[论文解读] Families of localized modes of Bose-Einstein condensates enabled by incommensurate optical lattice and photon-atom interactions

Pedro S. Gil, V. V. Konotop|arXiv (Cornell University)|Feb 19, 2026

Cold Atom Physics and Bose-Einstein Condensates被引用 0

一句话总结

tldr: 调查在光腔内的 1D 非一致光晶格中，玻色-爱因斯坦凝聚体的一类非线性局部化模态族，揭示可移动边缘、双稳态、伪简并以及来自光子-原子反馈作用的 XOR 样动态。

ABSTRACT

We consider a Bose-Einstein condensate (BEC) loaded into a one-dimensional optical cavity under the combined action of an external potential and atom-cavity coupling with mutually incommensurate periods. Such configuration enables the localization of matter waves even in the absence of two-body interactions. We study families of localized modes within the mean-field approximation for red and blue detunings from atomic and cavity resonances in relatively shallow quasiperiodic lattices, beyond the validity of the tight-binding approximation. The parameter regimes supporting localization of atomic wave packets are identified. The system exhibits two types of bistability manifested as distinct photon numbers under otherwise identical conditions. One type arises from the coexistence of multiple families of localized modes, typical of conservative nonlinear systems, while the other stems from the multivalued dependence of the families on system parameters, characteristic of systems exhibiting hysteresis. BEC in a cavity may also display pseudodegeneracy, understood as the existence of two distinct atomic-density distributions corresponding to the same atomic and photon numbers (although different chemical potentials). The stability of the localized modes is analyzed. It is shown that, owing to the strong impact of long-range interactions on stability, a two-localized-mode configuration can operate as an XOR logic gate.

研究动机与目标

• Motivate understanding of localization phenomena for BECs in coupled atom-cavity systems with incommensurate potentials.
• Characterize families of nonlinear localized modes and how their existence depends on atom number and cavity photon number.
• Identify mobility edges and bistability mechanisms arising from long-range photon-atom backaction.
• Explore stability and dynamical behavior of localized modes under various detuning configurations.

提出的方法

• Model the BEC in a 1D optical cavity with an external quasi-periodic potential and a backaction term from the cavity field.
• Use a mean-field Gross-Pitaevskii equation coupled to a cavity field equation to capture nonlocal nonlinearities.
• Analyze stationary solutions via an ansatz Psi(x,t)=e^{-i mu t} phi(x) and solve the eigenproblem with an effective potential including V0 cos^2(beta x+vartheta) and sigma A cos^2 x.
• Express cavity photon number A as a functional of the atomic distribution via A = eta^2/[(sigma Delta - theta)^2 + kappa^2], with theta = N <cos^2 x> and Phi=Psi/sqrt(N).
• Classify solutions by N(mu) or A(N) and quantify localization with the inverse participation ratio (IPR).
• Study stability by direct time evolution and map out regimes of localization, delocalization, and bifurcations across detuning configurations.

Figure 1: (a) Lowest 88 families of stationary modes for $\sigma=+1$ and $\Delta=150$ on the diagram $(A,\mathcal{N})$ . (b) Examples of three families from the bundle shown in (a) (note that the range of $A$ is changed). The crosses indicate crossing of the families. The colored circles, labeled "A

实验结果

研究问题

• RQ1 What parameter regimes support localized atomic states in the presence of incommensurate optical lattices and cavity backaction?
• RQ2 How do the numbers of atoms and cavity photons determine localization-delocalization transitions and mobility edges?
• RQ3 What forms of bistability and pseudo-degeneracy arise in this nonlocal nonlinear system?
• RQ4 How does detuning configuration (blue/blue, red/red, blue/red, red/blue) affect localization, stability, and mode structure?
• RQ5 Can the long-range photon-atom interactions yield dynamics akin to logical operations (e.g., XOR) for localized mode configurations?

主要发现

• Localized nonlinear modes exist due to the combined incommensurate potentials and photon-atom backaction, even without two-body interactions.
• There can be one or two nonlinear mobility edges (MEs) within a given family, separating localized and extended states in the same branch.
• Two distinct types of bistability are observed: multi-family bistability and hysteresis-like multivalued A(N) within a single family.
• Pseudo-degeneracy occurs where two distinct atomic density distributions share the same atom and photon numbers but differ in chemical potential.
• Long-range interactions enable configurations where two localized modes can operate as an XOR logic gate.
• Localization strength and the interval of N supporting localized modes can be tuned by the driving strength (eta) and detunings.

Figure 2: Distributions of the localized modes for $\sigma=+1$ , $\Delta=150$ and $\tilde{\eta}=141$ , with $\mathcal{N}\approx 7\times 10^{2}$ on the diagram $(X/L,A)$ (the leftmost panel). The panels on the right show the wavefunctions of the modes, labeled A and B in the left panel and in Figs. 1