Emergence of dark soliton signatures in a one-dimensional unpolarized attractive Fermi gas on a ring

2018/05/31 by Andrzej Syrwid, Dominique Delande, Krzysztof Sacha
Physics and Astronomy · #Bethe ansatz #Cold Atom Physics and Bose-Einstein Condensates #Dispersion relation #Eigenvalues and eigenvectors #Fermi Gamma-ray Space Telescope #Fermion #Mathematical physics #Neutron #Nonlinear system #Physics #Physics of Superconductivity and Magnetism #Quantum electrodynamics #Quantum mechanics #Soliton #Spin (aerodynamics) #Strong Light-Matter Interactions #Yrast #cond-mat.quant-gas #quant-ph

paper · pdf · doi:10.1103/physreva.98.023616

published as Phys. Rev. A 98, 023616 (2018) · 14 pages, 11 figures, version accepted for publication in Physical Review A

arxiv created 2018/08/05 · openalex publication_date 2018/08/14 · arxiv updated 2018/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The two-component Fermi gas with contact attractive interactions between different spin components can be described by the Yang-Gaudin model. Applying the Bethe ansatz approach, one finds analytical formulas for the system eigenstates that are uniquely parametrized by the solutions of the corresponding Bethe equations. Recent numerical studies of the so-called yrast eigenstates, i.e., lowest energy eigenstates at a given nonzero total momentum, in the Yang-Gaudin model show that their spectrum resembles an yrast dispersion relation of the Lieb-Liniger model which in turn matches the dark soliton dispersion relation obtained within the nonlinear Schr"odinger equation. It was shown that such a conjecture in the case of the Lieb-Liniger model was not accidental and that dark soliton features emerged in the course of measurement of positions of particles when the system was initially prepared in an yrast eigenstate. Here, we demonstrate that, starting with yrast eigenstates in the Yang-Gaudin model, the key soliton signatures are revealed by the measurement of pairs of fermions. We study soliton signatures in a wide range of interaction strengths.

Citations

• Optical generation of solitonlike pulses in a single-component gas of neutral fermionic atoms
• Quantum Inverse Scattering Method and Correlation Functions
• Quantized Superfluid Vortex Rings in the Unitary Fermi Gas
• Dynamic Projection on Feshbach Molecules: A Probe of Pairing and Phase Fluctuations
• Exactly Solvable Model of the BCS-BEC Crossover
• Dilute Fermi Gas in Quasi-One-Dimensional Traps: From Weakly Interacting Fermions via Hard Core Bosons to a Weakly Interacting Bose Gas
• Collective excitation of trapped degenerate Fermi gases
• Solitons and vortices in ultracold fermionic gases
• Extracting the Condensate Density from Projection Experiments with Fermi Gases
• Dark solitons in a superfluid Fermi gas
• Phase transitions and pairing signature in strongly attractive Fermi atomic gases
• Creation and Detection of a Mesoscopic Gas in a Nonlocal Quantum Superposition
• Oscillations and interactions of dark and dark–bright solitons in Bose–Einstein condensates
• Equation of State Calculations by Fast Computing Machines
• Experimental Observation of Oscillating and Interacting Matter Wave Dark Solitons
• Images of the dark soliton in a depleted condensate
• Phase Diagram of a Strongly Interacting Polarized Fermi Gas in One Dimension
• Production of Long-Lived UltracoldLi2Molecules from a Fermi Gas
• Bethe ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions
• Dark-soliton-like excitations in the Yang–Gaudin gas of attractively interacting fermions