Observation of entanglement in a cold atom analog of cosmological preheating

V. Gondret, C. Lamirault, R. Dias, L. Camier, A. Micheli, C. Leprince, Q. Marolleau, J.-R. Rullier, S. Robertson, D. Boiron, C. I. Westbrook

Physical Review Letters 135, 240603 (2025) · 10.1103/h7ws-g9z2 · arXiv:2506.22024

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Abstract

We observe entanglement between collective excitations of a Bose-Einstein condensate in a configuration analogous to particle production during the preheating phase of the early Universe. In our setup, the oscillation of the inflaton field is mimicked by the transverse breathing mode of a cigar-shaped condensate, which parametrically excites longitudinal quasiparticles with opposite momenta. After a short modulation period, we observe entanglement of these pairs that reveals the role played by vacuum fluctuations in seeding the parametric growth, confirming the quantum origin of the excitations. As the system continues to evolve, we observe a decrease in correlations and a disappearance of nonclassical features. These point toward future experimental probes of the late-time nonlinear regime where further analogies can be drawn with reheating, i.e., the thermalization of the postinflationary Universe.

Figures3

Five-panel figure: the excitation protocol and trap schematic; a time-of-flight density trace with a zoomed inset; a 3D scatter plot of detected atom velocities with two analysis-volume boxes; an auto-correlation peak; and probability distributions of detected atom number for four modulation depths. — **Figure 1.** (a) Diagram of the experimental apparatus and excitation protocol. (b) The position and arrival time of individual atoms is recorded and converted to an initial velocity; sidebands are visible at $\pm 11.7$ mm/s. A Bragg diffraction pulse shifts more than 97% of the BEC atoms to later times to avoid saturating the detector near the excitations. (c) A single shot showing the excitations in 3D velocity space; each dot is a single atom, and the boxes show the position and size of a typical analysis volume, or “voxel”. (d) Auto-correlation function of the measured sideband velocities, giving an estimate of the longitudinal mode size and showing its thermal nature. (e) Probability distribution in a single voxel for different modulation depths $A$ , each acquired over about 2800 realizations. The lines show the probability distribution of Eq. (3), computed from the mean detected atom numbers of 0.094(6), 0.37(1), 0.99(3), and 1.50(3) for increasing $A$ .

Two stacked plots of normalized variance and of the two-body correlator versus mean detected atom number, each with a red threshold line and, for the correlator, a gray shaded theoretical band and a zoomed inset. — **Figure 2.** Normalized variance (a) and two-body correlator (b) as a function of the mean *detected* atom number, for modulation amplitudes between $A = 3$ and $28\%$ . The hold time $\Delta t$ was fixed at 1.6 ms (3 breathing periods). The red line marks unity in (a) and the entanglement-witness threshold in (b), assuming a quantum efficiency of 25%. The gray curve is the expected value for a two-mode squeezed thermal state with an initial temperature of 25(5) nK and the same efficiency, its width reflecting the uncertainty on the temperature. Error bars denote one standard deviation, computed by bootstrap. $\xi^2$ was not corrected for the quantum efficiency.

Two stacked plots of mean detected population and cross-correlator versus hold time for two modulation depths, with an inset of the normalized variance. — **Figure 3.** Mean detected population (a) and cross-correlation (b) as a function of the hold time $\Delta t$ , for two modulation depths (orange circles, 18%; green squares, 25%). The inset shows the normalized variance. At late times, entanglement can no longer be inferred. Error bars denote one standard deviation, computed by bootstrap.

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Conclusion

We have observed entanglement between parametrically excited quasiparticle modes of a quantum fluid. This entanglement demonstrates the role of quantum fluctuations in seeding the parametric growth, in analogy with cosmological preheating. While it has its limitations, the relevance of the analogy is strengthened by the late-time dynamics. As noted above, the growing quasiparticle population leads to an interaction-dominated regime, of which the apparent loss of entanglement in Fig. 3 may be an indicator. This regime is characterized by a rich phenomenology, including decoherence of the resonant modes, secondary peaks as observed in similar hydrodynamic experiments, and loss of Gaussianity. These phenomena can be seen as steps towards thermalization, and taken together they are analogous to cosmological reheating. In addition, as the BEC keeps breathing, the energy and coherence of the driving field will be lost to backreaction from the produced quasiparticles, the effect of vacuum fluctuations playing again a crucial role. Future work will investigate these effects.

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