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arXiv:2512.08866

Low Energy Excitations of a 1D Fermi Gas with Attractive Interactions

Kafle, Aashish, Senaratne, Ruwan, Cavazos-Cavazos, Danyel, Cui, Hai-Ying, Thierry Giamarchi, Pu, Han, Guan, Xi-Wen, Randall G. Hulet

Published Dec 9, 2025• 0 citations
arXivHTMLPDF

Abstract

The low-energy excitations of a two-component repulsive Fermi gas confined to one dimension are linear dispersing spin- and charge-density waves whose respective propagation velocities depend on the strength and sign of their interaction. Quasi-1D fermions with attractive interaction realize the Luther-Emery liquid, which exhibits a rich array of phenomena, many of which are qualitatively different from those exhibited by their repulsive counterpart. We use a Feshbach resonance to access attractive interactions with $^6$Li atoms. We measured the spin and charge dynamic structure factors using Bragg spectroscopy and find that, contrary to repulsive interactions, the spin wave propagates faster than the charge density wave, thus producing an inversion of the classic spin-charge separation. We also find that a small spin polarization strongly suppresses the spin gap in the measured Bragg spectra. Evidence for pairing are a reduction in spin correlations with increasing attraction and RF spectra consistent with an atom/molecule mixture.

DOI
10.48550/arxiv.2512.08866

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The low-energy excitations of a two-component repulsive Fermi gas confined to one dimension are linear dispersing spin- and charge-density waves whose respective propagation velocities depend on the strength and sign of their interaction. Quasi-1D fermions with attractive interaction realize the Luther-Emery liquid, which exhibits a rich array of phenomena, many of which are qualitatively different from those exhibited by their repulsive counterpart. We use a Feshbach resonance to access attractive interactions with 6^66Li atoms. We measured the spin and charge dynamic structure factors using Bragg spectroscopy and find that, contrary to repulsive interactions, the spin wave propagates faster than the charge density wave, thus producing an inversion of the classic spin-charge separation. We also find that a small spin polarization strongly suppresses the spin gap in the measured Bragg spectra. Evidence for pairing are a reduction in spin correlations with increasing attraction and RF spectra consistent with an atom/molecule mixture.
Fermions in one dimension are vastly different from their higher-dimension counterparts. At the same time, many theoretical models in one dimension have the luxury of being integrable and exactly solvable, which makes them excellent test beds for quantum simulation. In using these test beds, we can understand and improve on the techniques of quantum simulation so that we move towards solving difficult problems that cannot be solved using other methods due to the sheer complexity of these systems. In this work, we prepare one-dimensional fermions using cold atom techniques and probe low-energy excitations in such systems. We do so using the technique of Bragg spectroscopy, which enables us to probe the dynamical structure factor of the system directly, which in turn tells us about the density-density and spin-density correlations in the system. Utilizing the extreme tunability of cold atom experiments, we can study different regimes of these 1D Fermi gases. In particular, moving on from our previous investigations in the repulsive interactions, we investigate the attractive interaction side, where the attraction of the fermions causes bound states to form. The binding energy of these bound states causes a gap in the spin excitation, a hallmark of a new class of model: Luther-Emery liquid. We investigate weakly attractive Fermi gases close to the Luther-Emery limit and observe an inversion of the spin-charge separation hierarchy compared to the repulsive side, confirming expectations from exact Bethe ansatz solutions for the homogeneous gas at zero temperature, in which weakly bound fermion pairs are predicted. The result presented here provides insight into physics in one dimension, an important realm that is well known to host many exciting physics and exotic phases.
One-dimensional (1D) interacting Fermi gases underpin a rich variety of quantum liquids, ranging from the Tomonaga-Luttinger liquid and the Fulde-Ferrell-Larkin-Ovchinnikov paired state to the Luther-Emery liquid (LEL). Notably, the LEL-characterized by gapless excitations in charge or spin degree of freedom and gapped excitations in the other-has long been theoretically predicted but has eluded definitive experimental observation to date. By exactly solving the attractive Yang-Gaudin model via the Bethe ansatz, we fully determine the low-energy excitation spectra for both spin and charge channels. For fully paired fermions, the spectrum features gapped spin excitation coexisting with gapless charge excitation. We further employ bosonization to derive analytical expressions for the dynamical structure factor (DSF) of the gapped spin excitation, which is a long-standing challenge in this study. In the trapped gas, we find that the spin Bragg spectroscopy peak occurs at a much higher frequency than the charge-mode peak, where the splitting frequency between these two peaks scales approximately linearly with the interaction strength. Crucially, the spin gap manifests as a sharp threshold in the spin DSF, below which spectral weight is completely absent, proving a direct and unambiguous spectroscopic fingerprint of the LEL. Our work establishes quasi-1D trapped attractive Fermi gases as a pristine experimental platform for the long-sought direct observation of the LEL.
Interacting fermions that are confined to 1D can only support collective excitations and are thus governed by the Tomonaga-Luttinger liquid (TLL) theory, in which collective excitations decouple into charge and spin modes instead of particle-like excitations. Over the course of this work we have realized analog quantum simulations of the TLL model using a 6-Li atomic system. By taking advantage of a magnetic Feshbach resonance we readily tune the interactions of the sample so that we can transition from a non-interacting gas to either a strongly repulsive or a strongly attractive system, and probe the dynamics of the system within these regimes. By using low-momentum Bragg spectroscopy we were able to measure and characterize the spin-charge separation of a TLL. Our work also presents the first observation of spin and charge density waves that are separately excited from the ground state through a Bragg perturbation. The observed dynamical response function of the spin and charge excitations remarkably captures both the universal behavior of the Tomonaga-Luttinger liquid, as well as the non-linear effects related to the band curvature effect in the charge sector and the back-scattering interaction effect in the spin sector. Up to now considering higher-order corrections to the linear dispersion in either the spin or charge degrees of freedom had remained out of reach for both theory and experiment. In addition to this, we also realized a spin-incoherent Luttinger liquid and characterized its temperature crossover between the coherent and incoherent regimes. On the attractive interactions regime we observe an inversion of spin-charge separation, and we also have seen preliminary signatures of confinement-induced 1D bound states.
At low temperature, collective excitations of one-dimensional (1D) interacting fermions exhibit spin-charge separation, a unique feature predicted by the Tomonaga-Luttinger liquid (TLL) theory, but a rigorous understanding remains challenging. Using the thermodynamic Bethe ansatz (TBA) formalism, we analytically derive universal properties of a 1D repulsive spin-1/2 Fermi gas with arbitrary interaction strength. We show how spin-charge separation emerges from the exact TBA formalism, and how it is disrupted by the interplay between the two degrees of freedom that brings us beyond the TLL paradigm. Based on the exact low-lying excitation spectra, we further evaluate the spin and charge dynamical structure factors (DSFs). The peaks of the DSFs exhibit distinguishable propagating velocities of spin and charge as functions of interaction strength, which can be observed by Bragg spectroscopy with ultracold atoms.
We present measurements of the dynamical structure factor S(q,ω) of an interacting one-dimensional Fermi gas for small excitation energies. We use the two lowest hyperfine levels of the ^{6}Li atom to form a pseudospin-1/2 system whose s-wave interactions are tunable via a Feshbach resonance. The atoms are confined to one dimension by a two-dimensional optical lattice. Bragg spectroscopy is used to measure a response of the gas to density ("charge") mode excitations at a momentum q and frequency ω, as a function of the interaction strength. The spectrum is obtained by varying ω, while the angle between two laser beams determines q, which is fixed to be less than the Fermi momentum k_{F}. The measurements agree well with Tomonaga-Luttinger theory.
The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.