Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0910.2269 · Physical Review Letters

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

Adilet Imambekov, Alexander A. Lukyanov, L. I. Glazman, Vladimir Gritsev

Published Jan 26, 2010• 30 citations
arXivHTMLPDF

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 holelike branches at small momenta, and rotonlike minima. We find that the frequency of the "breathing" mode in the harmonic trap provides an unambiguous signature of the effective range.

DOI
10.1103/physrevlett.104.040402

Related papers

Many-body stabilization of a resonant p -wave Fermi gas in one dimension

Lei Pan, Shu Chen, Xiaoling Cui

Using the asymptotic Bethe ansatz, we study the stabilization problem of the one-dimensional spin-polarized Fermi gas confined in a hard-wall potential with a tunable $p$-wave scattering length and finite effective range. We find that the interplay of two factors, i.e., the finite interaction range and the hard-wall potential, will stabilize the system near resonance. The stabilization occurs even on the positive scattering length side, where the system undergoes a many-body collapse if any of the factors is absent. At $p$-wave resonance, the fermion system is found to feature ``quasiparticle condensation'' for any value of effective range, which is stabilized if the range is above twice the mean particle distance. Slightly away from resonance, the correction to the stability condition linearly depends on the inverse scattering length. Finally, a global picture is presented for the energetics and stability properties of fermions from the weakly attractive to deep bound-state regime. Our results raise the possibility of achieving stable $p$-wave superfluidity in quasi-one-dimensional (1D) atomic systems, and meanwhile shed light on the intriguing $s$- and $p$-wave physics in 1D that violate the Bose-Fermi duality.

arXiv:1801.05902•Physical Review A•Jul 30, 2018•15 citations

Probing an effective-range-induced super fermionic Tonks-Girardeau gas with ultracold atoms in one-dimensional harmonic traps

Xiao-Long Chen, Xia-Ji Liu, Hui Hu

We theoretically investigate an ultracold spin-polarized atomic Fermi gas with resonant odd-channel $(p$-wave) interactions trapped in one-dimensional harmonic traps. We solve the Yang-Yang thermodynamic equations based on the exact Bethe ansatz solution, and predict the finite-temperature density profile and breathing mode frequency by using a local density approximation to take into account the harmonic trapping potential. The system features an exotic super fermionic Tonks-Girardeau (super-fTG) phase, due to the large effective range of the interatomic interactions. We explore the parameter space for such a fascinating super-fTG phase at finite temperature and provide smoking-gun signatures of its existence in both breathing mode frequencies and density profiles. Our results suggest that the super-fTG phase can be readily probed at temperatures of about $0.1{T}_{F}$, where ${T}_{F}$ is the Fermi temperature. These results are to be confronted with future cold-atom experiments with $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ atoms.

arXiv:1607.05908•Physical Review A•Sep 26, 2016•4 citations

Thermodynamic contacts and breathing-mode physics of one-dimensional p -wave Fermi gases in the high-temperature limit

Jeff Maki

An important tool for understanding the effects of interactions in harmonically trapped atomic gases is the examination of their collective modes. One such mode is the breathing or monopole mode, which is special as it is constrained to occur at twice the harmonic trapping frequency when the interactions are scale invariant. When the interactions are not scale invariant, the frequency of the breathing mode will deviate from twice the trap frequency. The deviation itself depends on the thermodynamic contacts, which describe how the energy changes with the interactions. In this work I examine how the thermodynamic contacts and the breathing-mode frequency of a spin-polarized one-dimensional (1D) $p$-wave Fermi gas depend on the 1D scattering volume $\ensuremath{\ell}$ and the effective range $r$ in the high-temperature limit. Such dynamics can be studied in experiments and provide a tool for understanding how the dynamics depends on interactions with a finite effective range.

arXiv:2110.05725•Physical Review A•Dec 20, 2021•5 citations

Variational ansatz for p-wave fermions confined in a one-dimensional harmonic trap

Przemysław Kościk, Tomasz Sowiński

Abstract We propose a very accurate and efficient variational scheme for the ground state of the system of p-wave attractively interacting fermions confined in a one-dimensional harmonic trap. By the construction, the method takes the non-analytical part of interactions exactly into account and thus it approximates the true ground-state wave function in a whole range of interactions very accurately. Within the method, we determine different properties of the system for a different number of particles and different interactions. In this way, we explore how the system and its features transit from the ideal non-interacting Fermi gas to the system of infinitely strong attractions. Additionally, we demonstrate that the ansatz may also be used on a repulsive branch of interactions where other numerical methods break down. The presented method of including zero-range interactions is very universal and may be easily generalized to other one-dimensional confinements.

