Polariton condensates show their nonequilibrium side

Electron micrograph of rows of gray cylinders approximately 2 microns in diameter and 8 microns in height
Credit: C2N/CNRS

Can a Bose-Einstein condensate form at room temperature? If it’s made of atoms, far from it. To get a gas of bosonic atoms to settle into their quantum ground state, researchers need to cool the gas to a few millionths of a degree of absolute zero. And they have to keep it isolated in an otherwise ultra-high vacuum.

More accessible condensates can be made by replacing the atoms with polaritons: quasiparticles of light and matter that are formed when photons trapped in an optical resonator couple with electronic excitations in a solid. Quantum condensation of polaritons starts at a much higher temperature, and polaritons systems are easier to integrate into semiconductor devices – both factors paving the way for potential technological applications. (See the article by David Snoke and Jonathan Keeling, physics todayOctober 2017, page 54.)

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But polaritons differ from atoms in their short lifetimes. Photons exit even the best cavities after a few picoseconds, so a polariton condensate must be constantly refreshed with new photons to replace the lost photons. The condensate therefore never really reaches thermal equilibrium; at best it reaches a steady state.

Now Jacqueline Bloch (University of Paris-Saclay), Léonie Canet (University of Grenoble Alpes) and colleagues have shown experimentally that a polariton condensate behaves differently from its equilibrium counterparts in an observable way due to its non-equilibrium nature. 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; cf physics todayDecember 2021, page 17) and Yi-Cheng Zhang to describe a variety of non-equilibrium systems, including raging forest fires and delicate ice crystals growing on a window.

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A plot of the condensate phase versus 2*pi as a function of position shows four regions from light green to dark blue of decreasing size as time decreases from 100 ps to 5 ps
Source: Adapted from Q. Fontaine et al., Nature 608687 (2022)

The hallmark of KPZ physics is a competition between smoothing and roughening. A developing interface – say between the burned and unburned parts of a forest – feels the effects of diffusion, which tend to smooth out unevenness. At the same time, the boundary surface advances locally in the direction perpendicular to the boundary surface during propulsion, i.e. fastest at the points that are already furthest forward. These effects, combined with stochastic noise, give KPZ interfaces their distinctive jagged profile.

Polariton condensates are not characterized by interfaces. But theorists predicted in 2015 that the same math would describe the evolving phase of the condensate wave function shown in the figure above. Although the phase is not directly observable, Bloch, Canet and colleagues used interferometry to measure correlations in phase over time and space, which was sufficient to verify the KPZ description.

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So far, experiments have been limited to one-dimensional polariton condensates, which are formed by confining polaritons to the chains of semiconductor columns shown in the micrograph above. But that is part of the course of KPZ physics, which is almost exclusively limited to the description of 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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