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arXiv:2004.13387 · Physical Review Research

Effect of mediated interactions on a Hubbard chain in mixed-dimensional fermionic cold atoms

Junichi Okamoto, Wen-Min Huang, Kyle Irwin, David K Campbell, Shan-Wen Tsai

Published Jul 10, 2020• 0 citations
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Abstract

This work studies a one-dimensional Fermi gas embedded in a two-dimensional noninteracting Fermi gas. The authors demonstrate that various quantum phases emerge due to the mediated interaction among the one-dimensional gas, which can be controlled by varying the density of the two-dimensional Fermi gas.
DOI
10.1103/physrevresearch.2.033054

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The recent realization of mixed-dimensional systems of cold atoms has attracted much attention from both experimentalists and theorists. In this article we investigate a two-species Fermi atom mixture: one species of atom exists in two hyperfine states and is confined to move in a two-leg ladder, interacting with an on-site interaction, and the other moves freely in a two-dimensional square lattice that contains the two-leg ladder. The two species of atoms interact via an on-site interaction on the ladder. In the limit of weak interspecies interactions, the two-dimensional gas can be integrated out, leading to an effective long-range mediated interaction in the ladder, generated by the on-site interspecies interaction. We show that the form of the mediated interaction can be controlled by the density of the two-dimensional gas and that it enhances the charge-density wave instability in the two-leg ladder after the renormalization-group transformation. Parametrizing the phase diagram with various experimentally controllable quantities, we discuss the possible tuning of the macroscopic quantum many-body phases of the two-leg ladder in this mixed-dimensional fermionic cold atom system.
We investigate the quantum phases of mixed-dimensional cold atom mixtures. In particular, we consider a mixture of a Fermi gas in a two-dimensional lattice, interacting with a bulk Fermi gas or a Bose-Einstein condensate in a three-dimensional lattice. The effective interaction of the two-dimensional system mediated by the bulk system is determined. We perform a functional renormalization group analysis, and demonstrate that by tuning the properties of the bulk system, a subtle competition of several superconducting orders can be controlled among $s\ensuremath{-}\mathrm{wave}, p\ensuremath{-}\mathrm{wave}, {d}_{{x}^{2}\ensuremath{-}{y}^{2}}\ensuremath{-}\mathrm{wave}$, and ${g}_{xy({x}^{2}\ensuremath{-}{y}^{2})}\ensuremath{-}\mathrm{wave}$ pairing symmetries. Other instabilities such as a charge-density-wave order are also demonstrated to occur. In particular, we find that the critical temperature of the $d\ensuremath{-}\mathrm{wave}$ pairing induced by the next-nearest-neighbor interactions can be an order of magnitude larger than that of the same pairing induced by doping in the simple Hubbard model. We expect that by combining the nearest-neighbor interaction with the next-nearest-neighbor hopping (known to enhance $d\ensuremath{-}\mathrm{wave}$ pairing), an even higher critical temperature may be achieved.
Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a ^{87}Rb BEC to measure the interaction mediated by a ^{40}K DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of η=1.45±0.05^{stat}±0.13^{syst} in the presence of the DFG, providing clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a_{bf_{2}}-a_{bf_{1}}=-5.36±0.44^{stat}±1.43^{syst}a_{0} between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Côté, A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance. Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.
The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show in addition to bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a yet unreported phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as an effective fermion-mediated long-range interaction between bosons with alternating sign.
Recently, many experiments with cold atomic gases have been conducted from interest in the non-equilibrium dynamics of correlated quantum systems. Of these experiments, the mixing dynamics of fermion clusters motivates us to research cluster-cluster collision dynamics in one-dimensional Fermi systems. We adopt the one-dimensional Fermi-Hubbard model and apply the time-dependent density matrix renormalization group method. We simulate collisions between two fermion clusters of spin-up and spin-down and calculate reflectance of the clusters R changing the particle number in each cluster and the interaction strength between two fermions with up and down spins. We also evaluate the quasi-classical (independent collision) reflectance R qc to compare it with R . The quasi-classical picture is quantitatively valid in the limit of weak interaction, but it is not valid when interaction is strong.