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Dynamical Response of an Interacting 1-Dimensional Fermi Gas

Tsung‐Lin Yang

Published May 10, 2018• 1 citation
OpenAlex

Abstract

Ultracold atoms with optical lattices provide a highly tunable system to measure the dynamic structure factor, $S(q,\omega)$, of an interacting one-dimensional (1D) Fermi gas. We use the two lowest hyperfine levels of the $^6$Li atom to form a pseudo-spin-1/2 system whose interactions are tunable via a Feshbach resonance. Bragg spectroscopy is used to measure the dynamic response of the 1D system to density (``charge'') mode excitations at a momentum $q$ and frequency $\omega$. In this thesis, we provide a quantitative comparison between the experimental result and the theoretical calculations based on Tomonaga-Luttinger theory.

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Ultracold atoms with optical lattices provide a highly tunable system to measure the dynamic structure factor, S(q,ω)S(q,\omega)S(q,ω), of an interacting one-dimensional (1D) Fermi gas. We use the two lowest hyperfine levels of the 6^66Li atom to form a pseudo-spin-1/2 system whose interactions are tunable via a Feshbach resonance. Bragg spectroscopy is used to measure the dynamic response of the 1D system to density (``charge'') mode excitations at a momentum qqq and frequency ω\omegaω. In this thesis, we provide a quantitative comparison between the experimental result and the theoretical calculations based on Tomonaga-Luttinger theory.
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.
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.
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.
Ultracold atoms confined to periodic potentials have proven to be a powerful tool for quantum simulation of complex many-body systems. We confine fermions to one dimension to realize the Tomonaga-Luttinger liquid model, which describes the highly collective nature of their low-energy excitations. We use Bragg spectroscopy to directly excite either the spin or charge waves for various strengths of repulsive interaction. We observe that the velocity of the spin and charge excitations shift in opposite directions with increasing interaction, a hallmark of spin-charge separation. The excitation spectra are in quantitative agreement with the exact solution of the Yang-Gaudin model and the Tomonaga-Luttinger liquid theory. Furthermore, we identify effects of nonlinear corrections to this theory that arise from band curvature and back-scattering.
Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a 87Rb^{87}\mathrm{Rb}87Rb condensate in a two-dimensional lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at T>0T>0T>0. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.
Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate-like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly-interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a 87^{87}87Rb condensate in a 2D lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at T>0T > 0T>0. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.