Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.02918

Intrinsic Zak Phase of Solitons: A Geometric Correspondence with the Center-of-Mass Position

Xiao-Xiao Hu·Chen Cheng·Hong-Gang Luo
View original source ↗Read source document ↗Export metadata ↓

Abstract

The center-of-mass position of a nonlinear soliton in a lattice is commonly attributed to the interplay between nonlinearity and lattice confinement. Here, we reveal its geometric origin by establishing an exact relation between the soliton position and an intrinsic Zak phase. Unlike the Zak phase of a linear Bloch band, this intrinsic Zak phase arises from the nonlinear self-consistent band of the lattice reconstructed by the soliton density. We construct a composite periodic function to define this phase and demonstrate that its topological winding during nonlinear Thouless pumping dictates the quantized soliton displacement. Our results establish band geometry as a fundamental descriptor of nonlinear soliton position in a lattice and provide a geometric framework for their topological transport.

Explore related subjects

cond-mat.quant-gas

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xiao-Xiao Hu, Chen Cheng, Hong-Gang Luo. 2026-11-02. Intrinsic Zak Phase of Solitons: A Geometric Correspondence with the Center-of-Mass Position. https://arxiv.org/abs/2611.02918

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Altermagnetism-induced Fulde-Ferrell-Larkin-Ovchinnikov superfluids and momentum-selective pairing channels in optical lattices

We study the superfluid phases of a two-dimensional degenerate Fermi gas in an optical lattice subject to a $d_{xy}$-wave altermagnetic term that couples to the in-plane spin component. The single-particle Hamiltonian generates anisotropic Fermi surfaces for the two pseudo-spin species while maintaining zero net polarization. Using the Bogoliubov-de Gennes approach, we show that this anisotropy favors Cooper pairing at a finite center-of-mass momentum, producing a competition between Bardeen-Cooper-Schrieffer (BCS) and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing and leading to FFLO superfluids. We further examine the effect of a Zeeman-induced spin polarization and find that triplet and singlet pairing channels coexist and compete, resulting in a momentum-selective pairing pattern. Remarkably, this triplet pairing emerges exclusively in the FFLO phase and is entirely absent in the BCS phase. The model is readily realizable in ultracold atoms with current experimental techniques, providing a feasible route for quantum emulation and for studying unconventional superfluid phases.

cond-mat.quant-gas↗
arXiv2026

Bayesian optimization enhanced magnetic field gradient detection based on spin-orbit coupled Bose-Einstein condensates

Magnetic field detection is of great significance in modern fields such as medical diagnostics, geological exploration, inertial navigation, and space physics. We have previously investigated the expansion dynamics of a spin-orbit-coupled Bose-Einstein condensate. Building on these results, here we propose a scheme for magnetic-field-gradient detection by establishing a quantitative relationship between the condensate's rotational deflection angle and the magnetic-field gradient. In this work, we present the parameter dependence of this scheme and perform a systematic optimization. We introduce a Bayesian optimization algorithm to automatically and efficiently search for the optimal combination of key parameters, thereby significantly enhancing the sensitivity of the magnetic field gradient measurement. The results show that the optimized gradiometer improves the sensitivity by a factor of five. This work not only provides a new approach for magnetic field gradient measurement but also serves as a reference for machine learning-empowered quantum precision measurement.

cond-mat.quant-gas↗
arXiv2026

Rotating two-dimensional Bose--Einstein condensates in power-law traps: collapse, Thomas--Fermi scaling, and the inverse-square endpoint

In two dimensions, the kinetic and contact energies scale identically under dilation, a trap $V=r^s/s$ as $λ^{-s}$. We follow this balance through the power-law family $-2\le s\le4$, $s\neq0$, for both signs of the coupling $g$, with rotation, using scaling bounds, radial solutions, Bogoliubov spectra, and two-dimensional imaginary-time states. Attraction collapses the cloud at the Townes coupling $g_{*}$ in every trap, with width $\ell\proptoδ^{1/(s+2)}$, $δ=1-|g|/g_{*}$; repulsion spreads it to a Thomas--Fermi (TF) radius $\propto g^{1/(s+2)}$. A rotating collapse leaves the axis once the rotation frequency $Ω$ exceeds its dipole frequency, which softens only for $s>2$; in a quartic trap this happens at $δ\simeq0.32\,Ω^6$, within $3\%$ of the Bogoliubov threshold; it then collapses on the minimum ring of the rotating-frame potential, which also empties a repulsive TF cloud at $Ω=(3g/π)^{1/6}$. For repulsive vortex states the TF energy error splits exactly into a density-gradient and a flow part of comparable or larger size. At $s=-2$ only the cutoff sets a length: the energy is exactly covariant with it, the condensate falls to the center for both signs, and repulsion leaves a halo of density $\propto1/(gr^2)$ whose extent grows exponentially with $g$. Near collapse, split-step imaginary time has a first-order stationary bias invisible to residual tests.

cond-mat.quant-gas↗