Exact Solution for 1D Spin-Polarized Fermions with Resonant Interactions

Abstract

Using the asymptotic Bethe Ansatz, we obtain an exact solution of the many-body problem for 1D spin-polarized fermions with resonant p-wave interactions, taking into account the effects of both scattering volume and effective range. Under typical experimental conditions, accounting for the effective range, the properties of the system are significantly modified due to the existence of "shape" resonances. The excitation spectrum of the considered model has unexpected features, such as the inverted position of the particle- and hole-like branches at small momenta, and roton-like minima. We find that the frequency of the "breathing" mode in the harmonic trap provides an unambiguous signature of the effective range.

final version to be published in Phys. Rev. Lett

References in corpus (20)

• Realization of an Excited, Strongly-Correlated Quantum Gas Phase
• Attractive Fermi gases with unequal spin populations in highly elongated traps
• Universal theory of nonlinear Luttinger liquids
• Phase diagram of a strongly interacting polarized Fermi gas in one dimension
• p-wave Feshbach molecules
• An exactly solvable model of the BCS-BEC crossover
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Anisotropic Fermi Superfluid via p-wave Feshbach Resonance
• Exact solution for infinitely strongly interacting Fermi gases in tight waveguides
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Collisional Properties of p-Wave Feshbach Molecules
• Binding Energies of 6Li p-wave Feshbach Molecules
• Strongly-resonant p-wave superfluids
• Applications of exact solution for strongly interacting one dimensional bose-fermi mixture: low-temperature correlation functions, density profiles and collective modes
• Resonant Scattering of Ultracold Atoms in Low Dimensions
• Exact results for the 1D interacting mixed Bose-Fermi gas
• Correlation functions of one-dimensional Bose-Fermi mixtures
• Modeling interactions for resonant p-wave scattering
• Paired state in an integrable spin-1 boson model

Cited by in corpus (22)

• Fermi gases in one dimension: From Bethe Ansatz to experiments
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Universal One-dimensional Atomic Gases Near Odd-wave Resonance
• Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
• Effective Field Theory for Rydberg Polaritons
• Coupled $\ell$-wave confinement-induced resonances in cylindrically symmetric waveguides
• Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions
• Comparative study of one-dimensional Bose and Fermi gases with contact interactions from the viewpoint of universal relations for correlation functions
• Itinerant ferromagnetism in 1D two-component Fermi gases
• Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction
• Discretized vs. continuous models of p-wave interacting fermions in 1D
• Many-body stabilization of a resonant p-wave Fermi gas in one dimension
• Ground-state properties of dilute spinless fermions in fractional dimensions
• Resonantly interacting $p$-wave Fermi superfluid in two dimensions: Tan's contact and breathing mode
• Probing an effective-range-induced super fermionic Tonks-Girardeau gas with ultracold atoms in one-dimensional harmonic traps
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• One-dimensional ultracold atomic gases: Impact of the effective range on integrability
• One-dimensional model of chiral fermions with Feshbach resonant interactions
• Exact Solutions to Two-Component Many-Body Systems in One Dimension
• One-dimensional two-component fermions with contact even-wave repulsion and SU(2) breaking near-resonant odd-wave attraction
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons