High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)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. 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)].

Tan’s contact of a harmonically trapped one-dimensional Bose gas: Strong-coupling expansion and conjectural approach at arbitrary interactions

“…This expression agrees with the zero order one obtained in [17] and with the one derived for a κ-component balanced spinful Fermi gas in [26] to order 2: in fact one may find the bosonic result by taking the limit of very large number of fermionic components κ → ∞ [36]. The weak-coupling expansion obtained from Section 3.3 reads:…”

“…Tan's contact of an interacting one-dimensional Bose gas under harmonic confinement has been first studied in reference [17], where a numerical solution based on the local-density approximation (LDA) of the homogeneous-system result has been provided. Analytically, again in the local-density approximation, a strong-coupling expansion has been derived to zeroth order [17], as well as corrections to first and second order [26]. A comparison with matrix-product state simulations has shown that the local-density approximation works surprisingly well [26], even for a small number of particles.…”

“…Analytically, again in the local-density approximation, a strong-coupling expansion has been derived to zeroth order [17], as well as corrections to first and second order [26]. A comparison with matrix-product state simulations has shown that the local-density approximation works surprisingly well [26], even for a small number of particles.…”

“…In order to determine Tan's contact of the harmonically-confined gas, we employ the density-functional approach developed in [26]. In detail, we define a functional E[ρ] of the density ρ(x) which, in the local-density approximation, reads…”

Connection between nonlocal one-body and local three-body correlations of the Lieb-Liniger model

“…Knowing more terms of the Taylor expansion of g 1 and n(p) also allows to probe in a finer way the validity of the Renormalization Group-Luttinger liquid approach by comparing their predictions at large distances or short momenta [10]. In the perspective of taking an harmonic trapping into account, it also allows to discuss the validity of the Local Density Approximation [18] by comparison with exact numerics [31]. To this aim, the equation of state from the 1/γ expansion is accurate in the strongly-interacting regime, while the conjecture thereby deduced is also accurate at intermediate γ [32].…”