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arXiv:1907.09045 · Physical Review Letters

Simulating a Mott Insulator Using Attractive Interaction

Marcell Gall, C. F. Chan, Nicola Wurz, Michael Köhl

Published Jan 8, 2020• 14 citations
arXivHTMLPDF

Abstract

We study the particle-hole symmetry in the Hubbard model using ultracold fermionic atoms in an optical lattice. We demonstrate the mapping between charge and spin degrees of freedom and, in particular, show the occurrence of a state with "incompressible" magnetization for attractive interactions. Our results present a novel approach to quantum simulation by giving access to strongly correlated phases of matter through an experimental mapping to easier detectable observables.

DOI
10.1103/physrevlett.124.010403

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We study the particle-hole symmetry in the Hubbard model using ultracold fermionic atoms in an optical lattice. We demonstrate the mapping between charge and spin degrees of freedom and, in particular, show the occurrence of a state with "incompressible" magnetization for attractive interactions. Our results present a novel approach to quantum simulation by giving access to strongly correlated phases of matter through an experimental mapping to easier detectable observables.
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We review recent experimental and theoretical progress in realizing and simulating many-body phases of ultracold atoms in optical lattices, which gives access to analog quantum simulations of fundamental model Hamiltonians for strongly correlated condensed matter systems, such as the Hubbard model. After a general introduction to quantum gases in optical lattices, their preparation and cooling, and measurement techniques for relevant observables, we focus on several examples, where quantum simulations of this type have been performed successfully during the past years: Mott-insulator states, itinerant quantum magnetism, disorder-induced localization and its interplay with interactions, and topological quantum states in synthetic gauge fields.
We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely, a Mott insulator in the paramagnetic and antiferromagnetic phases, and a putative ddd-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultracold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We argue that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are easier to observe in the attractive Hubbard mode as a band insulator of Cooper pairs and superfluid phase, respectively. The putative ddd-wave superfluid phase of the repulsive Hubbard model doped away from half filling is related to a ddd-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to ``quantum simulate'' the Hubbard model in an optical lattice over the simulation of the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.
The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. We have realized this Hamiltonian in a repulsively interacting spin mixture of ultracold (40)K atoms in a three-dimensional (3D) optical lattice. Using in situ imaging and independent control of external confinement and lattice depth, we were able to directly measure the compressibility of the quantum gas in the trap. Together with a comparison to ab initio dynamical mean field theory calculations, we show how the system evolves for increasing confinement from a compressible dilute metal over a strongly interacting Fermi liquid into a band-insulating state. For strong interactions, we find evidence for an emergent incompressible Mott insulating phase. This demonstrates the potential to model interacting condensed-matter systems using ultracold fermionic atoms.
Based on the consideration of the system symmetry and its Hilbert space, we show that strongly interacting fermions near a wide Feshbach resonance in an optical lattice or superlattice can be generically described by a lattice resonance Hamiltonian. The latter can be mapped to a general Hubbard model with particle-assisted tunnelling rates. We investigate the model under population imbalance and show that the attractive and the repulsive models have the same complexity in the phase diagram under the particle-hole mapping. Using this mapping, we propose an experimental method to detect possible exotic superfluid/magnetic phases for this system.
"Based on the consideration of the system symmetry and its Hilbert space, we show that strongly interacting fermions near a wide Feshbach resonance in an optical lattice or superlattice can be generically described by a lattice resonance Hamiltonian. The latter can be mapped to a general Hubbard model with particle-assisted tunnelling rates. We investigate the model under population imbalance and show that the attractive and the repulsive models have the same complexity in the phase diagram under the particle-hole mapping. Using this mapping, we propose an experimental method to detect possible exotic superfluid/magnetic phases for this system."