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arXiv:2411.19948 · Physical Review A

Scaling laws governing the collapse of a Bose-Einstein condensate

Sebastian J. Morris, C. J. Ho, Simon M. Fischer, Jiří Etrych, Gevorg Martirosyan, Zoran Hadzibabic, Christoph Eigen

Published Apr 7, 2025• 1 citation
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Abstract

We study the collapse of an attractive Bose-Einstein condensate, where an unstable system evolves towards a singularity, by numerically solving the underlying cubic-quintic nonlinear Schrödinger equation. We find good agreement between our simulations and the atom-loss measurements with a K 39 condensate. Our simulations reveal an interplay of weak collapse and the propensity of the system to form a hotspot and we uncover scaling laws that govern this behavior. We also identify promising signatures of the theoretically predicted, but so far experimentally elusive, elastic three-body interactions.

DOI
10.1103/physreva.111.l041301

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We study the collapse of an attractive atomic Bose-Einstein condensate prepared in the uniform potential of an optical-box trap.We characterize the critical point for collapse and the collapse dynamics, observing universal behavior in agreement with theoretical expectations.Most importantly, we observe a clear experimental signature of the counterintuitive weak collapse, namely, that making the system more unstable can result in a smaller particle loss.We experimentally determine the scaling laws that govern the weak-collapse atom loss, providing a benchmark for the general theories of nonlinear wave phenomena.
Collapsing Bose-Einstein condensates are rich and complex quantum systems for which quantitative explanation by simple models has proved elusive. We present experimental data on the collapse of high-density 85{}^{85}85Rb condensates with attractive interactions and find quantitative agreement with the predictions of the Gross-Pitaevskii equation. The collapse data and measurements of the decay of atoms from our condensates allow us to put new limits on the value of the 85{}^{85}85Rb three-body loss coefficient K3{K}_{3}K3​ at small positive and negative scattering lengths.
The critical behavior of collective modes and the collapsing dynamics of trapped Bose-Einstein condensates with attractive interactions are studied analytically and numerically. The time scales of these dynamics both below and above the critical point of the collapse are found to obey power laws with a single parameter of ${N/N}_{c}\ensuremath{-}1,$ where N is the number of condensate atoms and Nc{N}_{c}Nc​ is the critical number. The collapsing condensate eventually undergoes rapid implosion, which occurs several times intermittently, and then the implosion turns to an explosion. The release energy of the explosion is found to be proportional to the square of the interaction strength, inversely proportional to the three-body recombination rate, and independent of the number of condensate atoms and the trap frequency.
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