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arXiv:2609.37142

Second-order coherence properties of ultrafast polariton dynamics in plasmonic lattices

Evgeny A. Mamonov, Lukas Freter, Sioneh Eyvazi, Elliot W. Lloyd, Päivi Törmä

cond-mat.quant-gasphysics.opticsquant-phSubmitted Sep 29, 2026• Announced Sep 30, 2026

Abstract

The first-order coherence properties of strongly coupled systems supporting polariton lasing and Bose-Einstein condensation (BEC) have been thoroughly studied and show consistent results. In contrast, second-order coherence properties have been found to vary for different systems, and the second-order coherence function can deviate from the value of one, typical for atomic BEC, revealing super-Poissonian fluctuations even above the BEC/polariton lasing threshold. This calls for a deeper understanding of the emission statistics and dynamics in light-based condensates, especially in the non-equilibrium regime. Here we demonstrate a coherent state of polariton emission from a plasmonic lattice measured as the second-order coherence function value separately for $\mathrmΓ$- and non-$\mathrmΓ$-point radiation (ground state and high-energy tail). We observe a high degree of coherence with the value $g^{(2)}(τ=0)-1<10^{-4}$. We also demonstrate the ultrafast ($>$1 THz) nature of the dynamics. The process can be interpreted as a BEC with ultrafast, sub-50-fs thermalization, but we also suggest an alternative explanation as superradiance in a system where the emitters have vibrational degrees of freedom.

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The first-order coherence properties of strongly coupled systems supporting polariton lasing and Bose-Einstein condensation (BEC) have been thoroughly studied and show consistent results. In contrast, second-order coherence properties have been found to vary for different systems, and the second-order coherence function can deviate from the value of one, typical for atomic BEC, revealing super-Poissonian fluctuations even above the BEC/polariton lasing threshold. This calls for a deeper understanding of the emission statistics and dynamics in light-based condensates, especially in the non-equilibrium regime. Here we demonstrate a coherent state of polariton emission from a plasmonic lattice measured as the second-order coherence function value separately for

\mathrmΓ

- and non-

\mathrmΓ

-point radiation (ground state and high-energy tail). We observe a high degree of coherence with the value

g^{(2)}(τ=0)-1<10^{-4}

. We also demonstrate the ultrafast (

>

1 THz) nature of the dynamics. The process can be interpreted as a BEC with ultrafast, sub-50-fs thermalization, but we also suggest an alternative explanation as superradiance in a system where the emitters have vibrational degrees of freedom.

The fascination of macroscopic quantum coherence formed in a degenerate Bose gas drives the worldwide work on atomic Bose-Einstein condensates. Semiconductor polaritons1 are another promising system to explore the physics of degenerate Bose gases in a stronger interaction regime. It is also a system easily produced and probed through optical methods. In this work we present the first observation of the onset of a quantum coherence formed out of an initially thermal population of polaritons in a microcavity quantum well system. The quantum coherence is measured by a time domain second order coherence g(2)(0) of the light emitted from the polaritons. Second and higher order coherence functions are crucial in quantum optics to distinguish among various pure states of light, such as coherent state or squeezed state, from classical thermal light2. They have been measured indirectly in the spatial domain for atomic BECs3,4. In our system, with supporting evidence from measurements of the input-output, dispersion, and time evolution of the emission, the phase transition was identified by a decrease of g(2)(0) ≈2, the value for a thermal state, toward g(2)(0) ≈1 for a coherent state. This is a direct evidence of the formation of a macroscopic quantum coherence in the lower polariton ground state.

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

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.

We report on the experimental observation of stimulated cooling in the non-equilibrium Bose-Einstein condensate (BEC) of weakly interacting exciton-polaritons from approximately room temperature down to 20K. By resolving the condensate in energy-momentum space and performing interferometric measurements, we distinguish the condensate from thermalized particles yet occupying excited states macroscopically. In contrast to the analytical quantum theories of non-equilibrium BEC [Shishkov et al., Phys. Rev. Lett. 128, 065301 (2022)], we observe segmentation of the particle density along the excited states into two fractions both following Bose-Einstein distribution, albeit with different effective temperatures and chemical potentials. Our results indicate that the temperature of the weakly interacting Bose gas is universally set by the density-dependent chemical potential, revealing a defining property of non-equilibrium BECs. Finally, we demonstrate that the stimulated nature of the cooling process directly governs the emergence of quantum coherence of the condensate and shapes the dissipative properties of the excited states.

We have measured the two-particle correlation function of atoms from a Bose-Einstein condensate participating in a superradiance process, which directly reflects the second-order coherence of the emitted light. We compare this correlation function with that of atoms undergoing stimulated emission. Whereas the stimulated process produces correlations resembling those of a coherent state, we find that superradiance, even in the presence of strong gain, shows a correlation function close to that of a thermal state, just as for ordinary spontaneous emission.