# CQD special colloquium

### 14. February 2018 11:00

Konferenzraum 1, 00.101, Physikalisches Institut, INF 226### Strongly-correlated SU(N)-fermionic mixtures in one-dimensional harmonic traps

**J-Prof. Dr. Matteo Rizzi**

Johannes-Gutenberg-Universität Mainz

We consider a repulsively interacting multicomponent Fermi gas under harmonic confinement, as recently realized in the experiment of Pagano et al. [Nat. Phys. 10, 198 (2014)]. This setup realizes a gas with tunable $SU(N)$ symmetry. In this talk, we concentrate on the density- and momentum-distributions of particles in such a setup, and present results both for the strongly-interacting limit and for finite interactions.

A particular focus will be on the so-called Tan's contact - the weight of a $k^{-4}-scaling which is observed in the tails of momentum distributions of general contact-interacting systems.

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 N 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 an alternative route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques.

Departing from the exact solution in the infinitely-interacting regime, we then present an analytical scaling prediction for the Tan's contact at finite interactions with respect to the number of fermions, the number of components and the interaction strength and show its qualitative agreement with recent experiments. Along the way, we introduce the analytical (low density approximation, Bethe-ansatz) and numerical techniques (MPS/DMRG) used in the investigation.

Finally, we briefly discuss extensions of the previous approach to multi-component quantum mixtures (bosonic, fermionic, or both) and we show that the ground state of the system always displays the most symmetric spatial wave function allowed by the type of mixture.

References:

J. Decamp, J. Jünemann, M. Albert, M. Rizzi, A. Minguzzi, and P. Vignolo,

„High-momentum tails as magnetic structure probes for strongly-correlated SU(k) fermionic mixtures in one-dimensional traps”, PRA 94, 053614 (2016)

"Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations”, New J. Phys. 19 125001 (2017)