arXiv subjects

Jakub Kopyciński

Publications and source records attributed to Jakub Kopyciński.

7 recordsLinked to original sources

arXiv2026

Super-Tonks-Girardeau Quench in the Extended Bose-Hubbard Model

We investigate the effect of a quench from a one-dimensional gas with strong and repulsive local interactions to a strongly attractive one, known as the super-Tonks-Girardeau effect. By incorporating both an optical lattice and non-local interactions (specifically nearest-neighbor), we discover a previously unexplored phenomenon: the disruption of the state during the quench, but within a specific range of interactions. Our study employs the extended Bose-Hubbard model across various system sizes, starting with analytical results for two atoms and progressing to few-body systems using exact diagonalization, DMRG and TDVP methods. Finally, we use a numerical implementation of the local density approximation for a macroscopic number of atoms. Consistently, our findings unveil a region where the initially self-bound structure expands due to the super-Tonks-Girardeau quench. The fast evaporation provides a tool to characterize the phase diagram in state-of-art experiments exploring the physics of the extended Bose-Hubbard model.

cond-mat.quant-gas↗

arXiv2025

Phase diagram and elementary excitations of strongly interacting droplets with non-local interactions

A one-dimensional bosonic gas with strong contact repulsion and attractive non-local interactions may form a quantum droplet with a flat-top density profile. We focus on a system in the Tonks-Girardeau limit of infinitely strong contact repulsion. We show that the main system features are the same for a broad class of non-local interaction potentials. Then, we focus on a limiting case, the one of slowly varying density profiles, to find approximate formulas for the surface and bulk energies of a droplet. We further characterise the system by numerically finding the excitation spectrum. It consists of two families: phononic-like excitations inside droplets and scattering modes. Analysis within the linearised regime is supplemented with the full, nonlinear dynamics of small perturbations.

cond-mat.quant-gas↗

arXiv2023

Propagation properties and stability of dark solitons in weakly interacting Bose-Bose droplets

We investigate dark solitons in two-component Bose systems with competing interactions in one dimension. Such a system hosts a liquid phase stabilized by the beyond-mean field corrections. Using the generalized Gross-Pitaevskii equation, we reveal the presence of two families of solitonic solutions. The solitons in both of them can be engineered to be arbitrarily wide. One family of solutions, however, has got an anomalous dispersion relation and our analyses show one of its branches is unstable. We find the presence of a critical velocity demarcating the stable from unstable solutions. Nonetheless, grey anomalous solitons are able to exist inside quantum droplets and can be treated as solitonic excitations thereof.

cond-mat.quant-gas↗

arXiv2023

Quantum Monte Carlo-based density functional for one-dimensional Bose-Bose mixtures

We propose and benchmark a Gross-Pitaevskii-like equation for two-component Bose mixtures with competing interactions in 1D. Our approach follows the density-functional theory with the energy functional based on the exact Quantum Monte Carlo (QMC) simulations. Our model covers, but goes beyond, the popular approach with the Lee-Huang-Yang corrections. We first benchmark our approach against available QMC data in all interaction regimes and then study dynamical properties, inaccessible by ab initio many-body simulations. Our analysis includes a study of monopole modes and reveals the presence of anomalous dark solitons.

cond-mat.quant-gas↗

arXiv2022

Ultrawide dark solitons and droplet-soliton coexistence in a dipolar Bose gas with strong contact interactions

We look into dark solitons in a quasi-1D dipolar Bose gas and in a quantum droplet. We derive the analytical solitonic solution of a Gross-Pitaevskii-like equation accounting for beyond mean-field effects. The results show there is a certain critical value of the dipolar interactions, for which the width of a motionless soliton diverges. Moreover, there is a peculiar solution of the motionless soliton with a non-zero density minimum. We also present the energy spectrum of these solitons with an additional excitation subbranch appearing. Finally, we perform a series of numerical experiments revealing the coexistence of a dark soliton inside a quantum droplet.

cond-mat.quant-gas↗

arXiv2021

Vortex lattice in spin-imbalanced unitary Fermi gas

We investigate the properties of a spin-imbalanced and rotating unitary Fermi gas. Using a density functional theory (DFT), we provide insight into states that emerge as a result of a competition between Abrikosov lattice formation, spatial phase separation and the emergence of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. A confrontation of the experimental data [M. Zwierlein et al., Science 311, 492 (2006)] with theoretical predictions provides a remarkable qualitative agreement. In case of gas confined in a harmonic trap, the phase separation into a superfluid core populated by the Abrikosov lattice and a spin-polarized corona is the dominant process. Changing confinement to a box-like trap, reverts the spatial location of the component: gas being in the normal state is surrounded by superfluid threaded by quantum vortices. The vortex lattice no longer exhibits the triangular symmetry, and emergence of exotic geometries may be an indirect signature of the FFLO-like state formation in the system.

cond-mat.quant-gas↗

arXiv2021

Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons

Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a hydrodynamic approach. We use linearization to study particle (type-I) excitations and numerical minimization to study hole (type-II) excitations. We observe a good agreement between our approach and exact solutions of the Lieb-Liniger model for the particle modes and discrepancies for the hole modes. Therefore, the hydrodynamical equations find to be useful for long-wave structures like phonons and of a limited range of applicability for short-wave ones like narrow solitons. We discuss potential further applications of the method.

cond-mat.quant-gas↗