We study the stability of a Bose-Fermi system loaded into an array of coupled one-dimensional (1D) ``tubes,'' where bosons and fermions experience different dimensions: Bosons are heavy and strongly localized in the 1D tubes, whereas fermions are light and can hop between the tubes. Using the ${}^{174}$ Yb- ${}^{6}$ Li system as a reference, we obtain the equilibrium phase diagram. We find that, for both attractive and repulsive interspecies interaction, the exact treatment of 1D bosons via the Bethe ansatz implies that the transitions between pure fermion and any phase with a finite density of bosons can only be first order and never continuous, resulting in phase separation in density space. In contrast, the order of the transition between the pure boson and the mixed phase can either be second or first order depending on whether fermions are allowed to hop between the tubes or they also are strictly confined in 1D. We discuss the implications of our findings for current experiments on ${}^{174}$ Yb- ${}^{6}$ Li mixtures as well as Fermi-Fermi mixtures of light and heavy atoms in a mixed-dimensional optical-lattice system.We study the stability of a Bose-Fermi system loaded into an array of coupled one-dimensional (1D) ``tubes,'' where bosons and fermions experience different dimensions: Bosons are heavy and strongly localized in the 1D tubes, whereas fermions are light and can hop between the tubes. Using the ${}^{174}$Yb-${}^{6}$Li system as a reference, we obtain the equilibrium phase diagram. We find that, for both attractive and repulsive interspecies interaction, the exact treatment of 1D bosons via the Bethe ansatz implies that the transitions between pure fermion and any phase with a finite density of bosons can only be first order and never continuous, resulting in phase separation in density space. In contrast, the order of the transition between the pure boson and the mixed phase can either be second or first order depending on whether fermions are allowed to hop between the tubes or they also are strictly confined in 1D. We discuss the implications of our findings for current experiments on ${}^{174}$Yb-${}^{6}$Li mixtures as well as Fermi-Fermi mixtures of light and heavy atoms in a mixed-dimensional optical-lattice system.

arXiv:1304.6303Physical Review ASep 3, 20133 citations

Interacting Mixtures of Bosons and Fermions in Optical Lattices

Sebastian Will, Thorsten Best, Simon G. Braun +3 more

Bulletin of the American Physical SocietyMar 17, 20090 citations

The Bose-Fermi Hubbard model in the light and heavy fermion limits

Alexander Mering, Dominik Muth, Michael Fleischhauer

We discuss mixtures of bosons and spin-polarized fermions in optical lattices in the limits of heavy and light fermions. The first case is mapped to a Bose-Hubbard system with binary disorder or a super-lattice potential. Boundaries between Mott-insulating and compressible phases are determined analytically within an extended strong-coupling expansion. DMRG calculations reveal furthermore a novel phase with Bose-glass character. In the opposite limit of ultra-light fermions an effective boson Hamiltonian is derived with an oscillatory long-range interactions leading to additional phases such as compressible density-waves. We show that CDW and Luttinger-liquid phase are separated by a Bose-glass phase.We discuss mixtures of bosons and spin-polarized fermions in optical lattices in the limits of heavy and light fermions. The first case is mapped to a Bose-Hubbard system with binary disorder or a super-lattice potential. Boundaries between Mott-insulating and compressible phases are determined analytically within an extended strong-coupling expansion. DMRG calculations reveal furthermore a novel phase with Bose-glass character. In the opposite limit of ultra-light fermions an effective boson Hamiltonian is derived with an oscillatory long-range interactions leading to additional phases such as compressible density-waves. We show that CDW and Luttinger-liquid phase are separated by a Bose-glass phase.

Bulletin of the American Physical SocietyMay 28, 20080 citations

The Bose-Fermi Hubbard model in the light and heavy fermion limits

Alexander Mering, Dominik Muth, Michael Fleischhauer

Quantum-Atom Optics Downunder (QAO)Jan 1, 20070 citations

Strongly interacting Bose–Fermi mixtures in 4−ϵ dimensions

V. Pastukhov

Annals of PhysicsJul 17, 20240 citations

{}^{174}

Yb-

{}^{6}

Li system as a reference, we obtain the equilibrium phase diagram. We find that, for both attractive and repulsive interspecies interaction, the exact treatment of 1D bosons via the Bethe ansatz implies that the transitions between pure fermion and any phase with a finite density of bosons can only be first order and never continuous, resulting in phase separation in density space. In contrast, the order of the transition between the pure boson and the mixed phase can either be second or first order depending on whether fermions are allowed to hop between the tubes or they also are strictly confined in 1D. We discuss the implications of our findings for current experiments on

{}^{174}

Yb-

{}^{6}

Li mixtures as well as Fermi-Fermi mixtures of light and heavy atoms in a mixed-dimensional optical-lattice system.