Observation of entanglement in a cold atom analog of cosmological preheating

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 which 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 non-classical features. These point towards future experimental probes of the late-time nonlinear regime where further analogies can be drawn with reheating, i.e. the thermalization of the post-inflationary Universe.

Figures (4)

• Figure 1: (a) Diagram of the experimental apparatus and excitation protocol (see text for description). (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 in the vicinity of the excitations. (c) A single shot showing the excitations in a 3D velocity space. Each dot represents a single atom. 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 of these acquired over $\sim2800$ realizations. The lines show the probability distribution in Eq. (\ref{['eqn:ThermalStateDistribuition']}) computed from the mean detected atom numbers of 0.094(6), 0.37(1), 0.99(3) and 1.50(3) for increasing value of $A$.
• 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 indicates unity (a) and the threshold for the entanglement witness of Ref. gondret.2025.quantifying in panel (b), assuming a quantum efficiency of 25%. The gray curve shows the expected value assuming a two-mode squeezed thermal state with an initial temperature of 25(5) nK and a quantum efficiency of 25%. The width of the gray band reflects the uncertainty in the temperature. Error bars denote one standard deviation uncertainty and are computed using a bootstrap analysis. The value of $\xi^2$ was not corrected for the quantum efficiency.
• Figure 3: Mean detected population (a) and cross-correlation (b) as a function of the hold time $\Delta t$. Data is shown for two different modulation depths (orange circles 18%, green squares 25%). The inset shows the normalized variance. At late times, entanglement cannot be inferred. Error bars denote one standard deviation computed using a bootstrap analysis.
• Figure 4: (a) The auto-correlator computed with the same dataset as in Fig. \ref{['fig2']}, in which we vary the modulation depth for a constant hold time. Panels (b) and (c) show the corresponding auto-correlator for the dataset of Fig. \ref{['fig3']} where the hold time is varied with a modulation depth of respectively 18% and 25%. The light square markers show the negative velocity sideband and the dark stars the positive velocity one. The error bars are computed from the expected error for a thermal law with the same detected atom number.