Nonequilibrium Prethermal States in a Two-Dimensional Photon Fluid

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Nonequilibrium Prethermal States in a Two-Dimensional Photon Fluid

Murad Abuzarli, Nicolas Cherroret, Tom Bienaimé, and Quentin Glorieux

Phys. Rev. Lett. 129, 100602 – Published 1 September 2022

Abstract

We report on the observation of a prethermal state in a nonequilibrium, two-dimensional fluid of light. Direct measurements of the first order coherence function of the fluid reveal the dynamical emergence of algebraic correlations, a quasi-steady-state with properties close to those of thermal superfluids. By a controlled increase of the fluctuations, we observe a crossover from algebraic to short-range (exponential) correlations. We interpret this phenomenon as a nonequilibrium precursor of the Kosterlitz-Thouless transition.

Received 20 April 2022
Revised 27 June 2022
Accepted 9 August 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.100602

Physics Subject Headings (PhySH)

Bosons Cold atoms & matter waves Critical phenomena Decoherence in quantum gases Dynamical phase transitions Effects of atomic coherence on light propagation Light-matter interaction Nonlinear optics Quantum phase transitions Quasiparticles & collective excitations Superfluidity

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Murad Abuzarli¹, Nicolas Cherroret ^1,*, Tom Bienaimé ^1,2, and Quentin Glorieux ^1,†

¹Laboratoire Kastler Brossel, Sorbonne University, CNRS, ENS-PSL University, Collège de France, 4 Place Jussieu, 75005 Paris, France
²CESQ and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France

^*nicolas.cherroret@lkb.upmc.fr
^†quentin.glorieux@lkb.upmc.fr

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Vol. 129, Iss. 10 — 2 September 2022

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Images

Figure 1
Measurement of the coherence function demonstrating light-cone spreading of algebraic correlations in a 2D photon fluid. (a) Experimental setup. (b) Scenario of prethermalization in 2D. Upon propagation, the initial short-range speckle fluctuations are amplified and exhibit algebraic correlations associated with long-lived phononic excitations and spreading within a light cone of boundary $Δ r = 2 c_{s} L$ . Out of the light cone, $g_{1}$ is independent of $Δ r$ , reproducing the initial state long-range coherence (c) The initial state is prepared using a SLM with a random phase mask superimposed on a Gaussian laser beam. This results in a weakly fluctuating field that propagates in a hot ${}^{87}{Rb}$ vapor cell of length $L$ . (d) After propagation in the cell, the beam is split within a Mach-Zehnder interferometer and flipped using two Dove prisms. (e) The two inverted copies interfere and the fringe visibility is recorded. (f) The coherence function $g^{(1)} (Δ r = 2 r) = ⟨ Ψ^{*} (r, L) Ψ (- r, L) ⟩$ is obtained by computing the ensemble average of the measured contrast over 2000 realizations. (g) Experimental $g^{(1)}$ functions at $z = 0$ and $z = L$ . Light colored data are raw signals, and thin solid curves their azimuthal average. Thick solid curves are the final measurements, obtained by subtracting laser background imperfections. The light-cone position at $2 c_{s} L$ is indicated by the red arrow. The dashed line is a guide emphasizing the algebraic decay.
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Figure 2
Direct observation of the long-range algebraic order in a 2D prethermal state of light. (a) Normalized coherence function $g^{(1)} (Δ r) / I_{0}$ vs $Δ r$ for increasing values of the nonlinear phase $Φ_{NL}$ , at fixed $σ = 25 μ m$ and $ε^{2} = 2.2 %$ . Notice the double logarithmic scale. Dashed curves are algebraic fits to $1 / Δ r^{α}$ in the central region. (b) Extracted algebraic exponents $α$ vs $Φ_{NL}$ , for three fluctuation strengths (blue: $ε^{2} = 2.2 %$ , red: $ε^{2} = 5.3 %$ , yellow: $ε^{2} = 9.5 %$ ) (c) Algebraic exponent $α / σ^{2}$ at fixed $ε^{2} = 5.3 %$ , for two different speckle correlation lengths $σ$ (green circles: $σ = 25 μ m$ , red squares: $σ = 35 μ m$ ). All data points fall on the same curve, confirming the scaling $α \propto σ^{2}$ . Solid curves are linear fits to Eq. (3).
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Figure 3
Impact of the initial fluctuation amplitude $ε$ on the prethermal state. Normalized coherence function $g^{(1)} (Δ r) / I_{0}$ vs $Δ r$ for increasing values of the fluctuation amplitude $ε$ ( $ε^{2} = 0$ , 0.027, 0.04, 0.05, 0.07, 0.11, 0.16, 0.23, 0.35 from top to bottom). Here $σ = 35 μ m$ and $Φ_{NL} = 20 rad$ . Dashed curves are algebraic fits to $1 / Δ r^{α}$ in the central region. The inset shows the extracted algebraic exponents (blue dots), together with the prediction (3) [with no free parameters since we set the proportionality coefficient with that of Fig. 2].
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Figure 4
Crossover from algebraic to short-range (exponential) correlations at stronger fluctuation amplitudes, with the interaction strength set to a value $Φ_{NL} = 44 rad$ , twice larger than in the previous data (notice the log scale). (a) Normalized coherence function $g^{(1)} (Δ r) / I_{0}$ vs $Δ r$ when increasing more significantly $ε$ ( $ε^{2} = 0$ , 0.027, 0.04, 0.05, 0.07, 0.11, 0.16, 0.23, 0.35, 0.64 from top to bottom). Here $σ = 35 μ m$ is fixed. (b) Sum-squared error between experimental data and exponential (orange) vs algebraic (blue) fit. For $ε^{2} > 0.35$ the exponential fit becomes more accurate than the algebraic fit. (c) Rate $1 / r_{c}$ of the exponential decay, see Eq. (4), vs the fluctuation amplitude. The linear fit (black) confirms the theoretical scaling of Eq. (5).
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