High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps

Abstract

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. {\bf 10}, 198 (2014)], realizing a gas with tunable $SU(\kappa )$ 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 $\kappa$ components of the gas and the Young tableaux for the $S_N$ permutation symmetry group identifying the magnetic structure of the ground-state. 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 in the limit of infinite interactions, we show that the contact 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. {\bf 10}, 198 (2014)].

13 pages, 6 figures

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• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• A one-dimensional liquid of fermions with tunable spin
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Ground-state properties of hard-core bosons confined on one-dimensional optical lattices
• Exact Diagonalization of Heisenberg SU(N) models
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Universal contact of strongly interacting fermions at finite temperatures
• Phase Separation in Mixtures of Repulsive Fermi Gases Driven by Mass Difference
• Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations
• Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension

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• Analytic thermodynamic properties of the Lieb-Liniger gas
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Thermal disruption of a Luttinger liquid
• Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• Many-body density and coherence of trapped cold bosons
• Full Counting Statistics of the momentum occupation numbers of the Tonks-Girardeau gas
• Variational ansatz for $p$-wave fermions confined in a one-dimensional harmonic trap
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• High-momentum oscillating tails of strongly interacting 1D gases in a box
• Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• Persistent currents in a strongly interacting multicomponent Bose gas on a ring
• Exact one-particle density matrix for SU($N$) fermionic matter-waves in the strong repulsive limit
• Statistical properties of the momentum occupation numbers of the Tonks-Girardeau gas in a harmonic trap
• Dynamical probing of high-order spin coherence in one-dimensional mixtures
• Persistent Current of SU(N) Fermions
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Necklace Ansatz for strongly repulsive spin mixtures on a ring
• Symmetry oscillations sensitivity to SU(2)-symmetry breaking in quantum mixtures