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Observation of Joule–Thomson photon-gas expansion

Nature Physics volume 21, pages 214–220 (2025)Cite this article

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Abstract

In recent years, a self-consistent optical thermodynamic framework has emerged that offers a systematic methodology to understand, harness and exploit the complex collective dynamics of multimode nonlinear systems. These developments now allow consideration of a series of long-standing problems in optics, including the prospect of funnelling the entire power flowing in a multimode system into its ground state, for which no methodology currently exists. Here we demonstrate an all-optical Joule–Thomson expansion process mediated by photon–photon interactions whereby the temperature of the optical gas drops abruptly to zero. Our experiments in various configurations of coupled multicore nonlinear waveguide arrangements illustrate how light undergoing expansion-induced cooling can be channelled from arbitrary input states into the fundamental mode with near-unity efficiency. We show that the stability of the post-expansion state is ensured through an irreversible process of energy conversion. The all-optical thermodynamic phenomena explored in this study may enable innovative techniques where various uncorrelated but identical sources are merged into a unified spatially coherent state, offering a route for direct beam combining.

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Fig. 1: Optical JT expansion effects.
Fig. 2: Experimental set-up.
Fig. 3: JT expansion in a triangular lattice.
Fig. 4: Impact of lattice connectivity, system shape and excitation position.

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Data availability

Source data are provided with this paper. Additional experimental data that support the findings of this study are available from M.S.K. upon reasonable request.

Code availability

The MATLAB codes that support the numerical analysis of this study are available from G.G.P.

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Acknowledgements

We thank C. Otto for preparing the high-quality fused silica samples used for the inscription of all photonic structures employed in this work. A.S. acknowledges funding from the Deutsche Forschungsgemeinschaft (grants SZ 276/9-2, SZ 276/19-1, SZ 276/20-1, SZ 276/21-1, SZ 276/27-1 and GRK 2676/1-2023 ‘Imaging of Quantum Systems’, project no. 437567992). A.S. also acknowledges funding from the Krupp von Bohlen and Halbach Foundation as well as from the FET Open Grant EPIQUS (grant no. 899368) within the framework of the European H2020 programme for Excellent Science. A.S. and M.H. acknowledge funding from the Deutsche Forschungsgemeinschaft by means of SFB 1477 ‘Light–Matter Interactions at Interfaces’ (project no. 441234705). T.A.W.W. is supported by a European Commission Marie Skłodowska-Curie Actions Individual Fellowship ‘Quantum correlations in PT-symmetric photonic integrated circuits’, project no. 895254. This work was partially supported by the following agencies and organizations: W.M. Keck Foundation, Israel Ministry of Defense (4441279927), MPS Simons Collaboration (733682), National Science Foundation (CCF-2320937), Army Research Office (W911NF-23-1-0312), Office of Naval Research (N00014-20-1-2789), Air Force Office of Scientific Research (FA9550-20-1-0322, FA9550-21-1-0202), US Air Force Research Laboratory (FA86511820019, FA8650-19-C-1692) and the Department of Energy (DE-SC0022282, DE-SC0025224).

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Author notes

  1. These authors contributed equally: Marco S. Kirsch, Georgios G. Pyrialakos.

Authors and Affiliations

  1. Institute of Physics, University of Rostock, Rostock, Germany

    Marco S. Kirsch, Richard Altenkirch, Julius Beck, Tom A. W. Wolterink, Alexander Szameit & Matthias Heinrich

  2. Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA

    Georgios G. Pyrialakos, Mahmoud A. Selim, Huizhong Ren, Mercedeh Khajavikhan & Demetrios N. Christodoulides

  3. College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, USA

    Pawel S. Jung

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Contributions

G.G.P and D.N.C initiated the idea. G.G.P conceived the theoretical framework. M.S.K. and J.B. designed and fabricated the samples. The experimental set-up was constructed by M.S.K., T.A.W.W. and M.H. The measurements were conducted by M.S.K. Numerical simulations were performed by G.G.P, M.A.S., H.R. and P.S.J. The obtained data were evaluated and interpreted by M.S.K., R.A., M.H. and G.G.P. M.K., A.S. and D.N.C. supervised the efforts of their respective groups.

Corresponding authors

Correspondence to Georgios G. Pyrialakos or Demetrios N. Christodoulides.

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Nature Physics thanks Vincent Couderc and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Expansion in the presence of losses: BPM simulations.

(a) In an ideal lossless system, the overall power is conserved, and the total power contained in the fundamental mode steadily grows during the cooling process. (b) The presence of losses introduces a global power decay (dashed red line), but the relative fraction of power contained in the fundamental mode (solid blue line) at a given propagation distance nevertheless increases as nonlinear expansion proceeds. As shown in Fig. 3b, even in the presence of significant propagation losses attenuation 0.3 dB/cm, a value beyond the typical losses of 0.4 dB/cm for laser-written waveguides in fused silica, the efficiency of the JT power transfer to the ground state only decreases by approximately 10%.

Source data

Extended Data Fig. 2 Nonlinear dynamics in the (b) square and (a,c) triangular lattices: tight-binding simulations.

In all lattices, light was injected from a single site with peak power favoring a JT irreversible expansion, just below the threshold of self-focusing collapse. The average (Rayleigh-Jeans) conversion efficiency to the fundamental mode is 85.3%, 79.3% and 91% for the, triangular (hexagonal), square, and triangular (irregular) lattice, respectively. An irreversible exchange of energy is observed between \(U\) and \({H}_{{NL}}\), matching almost perfectly with theoretical prediction. The teal dashed line represents Eq. 4 while the teal solid line includes a correction term, \({U}_{L}=-1/2{P}^{2}+{H}_{{NL},\min }=-1/2{P}^{2}+1/(2M){P}^{2}\).

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–10 and Sections 1–8.

Source data

Source Data

Source data Figs. 1, 3 and 4 and Extended Data Figs. 1 and 2.

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Kirsch, M.S., Pyrialakos, G.G., Altenkirch, R. et al. Observation of Joule–Thomson photon-gas expansion. Nat. Phys. 21, 214–220 (2025). https://doi.org/10.1038/s41567-024-02736-1

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