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arXiv:1001.1918 · Physical Review A

Controlled hole doping of a Mott insulator of ultracold fermionic atoms

André Eckardt, Maciej Lewenstein

Published Jul 16, 2010• 17 citations
arXivHTMLPDF

Abstract

Considering a system of ultracold atoms in an optical lattice, we propose a simple and robust implementation of a quantum simulator for the homogeneous $t$-$J$ model with a well-controlled fraction of holes $x$. The proposed experiment can provide valuable insight into the physics of cuprate superconductors. A similar scheme applied to bosons, moreover, allows one to investigate experimentally the subtle role of inhomogeneity when a system passes from one quantum phase to another.

DOI
10.1103/physreva.82.011606

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Considering a system of ultracold atoms in an optical lattice, we propose a simple and robust implementation of a quantum simulator for the homogeneous ttt-JJJ model with a well-controlled fraction of holes xxx. The proposed experiment can provide valuable insight into the physics of cuprate superconductors. A similar scheme applied to bosons, moreover, allows one to investigate experimentally the subtle role of inhomogeneity when a system passes from one quantum phase to another.
The control of transport properties is a key tool at the basis of many technologically relevant effects in condensed matter. The clean and precisely controlled environment of ultracold atoms in optical lattices allows one to prepare simplified but instructive models, which can help to better understand the underlying physical mechanisms. Here we show that by tuning a structural deformation of the unit cell in a bipartite optical lattice, one can induce a phase transition from a superfluid into various Mott insulating phases forming a shell structure in the superimposed harmonic trap. The Mott shells are identified via characteristic features in the visibility of Bragg maxima in momentum spectra. The experimental findings are explained by Gutzwiller mean-field and quantum Monte Carlo calculations. Our system bears similarities with the loss of coherence in cuprate superconductors, known to be associated with the doping-induced buckling of the oxygen octahedra surrounding the copper sites.
The authors show that critical opalescence - enhanced density fluctuations at all length scales - occurs in quantum matter, specifically in a doped Mott-insulating system that can be realized with ultracold atoms in optical lattices. These findings provide a theoretical framework and new predictions for ultracold-atom experiments. Looking for critical opalescence across the doping-driven Mott transition in ultracold systems may give insights on the origin of the pseudogap in cuprate high-temperature superconductors.
Manipulation of ultracold atoms in optical lattices is one of the optimal ways to observe phase transitions of the Hubbard model which is useful in a variety of condensed-matter systems. Bosonic atoms in this model experience a phase transition from superfluids to Mott insulators by tuning systematic parameters. However, in conventional setups, phase transitions take place over a large range of parameters instead of one critical point due to the background inhomogeneity caused by the Gaussian shape of optical-lattice lasers. To probe the phase transition point more precisely in our lattice system, we apply a blue-detuned laser to compensate for this local Gaussian geometry. By inspecting the change of visibility, we find a sudden jump point at one particular trap depth of optical lattices, corresponding to the first appearance of Mott insulators in inhomogeneous systems. This provides a simple method to detect the phase transition point in such inhomogeneous systems. We believe it will be a useful tool for most cold atom experiments.
Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high- T c superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.
We present a scheme to implement a Fermi-Hubbard-like model in ultracold atoms in optical lattices and analyze the topological features of its ground state. In particular, we show that the ground state for appropriate parameters has a large overlap with a lattice version of the bosonic Laughlin state at filling factor one-half. The scheme utilizes laser assisted and normal tunneling in a checkerboard optical lattice. The requirements on temperature, interactions, and hopping strengths are similar to those needed to observe the N\'eel antiferromagnetic ordering in the standard Fermi-Hubbard model in the Mott insulating regime.
In recent years ultracold atoms in optical lattices have been extensively employed as quantum simulators to study the physics of conventional solid state systems. Due to the possibility of introducing controlled disorder, it appears now a straightforward progression to use ultracold atoms in optical potentials to also study the physics of complex systems. We experimentally study a system of bosonic 87Rb atoms in a 3D optical lattice, where disorder is introduced on the length scale of the lattice sites by using an auxiliary optical lattice with a non‐commensurate wavelength. Increasing the amount of disorder, we observe the transition from a Mott Insulator state to a novel gapless insulating phase induced by the cooperation of interactions and disorder, which could be identified with a Bose Glass phase. We discuss the experimental results as well as possible additional techniques for a better diagnostic of the system and future implementations of the two‐color lattices in the study of different disorder‐induced phenomena.