Polariton condensates show their nonequilibrium side


Credit: C2N/CNRS

Can a Bose–Einstein condensate form at room temperature? If it’s made of atoms, not by a long shot. To coax a gas of bosonic atoms to pile up in their quantum ground state, researchers must cool the gas to within a few millionths of a degree of absolute zero. And they must keep it isolated in an otherwise ultrahigh vacuum.

More accessible condensates can be made by replacing the atoms with polaritons: quasiparticles of light and matter that form when photons trapped in an optical cavity coupled to electronic excitations in a solid. Quantum condensation of polaritons sets in at a much higher temperature, and polariton systems are more easily integrated with semiconductor devices—both factors that pave the way for potential technological applications. (See the article by David Snoke and Jonathan Keeling, PhysicsTodayOctober 2017, page 54.)

But polaritons differ from atoms because of their short lifetime. Photons leak out of even the best cavities after a few picoseconds, so a polariton condensate must be continually refreshed with new photons to replace the ones that are lost. The condensate, therefore, never truly reaches thermal equilibrium; at best, it reaches a steady state.

Now Jacqueline Bloch (University of Paris–Saclay), Léonie Canet (Grenoble Alpes University), and colleagues have shown experimentally that because of its nonequilibrium nature, a polariton condensate behaves in an observably different way from its equilibrium counterparts. The behavior follows the form of the Kardar-Parisi-Zhang (KPZ) equation, derived in 1986 by Mehran Kardar, Giorgio Parisi (recipient of a share of the Nobel Prize in Physics; see PhysicsTodayDecember 2021, page 17), and Yi-Cheng Zhang to describe a wide variety of nonequilibrium systems, including raging wildfires and delicate frost crystals growing on a window.

A graph of condensate phase over 2*pi as a function of position showing four areas from light green to dark blue of decreasing size as the time decreases from 100 ps to 5 ps
Credit: Adapted from Q. Fontaine et al., Nature 608687 (2022)

The hallmark of KPZ physics is a competition between smoothing and roughening. An evolving interface—between the burnt and unburnt parts of a forest, say—feels the effects of diffusion that tend to even out any bumps. At the same time, when the interface is being driven forward, it advances locally in the direction perpendicular to the interface, so it advances fastest at the points that are already farthest in front. Those effects, combined with stochastic noise, give KPZ interfaces their distinct jagged profile.

Polariton condensates aren’t characterized by interfaces. But theorists predicted in 2015 that the same mathematics would describe the evolving phase of the condensate wavefunction, depicted in the figure above. Although the phase isn’t directly observable, Bloch, Canet, and colleagues used interferometry to measure correlations in the phase across time and space, which was enough to verify the KPZ description.

So far, the experiments are limited to one-dimensional polariton condensates, created by confining polaritons to the chains of semiconductor pillars shown in the micrograph at top. But that’s par for the course in KPZ physics, which is almost entirely limited to describing 1D interfaces in 2D systems. What happens in higher dimensions is a hotly debated open question, both mathematically and experimentally. (Q. Fontaine et al., Nature 608687, 2022.)

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