Spinor Bose-Einstein condensate as an analog simulator of molecular bending vibrations

Ayaka Usui; Artur Niezgoda; Manuel Gessner

doi:10.22331/q-2026-10-01-2226

Spinor Bose-Einstein condensate as an analog simulator of molecular bending vibrations

Ayaka Usui¹, Artur Niezgoda², and Manuel Gessner³

¹Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
²ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
³Departament de Física Teòrica and IFIC, Universitat de València-CSIC, C/Dr Moliner 50, 46100 Burjassot (Valencia), Spain

Published:	2026-10-01, volume 10, page 2226
Eprint:	arXiv:2505.19836v2
Doi:	https://doi.org/10.22331/q-2026-10-01-2226
Citation:	Quantum 10, 2226 (2026).

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Abstract

We demonstrate that spinor Bose-Einstein condensates (BECs) can be operated as an analog simulator of the two-dimensional vibron model. This algebraic model describes bending vibrations of molecules and, in the case of triatomic molecules, exhibits two phases where linear and bent configurations are stabilised. Spinor BECs can be engineered to simulate states that correspond to linear or bent triatomic molecules, with the Wigner function of the BEC encoding information about the molecular configuration. We show how quantum simulations of the bending dynamics of linear molecules can be realised, and how preparing a linear configuration in the bent phase leads to a dynamical instability. In the dynamics triggered by the corresponding instability, a significant amount of entanglement is generated, and we characterise the dynamics with the squeezing parameter and the quantum Fisher information (QFI). The scaling of the non-Gaussian sensitivity, described by the difference between squeezing and QFI, grows with the system size once the spinor system crosses from the linear to the bent phase, thus serving as a dynamical witness for the quantum phase transition.

Featured image: (a) Trajectories on the mean-field model of spin-1 BEC with fixed energy $\eta$ mapped to phase space $(X,P_X)$ for 50 particles and $\gamma=0.5$. (b) Exact time evolution of the Wigner quasiprobability distribution in phase space $(X,P_X)$ for 50 particles.

Popular summary

Spin-1 Bose–Einstein condensates (BECs) can be engineered to reproduce the two-dimensional vibron model, a cornerstone algebraic framework for describing the bending motion of triatomic molecules. By mapping molecular vibrational degrees of freedom onto atomic spin modes, the condensate naturally adopts “linear” or “bent” configurations—direct analogues of straight and V-shaped molecules. Varying a single control parameter drives a sharp configurational phase transition between these geometries, faithfully reproducing the core physics of molecular bending.

A clear signature of molecular shape is given by the position and momentum distribution of the center atom. A rapid change of the control parameter can bend a straight configuration or straighten a bent one—and in the latter case the system becomes dynamically unstable. This instability generates a burst of many-body entanglement, which we identify using metrological entanglement criteria. Crucially, the growth of non-Gaussian entanglement serves as a real-time indicator of the underlying phase transition between linear and bent phases.

The exceptional experimental flexibility of spinor BECs—continuous tuning of interactions, precise state preparation, and real-time access to dynamics—combined with quantum information tools for detecting and quantifying entanglement, establishes these condensates as a powerful molecular simulator. Our results demonstrate that spinor BECs can deepen our understanding of triatomic molecular structure and open a clear path toward exploring the full quantum dynamics of molecular bending and vibration under controlled conditions.

► BibTeX data

@article{Usui2026spinorboseeinstein,
  doi = {10.22331/q-2026-10-01-2226},
  url = {https://doi.org/10.22331/q-2026-10-01-2226},
  title = {Spinor {B}ose-{E}instein condensate as an analog simulator of molecular bending vibrations},
  author = {Usui, Ayaka and Niezgoda, Artur and Gessner, Manuel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2226},
  month = oct,
  year = {2026}
}

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