A system of two species of fermions of different mass confined in a one-dimensional harmonic trap is studied with an exact diagonalization approach. It is shown that a mass difference between fermionic species induces a separation in the density of the lighter flavour independently of the number of particles. The mechanism behind the emergent separation is explained phenomenologically and confirmed by direct studies of the ground state of the system. Finally, it is shown that the separation driven by a mass difference, in contrast to the separation induced by a difference of populations, is robust to the interactions with a thermal environment.

The ground-state properties of a few spin-1/2 fermions with different masses and interacting via short-range contact forces are studied within an exact diagonalization approach. It is shown that, depending on the shape of the external confinement, different scenarios of the spatial separation between components manifested by specific shapes of the density profiles can be obtained in the strong interaction limit. We find that the ground-state of the system undergoes a specific transition between orderings when the confinement is changed adiabatically from a uniform box to a harmonic oscillator shape. We study the properties of this transition in the framework of the finite-size scaling method adopted to few-body systems.

A system of a few attractively interacting fermionic 6 Li atoms in one-dimensional harmonic confinement is investigated. Non-trivial inter-particle correlations induced by interactions in a particleimbalanced system are studied in the framework of the noise correlation. In this way, it is shown that evident signatures of strongly correlated fermionic pairs in the Fulde-Ferrell-Larkin-Ovchinnikov state are present in the system and they can be detected by measurements directly accessible within state-of-the-art techniques. The results convincingly show that the exotic pairing mechanism is a very universal phenomenon and can be captured in systems being essentially non-uniform and far from the many-body limit.One of the cornerstones of our understanding of strongly correlated states of quantum matter is based on the theory of superconductivity by Bardeen, Cooper, and Schrieffer [1]. In this theory, the existence of the superconducting phase is explained following the fundamental observation by Cooper [2] that the ground-state energy of an attractively interacting system is significantly decreased by the collective formation of Cooper pairsnon-trivially correlated states of two fermions with exactly opposite momenta. Based on this idea of collective pairing, a plethora of other pairing mechanisms have been proposed and investigated [3][4][5]. One of the most influential extensions of the Cooper's idea comes from the observation that in the case of imbalanced systems, due to the mismatch of Fermi spheres of different components, the formation of correlated pairs forced by attractive mutual interactions is inseparably connected with resulting non-zero net momentum of the pair [6,7]. This unconventional pairing mechanism named after Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) has been extensively examined theoretically, mostly in the case of various solid-state systems like iron-based superconductors [8][9][10][11], heavy-fermion compounds [11][12][13][14][15], or organic conductors [16][17][18]. However, it is also viewed as one of the possible ways to understand fundamental properties of neutron stars [19][20][21], specific quantum chromodynamics models [22], or fermionic ultra-cold gases [23]. The latter example is of high importance since ultra-cold atomic systems, due to their tremendous tunability, are believed to be the best candidates for the first experimental observation of the FFLO state. Unfortunately, up to this day, the FFLO state is ephemeral and there are only indirect signs of this state of matter (see [24] for a recent review).In this Letter, we show that the many-body groundstate of a few 6 Li atoms confined in a harmonic trap (in the presence of mutual attractions) possesses many characteristic properties of the FFLO state which can be experimentally captured. For example, if one would com-0 1 2 3 4 0 1 2 3 4 q 0 [ℏ/µm] Δp F [ℏ/µm] FIG. 1. The most probable FFLO momentum q0 as a function of the Fermi momenta mismatch ∆pF. Different points correspond to different number of particles and differen...

Detailed analysis of the system of four interacting ultra-cold fermions confined in a onedimensional harmonic trap is performed. The analysis is done in the framework of a simple variational ansatz for the many-body ground state and its predictions are confronted with the results of numerically exact diagonalization of the many-body Hamiltonian. Short discussion on the role of the quantum statistics, i.e. Bose-Bose and Bose-Fermi mixtures is also presented. It is concluded that the variational ansatz, although seemed to be oversimplified, gives surprisingly good predictions of many different quantities for mixtures of equal as well as different mass systems. The result may have some experimental importance since it gives quite simple and validated method for describing experimental outputs. arXiv:1703.08720v2 [cond-mat.quant-gas]