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arXiv:2408.01726

Quantum Lotka-Volterra dynamics

Yuechun Jiao, Yu Zhang, Jingxu Bai, Weilun Jiang, Yunhui He, Shen, Heng, Suotang Jia, Jianming Zhao, Charles S. Adams

Published Aug 3, 2024• 0 citations
arXivHTMLPDF

Abstract

Physical systems that display competitive non-linear dynamics have played a key role in the development of mathematical models of Nature. Important examples include predator-prey models in ecology, biology, consumer-resource models in economics, and reaction-diffusion equations in chemical reactions. However, as real world systems are embedded in complex environments, where it is difficult or even impossible to control external parameters, quantitative comparison between measurements and simple models remains challenging. This motivates the search for competitive dynamics in isolated physical systems, with precise control. An ideal candidate is laser excitation in dilute atomic ensembles. For example, atoms in highly-excited Rydberg states display rich many-body dynamics including ergodicity breaking, synchronisation and time crystals. Here, we demonstrate predator-prey dynamics by laser excitation and ionisation of Rydberg atoms in a room temperature vapour cell. Ionisation of excited atoms produce electric fields that suppress further excitation. This starves the ionisation process of resource, giving rise to predator-prey dynamics. By comparing our results to the Lotka-Volterra model, we demonstrate that as well applications in non-linear dynamics, our experiment has applications in metrology, and remote sensing of localised plasmas.

DOI
10.48550/arxiv.2408.01726

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One of the most fascinating and challenging topics of recent years is many- body physics. Owing to the large number of components of real physi- cal systems an analytical approach or numerical solutions are typically not practicable. However, an experimental approach to this problem is possible thanks to an unprecedented level of matter control on the atomic scale. In our setup we use atoms excited to high-lying energy states, called Rydberg atoms, which have peculiar properties like the extremely long lifetime and strong interactions. These experimental features make a cold ensem- ble of Rydberg atoms a very controllable example of a strongly interacting many-body system and provide a promising framework for quantum simulation.
Phase-space features of a reduced version of the Toda-like Hamiltonian H(x,k), written in a form constrained by the condition ∂^{2}H/∂x∂k=0, with x and k as canonically conjugate variables, are analyzed in terms of Wigner currents. For Wigner currents convoluted with either thermodynamic or Gaussian ensembles, the underlying Hamiltonian dynamics admits analytic corrections due to quantum distortions over the classical phase-space pattern, computed and interpreted through quantifiers of quantumness and stationarity. Notably, while emulating the Lotka-Volterra (LV) dynamics that describe ecological competition systems, the Toda-like classical dynamics allows for analytical solutions with computable periods corresponding to closed phase-space orbits of isotropic prey-predator population distributions. The essential conditions for understanding how classical and quantum evolution can coexist are provided at different scales of quantumness, driven by the associated convoluting ensemble parameter. In the case of Gaussian statistical ensembles, the exact profile of the quantum distortions over classical prey-predator phase-space trajectories is obtained nonperturbatively. Our results indicate that, besides the classical stability admitted by LV models, the Toda-like patterns also exhibit quantum stability. Therefore, this can be regarded as the first step as a predictive theoretical framework toward more robust descriptions of quantum patterns in competitive microscopic biosystems.