Optomechanical self-structuring in a cold atomic gas

Journal name:
Nature Photonics
Year published:
Published online


The rapidly developing field of optomechanics aims at the combined control of optical and mechanical modes1, 2, 3. In cold atoms, the spontaneous emergence of spatial structures due to optomechanical back-action has been observed in one dimension in optical cavities3, 4, 5, 6, 7, 8 or highly anisotropic samples9. Extensions to higher dimensions that aim to exploit multimode configurations have been suggested theoretically10, 11, 12, 13, 14, 15, 16. Here, we describe a simple experiment with many spatial degrees of freedom, in which two continuous symmetries—rotation and translation in the plane orthogonal to a pump beam axis—are spontaneously broken. We observe the simultaneous long-range spatial structuring (with hexagonal symmetry) of the density of a cold atomic cloud and of the pump optical field, with adjustable length scale. Being based on coherent phenomena (diffraction and the dipole force), this scheme can potentially be extended to quantum degenerate gases.

At a glance


  1. Self-organization scheme and experimental set-up.
    Figure 1: Self-organization scheme and experimental set-up.

    a, Mechanism for self-organization in the single-mirror feedback scheme. b, Experimental set-up and timing diagram for pump and probe pulses. NL, nonlinear medium; PBS, polarizing beamsplitter; M, mirror.

  2. Observation of self-organization.
    Figure 2: Observation of self-organization.

    a, Transmission images (normalized to the intensities of the transmitted beam recorded in the absence of atoms) recorded with pump and probe (three-dimensional intensity distributions shown in colour). Parameters: input intensity Iin = 129 mW cm−2, δ = +7Γ and d = 5 mm. b, Continuous symmetry-breaking and defect formation: (i) an extended pattern in the transmitted beam with long-range order (the colour image is a numerically calculated Fourier transform of the intensity pattern, showing hexagonal symmetry); (ii) another realization of the same experiment as in (i), but the hexagonal structures in the upper left and lower right have different orientations, producing a defect line.

  3. Pattern temporal lifetime and spatial period.
    Figure 3: Pattern temporal lifetime and spatial period.

    a, Decay of density pattern with increasing pump–probe delay. The long decay constant is attributed to atomic motion. b, Pattern length scale versus feedback mirror distance. Measured sizes (red filled circles) are obtained from far-field transmission images (insets). Results from a thick-medium model are shown as open squares (Supplementary Section I.C). Error bars correspond to four times the standard deviation obtained from 10 realizations.

  4. Optomechanical versus two-level nonlinearity.
    Figure 4: Optomechanical versus two-level nonlinearity.

    Measured pattern contrast in pump (a) and probe (b) transmission images, as a function of pump pulse duration. Different pump intensities are used: 1, Iin = 636 mW cm−2; 2, Iin = 404 mW cm−2; 3, Iin = 217 mW cm−2; 4, Iin = 91 mW cm−2. Error bars correspond to four times the standard deviation obtained from 20 realizations.


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  1. Institut Non Linéaire de Nice, UMR 7335 CNRS, 1361 route des Lucioles, 06560 Valbonne, France

    • G. Labeyrie &
    • R. Kaiser
  2. SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, UK

    • E. Tesio,
    • P. M. Gomes,
    • G.-L. Oppo,
    • W. J. Firth,
    • G. R. M. Robb,
    • A. S. Arnold,
    • R. Kaiser &
    • T. Ackemann


G.L. led the experimental effort and performed the experiment with the help of P.G. They were joined by T.A., A.A. and R.K. in data analysis. E.T., G.R., G.L.O. and W.J.F. performed the theoretical and computational analysis. T.A. conceived the experiment and coordinated the joint efforts with R.K. All authors contributed to the discussion and interpretation of results and commented on the manuscript.

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