Breaking a superfluid harmonic dam: Observation and theory of Riemann invariants and accelerating sonic horizons

TL;DR

The paper investigates accelerating sonic horizons arising from a dam-break flow in a harmonically trapped Bose-Einstein condensate, using a barrier-pulse scheme to extract local density, flow, and Riemann invariants $r_\pm = \frac{u}{2} \pm c_s$ with $c_s = \sqrt{\frac{g_{1\mathrm{d}} n}{m}}$. A reduced 1D Gross-Pitaevskii framework, supported by exact solutions and 3D simulations, captures the flow in the rarefaction region and reveals that harmonic confinement accelerates the sonic horizon; a matched-quadric profile further describes the flow away from the vacuum edge. The study predicts the emergence of two additional sonic horizons, their collision, and eventual annihilation, highlighting novel dynamics of interacting horizons in a nonuniform background. This work provides a robust RI-based diagnostic, validates analytical 1D/hydrodynamic models against full 3D GPE, and advances analogue gravity research by linking dam-break physics, horizon acceleration, and horizon interactions in a controllable quantum fluid.

Abstract

An experimental and theoretical study of sonic horizons emerging from the dam-break problem in a Bose-Einstein condensate confined in an anisotropic harmonic trap is presented. Measurements, analysis, and numerics reveal the formation of a sonic horizon that undergoes acceleration due to harmonic confinement. The superfluid is characterized using a robust measurement technique to determine Riemann invariants. Experimental observations agree with an analytical solution of the Gross-Pitaevskii equation and computations. The collision and annihilation between two sonic horizons at long times is predicted.

Figures (5)

• Figure 1: Evolution of a rarefaction flow. a) A repulsive optical barrier or dam (represented by the red dashed oval) is slowly swept 523(1) µm from the right to the center of the BEC in 2 s. b) The dam is removed at $t=0$ and atoms are allowed to flow into the $x>0$ region of the trap, e.g. for c) $t=20$ ms, d) $t=40$ ms, and e) $t=60$ ms. f) Integrated cross sections of the density are provided for panels b)-e), where the canonical parabolic profile appears at short times. Data has been averaged over five experimental runs of the same parameters.
• Figure 2: Barrier pulse procedure. a) A rarefaction flow imaged at $t=40~$ms prior to pulsing. b) The barrier is introduced around $x_c=21$ µm, pulsed for 0.5 ms, and imaged. c) Excitations are imaged 5 ms after the pulsing. d) Integrated cross sections of the density from panels (a)-(c) with arbitrary units. All images taken in a 5 ms time-of-flight. Images are averaged over 10 experimental runs with the same parameters.
• Figure 3: Experimentally measured slow ($r_{-}$) and fast ($r_{+}$) RIs along the channel, plotted against the similarity variable $x/t$ at different rarefaction flow times for $t\le 60$ ms (data points with error bars, see legend). Error bars of the measurement represent the standard deviation of the mean at each probed location. The 3D GPE numerical simulations (solid curves, upper panel) and matched solutions from Eq. \ref{['eq:matched_solutions']} (solid curves, lower panel) are shown for comparison. The shaded region indicates where the matched solution is valid.
• Figure 4: Evolution of the condensate density and sonic horizons. Background (see color bar) is the integrated cross-sectional density $\langle n \rangle$ from the 3D GPE simulations. Solid curves track three SHs: two "slow" horizons (red and green, where $u_{\rm loc} = c_{s,\rm loc}$) with their collision marked by a star, and one "fast" horizon (blue, where $u_{\rm loc} = -c_{s,\rm loc}$). Dotted black curves are predictions for the rarefaction edges from Eqs. \ref{['eq:density_phase_exact_solution']}-\ref{['eq:xl']}. Experimental data for the SH (squares) and right edge of the rarefaction (triangles) are overlaid. The horizontal dashed line indicates the 1D turnaround time, $\frac{1}{4}T_{\rm har}$. Insets magnify the vacuum point ($x_r(t)$) and SH locations ($x_\mathrm{SH}(t)$) for $t \leq 60$ ms, with error bars showing the standard deviation of the mean from multiple experimental runs.
• Figure 5: General experimental setup. An elongated BEC (blue) trapped in an optical dipole trap (yellow). A repulsive barrier (red) can move along the $x$-axis, along the BEC.