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Optical Materials Express

Spin noise and anti-bunching of the spin components of Bose-Einstein condensates of exciton-polaritons [Invited]

Ziqiu Shao, Alexey Vitalievich Kavokin

Published Jul 24, 2025• 2 citations
Publisher

Abstract

We study theoretically the correlation properties of exciton-polaritons in planar microcavities under pulsed excitation. In particular, we analyze the quantum statistics of two pseudo-spin components of an exciton-polariton condensate in the course of its formation. Below the bosonic condensation threshold, the statistics of two components correspond to a chaotic thermal state, while above the threshold, the coherence is built up, and the photons emitted by different spin components of the condensate become anticorrelated. This spin antibunching effect can be evidenced by spin-resolved Hanbury-Brown and Twiss spectroscopy of polariton lasers.

DOI
10.1364/ome.569322

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We study theoretically the correlation properties of exciton-polaritons in planar microcavities under pulsed excitation. In particular, we analyze the quantum statistics of two pseudo-spin components of an exciton-polariton condensate in the course of its formation. Below the bosonic condensation threshold, the statistics of two components correspond to a chaotic thermal state, while above the threshold, the coherence is built up, and the photons emitted by different spin components of the condensate become anticorrelated. This spin antibunching effect can be evidenced by spin-resolved Hanbury-Brown and Twiss spectroscopy of polariton lasers.
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.
Second-order time correlation measurements with a temporal resolution better than 3 ps were performed on a CdTe microcavity where spontaneous Bose-Einstein condensation is observed. After the laser pulse, the nonresonantly excited thermal polariton population relaxes into a coherent polariton condensate. Photon statistics of the light emitted by the microcavity evidences a clear phase transition from the thermal state to a coherent state, which occurs within 3.2 ps after the onset of stimulated scattering. Following this very fast transition, we show that the emission possesses a very high coherence that persists for more than 100 ps after the build-up of the condensate.
Second-order time correlations of polaritons have been measured across the condensation threshold in a CdTe microcavity. The onset of Bose-Einstein condensation is marked by the disappearance of photon bunching, demonstrating the transition from a thermal-like state to a coherent state. Coherence is, however, degraded with increasing polariton density, most probably as a result of self-interaction within the condensate and scatterings with noncondensed excitons and polaritons. Such behavior clearly differentiates polariton Bose condensation from photon lasing.
Summary form only given. Semiconductor microcavities can be engineered to produce strong coupling between photons and quantum well excitons leading to the formation of new eigenstates called polaritons. Due to their peculiar dispersion, enabling non-equilibrium Bose-Einstein condensation [1], and their straightforward experimental accessibility, microcavity polaritons have gained considerable interest in recent years. Polariton states can be selectively populated by choosing the excitation angle and the wavelength of the excitation laser. After a lifetime of a few picoseconds the polariton decays and a photon is emitted from the cavity, carrying the complete information on the underlying polariton state. Several theoretical works [2-3] suggest that polariton-polariton interactions can be a source of non-classical photon correlations, producing photon pairs that are entangled in either the energy, the polarization, or the momentum degree of freedom. One appeal of such a system is that many parameters such as the polariton-polariton interaction strength are tunable [4] and multipartite entangled states can be created in a single device [5]. However, due to the lack of high-quality samples, experimental realisations of these schemes have been elusive so far. In this contribution, we will discuss some of our experimental work on the statistics of polariton-polariton parametric scattering. Excited polaritons can scatter in a four-wave mixing process into signal and idler states lying on a figure-eight shaped curve in k-space, where phase-matching is fulfilled. We make use of a sample with ultra narrow exciton resonances, which allows for the generation and detection of correlated light. We present our measurements of the second order correlation functions using time-correlated photon counting. We discuss in detail, how polariton quantum correlations depend on a number of experimental parameters, such as phase space location and excitation density and find that the results can be understood in the framework of the well known Bogoliubov theory for 2D Bose gases utilised for microcavity polaritons [6]. We find bunching below the parametric threshold and a slow buildup of coherence above the threshold similar to the quantum statistics of a non-degenerate optical parametric oscillator, which is well known for its nonclassical properties [7]. We discuss in particular the influence of strong background processes on the observed photon statistics.