Abstract
Cold atom experiments can now realize mixtures where different components move in different spatial dimensions. We investigate a fermion mixture where one species is constrained to move along a one-dimensional lattice embedded in a two-dimensional lattice populated by another species of fermions, and where all bare interactions are contact interactions. By focusing on the one-dimensional fermions, we map this problem onto a model of fermions with non-local interactions on a chain. The effective interaction is mediated by the two-dimensional fermions and is both attractive and retarded, the form of which can be varied by changing the density of the two-dimensional fermions. By using the functional renormalization group in the weak-coupling and adiabatic limit, we show that the one-dimensional fermions can be controlled to be in various density-wave, or spin-singlet or triplet superconducting phases.
Highlights
Cold atom systems have proven to be an invaluable tool in studying a wide range of quantum many-body phenomena
When the interspecies interaction Uc f is weak or the 2D filling is very high, the total interaction is dominated by Uc, which leads to the spin-density waves (SDWs) instability
When the 2D fermions are half filled μ f = 0 or close to it, the mediated interaction is dominated by the q = π component, with |U (q = π )| > |U (q = 0)|, as shown in Fig. 2, and charge-density waves (CDWs) order becomes dominant
Summary
Cold atom systems have proven to be an invaluable tool in studying a wide range of quantum many-body phenomena. The complexity of cold atomic systems can be greatly enhanced by mixing different atoms. A degenerate Fermi gas immersed in a BEC can be realized with isotopes of Li atoms [8,9,10] or with different atomic species [11,12]. A two-species Fermi gas was first realized with Li and K atoms [13], and has been studied extensively [14,15,16]. The controllability of interspecies interactions permits these ultracold atomic mixtures to become valuable platforms to study novel many-body phenomena such as an impurity problem [17,18], polaron formation [19,20], or lattice gauge theories [21,22]
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