Emergent Weyl Nodes and Berry Curvature in Bose Polarons via $p$-Wave Feshbach Coupling

Abstract: We show that an impurity quasiparticle immersed in a Bose-Einstein condensate, known as a Bose polaron, exhibits topological properties characterized by a nonzero Berry curvature, which is induced by Weyl nodes that emerge via interspecies $p$-wave Feshbach resonance. Such nodes occur even in the absence of spin degrees of freedom and spin-orbit coupling. For charged impurities, the corresponding $p$-wave polarons are shown to be accompanied by chiral anomaly. The above predictions can be tested in a cold atomic environment by observing the Hall transport of the atomic or ionic impurity cloud.

• The paper introduces a two-channel model showing that p-wave Feshbach coupling induces Weyl nodes in the polaron excitation spectrum.
• The study reveals that emergent Berry curvature leads to an anomalous Hall response and chiral anomaly for charged impurities.
• The work offers a new pathway to simulate topological quantum matter in lattice-free ultracold atomic systems with tunable interactions.

Emergent Topological Properties in Bose Polarons via $p$-Wave Feshbach Coupling

Introduction

This paper presents a theoretical investigation into the emergence of topological phenomena in Bose polarons—impurity quasiparticles immersed within a Bose-Einstein condensate (BEC)—when the impurity-medium interaction is tuned via a $p$-wave Feshbach resonance. The study demonstrates that, even in the absence of spin degrees of freedom and spin-orbit coupling, the $p$-wave resonance induces Weyl nodes in the polaron excitation spectrum. These nodes act as sources of Berry curvature, yielding pronounced topological effects such as the anomalous Hall response and chiral anomaly for charged impurities. The predictions offer experimentally accessible signatures for ultracold atomic platforms and open a promising route for simulating topological quantum matter in highly controllable, lattice-free environments.

Theoretical Model and Weyl Point Formation

The authors construct a two-channel Hamiltonian capturing the essential physics of impurity atoms in a BEC with $p$-wave Feshbach coupling. The $p$-wave character introduces an $\ell_z$-dependent interaction between impurity and medium, allowing selective resonance with specific projections of orbital angular momentum. Near resonance, the effective low-energy Hamiltonian reduces to a two-band model in which mixing between the open (impurity) and closed (molecular) channels exhibits a $p$-wave momentum dependence. This construction supports Weyl points—momentum-space monopoles—at $p_z = \pm p_W$, with nonzero chirality, in the quasiparticle dispersion.

A key claim of the paper is that these Weyl nodes and associated Berry curvature are realized without the necessity of internal spin degrees of freedom or engineered spin-orbit coupling, setting this mechanism apart from conventional solid-state and cold atom systems. The analysis explicitly demonstrates the emergence of the Berry curvature, with the $z$-component diverging at the Weyl points and changing sign according to the chiralities associated with $\ell_z = \pm1$ resonance.

Berry Curvature and Anomalous Transport

The presence of Weyl nodes fundamentally restructures the topology of the polaron bands by introducing nontrivial Berry curvature distributed in momentum space. The calculation details the analytic expression for the Berry curvature, notably $p$0, and illustrates that it is strongly peaked at the Weyl points, providing Dirac monopole structure entirely determined by the $p$1-wave resonance and the BEC background.

The semiclassical dynamics of Bose polarons are developed, leading to an anomalous velocity component transverse to both applied forces and the Berry curvature, analogous to the anomalous Hall effect in electronic systems. The resulting Hall conductivity can be written as an integral over the Berry curvature weighted by the distribution function, drawing direct parallels with Weyl semimetals and topological phases in condensed matter. The paper provides quantitative predictions for the Hall response and addresses experimental detection via center-of-mass measurements of impurity clouds.

For charged impurities (ionic polarons), the coupling to external electromagnetic fields results in an emergent chiral anomaly, a feature previously thought exclusive to relativistic Weyl and Dirac systems. The anomalous non-conservation of chirality in the presence of parallel electric and magnetic fields is shown to have direct analogs in these cold atomic systems, laying a foundation for simulating quantum anomalies in a highly tunable environment.

Implications and Prospects

By demonstrating that Bose polarons acquire nontrivial topological characteristics through $p$2-wave Feshbach coupling, the paper provides a new paradigm for realizing and probing topological quasiparticles in ultracold atoms, sidestepping the need for artificial gauge fields or engineered lattice geometries. The topologically nontrivial bands, manifesting as Berry curvature and anomalous transport, can be directly interrogated in cold atom experiments using established transport and collective mode measurement protocols.

The work outlines implications for simulating two-component quantum systems with tunable topology, providing a flexible platform to engineer flat bands and study quantum geometric effects. The mediated $p$3-wave interactions among fermionic impurities may lead to topological superfluid phases with intrinsic Berry curvature, and the system is positioned as a candidate for flat-band superconductivity studies. Additionally, extensions toward quantum geometry response functions are indicated as promising directions.

Conclusion

This paper rigorously establishes the emergence of Weyl nodes and Berry curvature in Bose polarons as a direct consequence of $p$4-wave Feshbach coupling. The results demonstrate that impurity quasiparticles in a BEC can host Weyl-type band topology, with experimentally accessible anomalous Hall and chiral anomaly signatures. The work substantially broadens the scope of topological phenomena accessible in non-lattice, non-spinor atomic systems and lays a theoretical foundation for future explorations of topological and quantum geometric responses in highly controllable many-body settings.