Confinement Induced Molecules in a 1D Fermi Gas

Moritz, Henning; Stöferle, Thilo; Günter, Kenneth; Köhl, M.; Esslinger, Tilman

doi:10.1103/physrevlett.94.210401

Cited by 362 publications

(464 citation statements)

References 42 publications

(49 reference statements)

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“…The possibility to realize strongly interacting Fermi gases with tunable interactions in one dimension with ultracold gases in optical lattices [59,12] opens the chance to experimentally test the relations derived here. This is of particular interest since they apply even in situations that are still far from the ground state which is hard to reach in one dimension due to the typically long equilibration times.…”

Section: Resultsmentioning

confidence: 81%

Tan relations in one dimension

2011

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We derive exact relations that connect the universal C/k 4 -decay of the momentum distribution at large k with both thermodynamic properties and correlation functions of two-component Fermi gases in one dimension with contact interactions. The relations are analogous to those obtained by Tan in the three-dimensional case and are derived from an operator product expansion of the one-and two-particle density matrix. They extend earlier results by Olshanii and Dunjko [1] for the bosonic Lieb-Liniger gas. As an application, we calculate the pair distribution function at short distances and the dimensionless contact in the limit of infinite repulsion. The ground state energy approaches a universal constant in this limit, a behavior that also holds in the three-dimensional case. In both one and three dimensions, a Stoner instability to a saturated ferromagnet for repulsive fermions with zero range interactions is ruled out at any finite coupling.

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Section: Resultsmentioning

confidence: 81%

Tan relations in one dimension

2011

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“…Progress made in trapping ultracold atomic gases into different low-dimensional systems [1,2] has provided us grounds to describe and simulate the behavior of fascinating non-Fermi liquid in which the analysis may not be as tractable. The physical properties of such systems have attracted both experimental and theoretical interest.…”

Section: Introductionmentioning

confidence: 99%

Spin-density-functional theory for imbalanced interacting Fermi gases in highly elongated harmonic traps

Xianlong

Asgari

2008

Phys. Rev. A

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We numerically study imbalanced two component Fermi gases with attractive interactions in highly elongated harmonic traps. An accurate parametrization formula for the ground state energy is presented for a spin-polarized attractive Gaudin-Yang model. Our studies are based on an accurate microscopic spin-density-functional theory through the Kohn-Sham scheme which employs the onedimensional homogeneous Gaudin-Yang model with Luther-Emery-liquid ground-state correlation as a reference system. A Thomas-Fermi approximation is examined incorporating the exchangecorrelation interaction. By studying the charge and spin density profiles of the system based on these methods, we gain a quantitative understanding of the role of attractive interactions and polarization on the formation of the two-shell structure, with the coexisted Fulde-Ferrell-Larkin-Ovchinnikovtype phase in the center of the trap and either the BCS superfluid phase or the normal phase at the edges of the trap. Our results are in good agreement with the recent theoretical consequences.

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“…(52) reduces to the result obtained using degenerate perturbation theory. Equation (52) shows that the interplay between the s-wave interaction and the spin-orbit coupling term leads to an energy shift proportional to k so a ho . In the regime where the energy difference between states 1 and 2 is much greater than the coupling (C (2) qaa,qηaa k so a ho / √ 2 ≪ |∆|), we Taylor expand Eq.…”

Section: Arbitrary Atom-atom Scattering Length and Weak Spin-orbimentioning

confidence: 99%

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

Yin

Gopalakrishnan²,

Blume

2014

Phys. Rev. A

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The coupling between the spin degrees of freedom and the orbital angular momentum has a profound effect on the properties of nuclei, atoms and condensed matter systems. Recently, synthetic gauge fields have been realized experimentally in neutral cold atom systems, giving rise to a spin-orbit coupling term with "strength" kso. This paper investigates the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body s-wave interaction for cold atoms under external confinement. Specifically, we consider two different harmonically trapped two-atom systems. The first system consists of an atom with spin-orbit coupling that interacts with a structureless particle through a short-range two-body potential. The second system consists of two atoms that both feel the spin-orbit coupling term and that interact through a short-range two-body potential. Treating the spin-orbit term perturbatively, we determine the correction to the ground state energy for various generic parameter combinations. Selected excited states are also treated. An important aspect of our study is that the perturbative treatment is not limited to small s-wave scattering lengths but provides insights into the system behavior over a wide range of scattering lengths, including the strongly-interacting unitary regime. We find that the interplay between the spin-orbit coupling term and the s-wave interaction generically enters, depending on the exact parameter combinations of the s-wave scattering lengths, at order k 2 so or k 4 so for the ground state and leads to a shift of the energy of either sign. While the absence of a term proportional to kso follows straightforwardly from the functional form of the spin-orbit coupling term, the absence of a term proportional to k 2 so for certain parameter combinations is unexpected. The well-known fact that the spin-orbit coupling term couples the relative and center of mass degrees of freedom has interesting consequences for the trapped two-particle systems. For example, we find that the spin-orbit coupling term turns, for certain parameter combinations, sharp crossings into avoided crossings with an energy splitting proportional to kso. Our perturbative results are confirmed by numerical calculations that expand the eigenfunctions of the two-particle Hamiltonian in terms of basis functions that contain explicitly correlated Gaussians.

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Confinement Induced Molecules in a 1D Fermi Gas

Cited by 362 publications

References 42 publications

Tan relations in one dimension

Tan relations in one dimension

Spin-density-functional theory for imbalanced interacting Fermi gases in highly elongated harmonic traps

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

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