arXiv:2004.06610•New Journal of Physics•Aug 28, 2020•9 citations

Universal one-dimensional atomic gases near odd-wave resonance

Xiaoling Cui

We show the renormalization of the contact interaction for odd-wave scattering in one-dimension (1D). Based on the renormalized interaction, we exactly solve the two-body problem in a harmonic trap and further explore the universal properties of spin-polarized fermions near odd-wave resonance by using the operator-product-expansion method. It is found that the high-momentum distribution behaves as $C/{k}^{2}$, with $C$ being the odd-wave contact. Various universal relations are derived. Our work suggests a universal system emergent in 1D with large odd-wave scattering length.

arXiv:1605.04363•Physical Review A•Oct 19, 2016•52 citations

Analytical solutions for two atoms in a harmonic trap: p -wave interactions

Zbigniew Idziaszek

We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in $p$ wave and confined in an axially symmetric harmonic trap. To this end we utilize $p$-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a $p$-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the $p$-wave Feshbach resonance.

arXiv:0902.2167•Physical Review A•Jun 4, 2009•30 citations
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 holelike branches at small momenta, and rotonlike minima. We find that the frequency of the "breathing" mode in the harmonic trap provides an unambiguous signature of the effective range.
Using the asymptotic Bethe ansatz, we study the stabilization problem of the one-dimensional spin-polarized Fermi gas confined in a hard-wall potential with a tunable ppp-wave scattering length and finite effective range. We find that the interplay of two factors, i.e., the finite interaction range and the hard-wall potential, will stabilize the system near resonance. The stabilization occurs even on the positive scattering length side, where the system undergoes a many-body collapse if any of the factors is absent. At ppp-wave resonance, the fermion system is found to feature ``quasiparticle condensation'' for any value of effective range, which is stabilized if the range is above twice the mean particle distance. Slightly away from resonance, the correction to the stability condition linearly depends on the inverse scattering length. Finally, a global picture is presented for the energetics and stability properties of fermions from the weakly attractive to deep bound-state regime. Our results raise the possibility of achieving stable ppp-wave superfluidity in quasi-one-dimensional (1D) atomic systems, and meanwhile shed light on the intriguing sss- and ppp-wave physics in 1D that violate the Bose-Fermi duality.
We theoretically investigate an ultracold spin-polarized atomic Fermi gas with resonant odd-channel (p(p(p-wave) interactions trapped in one-dimensional harmonic traps. We solve the Yang-Yang thermodynamic equations based on the exact Bethe ansatz solution, and predict the finite-temperature density profile and breathing mode frequency by using a local density approximation to take into account the harmonic trapping potential. The system features an exotic super fermionic Tonks-Girardeau (super-fTG) phase, due to the large effective range of the interatomic interactions. We explore the parameter space for such a fascinating super-fTG phase at finite temperature and provide smoking-gun signatures of its existence in both breathing mode frequencies and density profiles. Our results suggest that the super-fTG phase can be readily probed at temperatures of about 0.1TF0.1{T}_{F}0.1TF​, where TF{T}_{F}TF​ is the Fermi temperature. These results are to be confronted with future cold-atom experiments with 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K atoms.
An important tool for understanding the effects of interactions in harmonically trapped atomic gases is the examination of their collective modes. One such mode is the breathing or monopole mode, which is special as it is constrained to occur at twice the harmonic trapping frequency when the interactions are scale invariant. When the interactions are not scale invariant, the frequency of the breathing mode will deviate from twice the trap frequency. The deviation itself depends on the thermodynamic contacts, which describe how the energy changes with the interactions. In this work I examine how the thermodynamic contacts and the breathing-mode frequency of a spin-polarized one-dimensional (1D) ppp-wave Fermi gas depend on the 1D scattering volume $\ensuremath{\ell}$ and the effective range rrr in the high-temperature limit. Such dynamics can be studied in experiments and provide a tool for understanding how the dynamics depends on interactions with a finite effective range.
Abstract We propose a very accurate and efficient variational scheme for the ground state of the system of p-wave attractively interacting fermions confined in a one-dimensional harmonic trap. By the construction, the method takes the non-analytical part of interactions exactly into account and thus it approximates the true ground-state wave function in a whole range of interactions very accurately. Within the method, we determine different properties of the system for a different number of particles and different interactions. In this way, we explore how the system and its features transit from the ideal non-interacting Fermi gas to the system of infinitely strong attractions. Additionally, we demonstrate that the ansatz may also be used on a repulsive branch of interactions where other numerical methods break down. The presented method of including zero-range interactions is very universal and may be easily generalized to other one-dimensional confinements.
We show the renormalization of the contact interaction for odd-wave scattering in one-dimension (1D). Based on the renormalized interaction, we exactly solve the two-body problem in a harmonic trap and further explore the universal properties of spin-polarized fermions near odd-wave resonance by using the operator-product-expansion method. It is found that the high-momentum distribution behaves as C/k2C/{k}^{2}C/k2, with CCC being the odd-wave contact. Various universal relations are derived. Our work suggests a universal system emergent in 1D with large odd-wave scattering length.
We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in ppp wave and confined in an axially symmetric harmonic trap. To this end we utilize ppp-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a ppp-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the ppp-wave Feshbach resonance.