultracold exciton gas. Based on a driven-dissipative mean-field model we show that the decay of correlations is mainly due to a shallow disorder and driven-dissipative conditions.

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.