Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides

Decamp, Jean; Armagnat, Pacome; Fang, Bess; Albert, Mathias; Minguzzi, Anna; Vignolo, Patrizia

doi:10.1088/1367-2630/18/5/055011

Cited by 40 publications

(65 citation statements)

References 41 publications

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“…Here we extend the results of [12] and show that each state of the many-body wave-function in Eq. (15) can be associated to a single Young Tableau, or equivalently a single symmetry, and that the ground state corresponds to the most symmetric configuration compatible with the imbalance.…”

Section: Symmetry Spectroscopysupporting

confidence: 81%

“…, φ N −1 are the eigenfunctions of the single particle Hamiltonian H (1p) j . We then write the full manybody wave-function as [10][11][12]:…”

Section: Symmetry Spectroscopymentioning

confidence: 99%

“…In the latter case, multi-component strongly interacting quantum particles, living in continuous space, appear to be a promising alternative to lattice systems where magnetic interaction parameters are hardly tunable [7]. Indeed, in the lowenergy regime, the κ internal degrees of freedom (interacting via highly-symmetric terms) can be mapped onto an effective SU (κ) spin chain subjected to a Sutherland Hamiltonian [8,9], which reduces to the most traditional SU (2) Heisenberg model in the case of two components [10][11][12]. Such systems are therefore currently at the focus of an intense experimental [7,13,14] and theoretical [15][16][17][18] activity.…”

Section: Introductionmentioning

confidence: 99%

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High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

et al. 2016

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A universal k −4 decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of Pagano et al. [Nat. Phys. 10, 198 (2014)], realizing a gas with tunable SU (κ) symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the κ components of the gas and the Young tableaux for the SN permutation symmetry group identifying the magnetic structure of the groundstate. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-states simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local density approximation (LDA) on the Bethe-Ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components and on interaction strength. Moreover, using a virial approach, we study the Tan's contact behaviour at large temperatures and in the limit of infinite interactions and we show that it increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in Ref. [Nat. Phys. 10, 198 (2014)].

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Section: Symmetry Spectroscopysupporting

confidence: 81%

“…, φ N −1 are the eigenfunctions of the single particle Hamiltonian H (1p) j . We then write the full manybody wave-function as [10][11][12]:…”

Section: Symmetry Spectroscopymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

et al. 2016

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“…Here we have used the wave function in the strongly interacting limit as described in Refs. [56,60,61]. Figure 2 further shows that the discrete-to-continuous mapping from Sect.…”

Section: Impurity Systemsmentioning

confidence: 90%

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

2017

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Abstract. Abstract is missing.e investigate one-dimensional harmonically trapped twocomponent systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between the interaction strength parameters from a continuous Hamiltonian and a discrete lattice Hamiltonian is derived. As an example, we show that this mapping does not depend neither on the state of the system nor on the number of particles. Energies, density profiles and correlation functions are obtained both numerically (DMRG and Exact diagonalization) and analytically. Since DMRG results do not converge as the interaction strength is increased, analytical solutions are used as a benchmark to identify the point where these calculations become unstable. We use the proposed mapping to set a quantitative limit on the interaction parameter of a discrete lattice Hamiltonian above which DMRG gives unrealistic results.

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“…The eigensolutions at the unitary limit H τ ∞ can be algebraically constructed from the eigensolutions of H τ 0 by restricting the particle permutation antisymmetric states (19b) to the domains X I and X II , also called the 'snippet' basis [42,43,49,50,61]:…”

Section: Fig 5 Potential Energy Of Hamiltonianmentioning

confidence: 99%

Infinite barriers and symmetries for a few trapped particles in one dimension

Harshman

2017

Phys. Rev. A

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This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are dependent on the specific shapes of the traps and the interactions, this article applies symmetry analysis to identify generic features in the spectrum of stationary states of few-particle, few-well systems. Extended attention is given to a simple but flexible threeparameter model of two particles in two wells in one dimension. A key insight is that two limiting cases, hard-core repulsion and no inter-well tunneling, can both be treated as emergent symmetries of the few-particle Hamiltonian. These symmetries are the mathematical consequences of infinite barriers in configuration space. They are necessary to explain the pattern of degeneracies in the energy spectrum, to understand how degeneracies are broken for models away from limiting cases, and to explain separability and integrability. These symmetry methods are extendable to more complicated models and the results have practical consequences for stable state control in fewparticle, few-well systems with ultracold atoms in optical traps.

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Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides

Cited by 40 publications

References 41 publications

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

Infinite barriers and symmetries for a few trapped particles in one dimension

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