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arXiv:0811.4333 · Europhysics Letters (EPL)

Coherence properties of the microcavity polariton condensate

David M. Whittaker, P. R. Eastham

Published Jul 1, 2009• 48 citations
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Abstract

A theoretical model is presented which explains the dominant decoherence process in a microcavity polariton condensate. The mechanism which is invoked is the effect of self-phase modulation, whereby interactions transform polariton number fluctuations into random energy variations. The model shows that the phase coherence decay, g (1) (τ), has a Kubo form, which can be Gaussian or exponential, depending on whether the number fluctuations are slow or fast. This fluctuation rate also determines the decay time of the intensity correlation function, g (2) (τ), so it can be directly determined experimentally. The model explains recent experimental measurements of a relatively fast Gaussian decay for g (1) (τ), but also predicts a regime, further above threshold, where the decay is much slower.

DOI
10.1209/0295-5075/87/27002

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A theoretical model is presented which explains the dominant decoherence process in a microcavity polariton condensate. The mechanism which is invoked is the effect of self-phase modulation, whereby interactions transform polariton number fluctuations into random energy variations. The model shows that the phase coherence decay, g (1) (τ), has a Kubo form, which can be Gaussian or exponential, depending on whether the number fluctuations are slow or fast. This fluctuation rate also determines the decay time of the intensity correlation function, g (2) (τ), so it can be directly determined experimentally. The model explains recent experimental measurements of a relatively fast Gaussian decay for g (1) (τ), but also predicts a regime, further above threshold, where the decay is much slower.
The fundamental mechanisms which control the phase coherence of the polariton Bose-Einstein condensate (BEC) are determined. It is shown that the combination of number fluctuations and interactions leads to decoherence with a characteristic Gaussian decay of the first-order correlation function. This line shape, and the long decay times ( approximately 150 ps) of both first- and second-order correlation functions, are explained quantitatively by a quantum-optical model which takes into account interactions, fluctuations, and gain and loss in the system. Interaction limited coherence times of this type have been predicted for atomic BECs, but are yet to be observed experimentally.
The demonstration of coherent polariton emission from a CdTe microcavity structure [1] has provided a new system for the study of condensate physics. Unlike atomic condensates, the microcavity system is not in equilibrium; the polariton life-time in the cavity is only ∼ 2ps, so the population has to be maintained by pumping. This raises interesting questions about how the properties of such a non-equilibrium condensate differ from those of an equilibrium system. Recent experimental measurements of the first (g(1)) and second (g(2)) order correlation functions of the emitted light have shown that the decay times of both are ∼ 100−200ps, much longer than the cavity life-time. In this work, we present a theroetical treatment which provides a quantitative explanation of these results, and shows that the ultimate cause of the coherence decay is interactions between polaritons in the condensate. The microcavity polariton condensate is a mesoscopic quantum system, consisting of N ∼ 102 po-laritons within the finite size excitation spot. As a result, number fluctuations of ∼ N 1 2 are expected. For a finite equilibrium condensate of interacting particles, it is straight forward to show that the decay
The importance of interaction effects in determining the temporal coherence of spectrally and spatially isolated single modes of the microcavity optical parametric oscillator (OPO) is demonstrated. As a function of macroscopic occupancy, the coherence time (tau c) first increases linearly and then exhibits saturation behavior, reaching maximum values of up to 500 ps. Good agreement is found with a model including fluctuations in polariton number and polariton-polariton interactions between the OPO states. tau c is a property of the coupled OPO system, a result confirmed by the finding of equal coherence times for signal and idler, even though the idler is subject to strong additional scattering.
We demonstrate theoretically the spontaneous formation of a stochastic polarization in exciton-polariton Bose-Einstein condensates in planar microcavities under pulsed excitation. Below the threshold pumping intensity (dependent on the polariton lifetime), the average polarization degree is close to zero, while above threshold the condensate acquires a polarization described by a (pseudospin) vector with random orientation, in general. It is shown that the polariton-polariton interaction leads to suppression of the linear polarization degree of the condensate due to the self-induced Larmor precession of the pseudospin. We establish the link between the second-order coherence of the polariton condensate and the distribution function of its polarization. We examine also the mechanisms of polarization dephasing and relaxation.
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.