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arXiv:0912.4762 · Physical Review A

Probing the Kondo lattice model with alkaline-earth-metal atoms

Michael Foss‐Feig, Michael Hermele, Ana María Rey

Published May 7, 2010• 108 citations
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Abstract

We study transport properties of alkaline-earth-metal atoms governed by the Kondo lattice Hamiltonian plus a harmonic confining potential, and suggest simple dynamical probes of several different regimes of the phase diagram that can be implemented with current experimental techniques. In particular, we show how Kondo physics at strong coupling, at low density, and in the heavy fermion phase is manifest in the dipole oscillations of the conduction band upon displacement of the trap center.

DOI
10.1103/physreva.81.051603

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Real materials are extremely complicated, and any attempt to understand their bulk properties must begin with the appropriate choice of an idealized model, or Hamiltonian. There are many situations where such models have furnished a decisive understanding of complex quantum phenomena, such as BCS superconductivity and quantum magnetism. There are also cases, for instance the unconventional superconductivity of doped cuprates or heavy-fermion metals, where even the simplest conceivable models are intractable to current theoretical techniques. A promising route toward understanding the physics of such models is to simulate them directly with a highly controlled quantum system. Ultracold neutral atoms, polar molecules, and ions are in many ways ideally suited to this task.\nIn this thesis, we emphasize how the unique features of particular atomic and molecular sys- tems can be leveraged to access interesting physics in experimentally feasible temperature regimes. In chapter 3, we consider prospects for simulation of the Kondo lattice model using alkaline- earth atoms. In particular, we show how groundstate properties--for instance anomalous mass enhancement--can be probed by looking at far-from equilibrium dynamics, which are a standard diagnostic tool in ultracold atom experiments. Chapter 4 describes a realistic implementation of a bosonic version of the Kondo lattice model, and we show how the Kondo interaction qualitatively changes the superfluid to Mott insulator phase transition. Chapters 5, 6, and 7 are unified through an attempt to understand the effects of dissipation in many-body quantum systems. In chapter 5, our goal is mainly to understand the detrimental effects of two-body reactive collisions on dipolar molecules in a 3D optical lattice. Chapter 6 takes a rather different perspective, and shows that this type of loss naturally induces quantum correlations in the steady state of reactive fermionic molecules or alkaline earth atoms. In chapter 7, we develop an exact analytic solution for the non-equilibrium dynamics of long-ranged Ising models with Markovian decoherence. We apply our solution to the benchmarking of dynamics in an existing trapped-ion quantum simulator, which due to its large size and long-ranged, frustrated, interactions is well beyond the reach of a brute force numerical description.

Bulletin of the American Physical Society•Jan 1, 2012•0 citations
We study transport properties of alkaline-earth-metal atoms governed by the Kondo lattice Hamiltonian plus a harmonic confining potential, and suggest simple dynamical probes of several different regimes of the phase diagram that can be implemented with current experimental techniques. In particular, we show how Kondo physics at strong coupling, at low density, and in the heavy fermion phase is manifest in the dipole oscillations of the conduction band upon displacement of the trap center.
We employ a mean-field theory to study ground-state properties and transport of a two-dimensional gas of ultracold alkaline-earth-metal atoms governed by the Kondo lattice Hamiltonian plus a parabolic confining potential. In a homogenous system, this mean-field theory is believed to give a qualitatively correct description of heavy-fermion metals and Kondo insulators: It reproduces the Kondo-like scaling of the quasiparticle mass in the former and the same scaling of the excitation gap in the latter. In order to understand ground-state properties in a trap, we extend this mean-field theory via local-density approximation. We find that the Kondo insulator gap manifests as a shell structure in the trapped density profile. In addition, a strong signature of the large Fermi surface expected for heavy-fermion systems survives the confinement and could be probed in time-of-flight experiments. From a full self-consistent diagonalization of the mean-field theory, we are able to study dynamics in the trap. We find that the mass enhancement of quasiparticle excitations in the heavy-Fermi liquid phase manifests as slowing of the dipole oscillations that result from a sudden displacement of the trap center.
We calculate the entanglement of the ground state of alkaline-earth-metal fermionic atoms confined in one-dimensional optical lattices. This system can be described using the Kondo lattice model plus a harmonic confining potential, and we adopt the density-matrix renormalization group to study its ground state. We find that the local von Neumann entropy is constant in the insulating domains, and a one-to-one correspondence with the variance of the local density is observed. We show that the average entropy and its derivative are useful tools for identifying quantum transitions in impurity systems.
The periodic Anderson model (PAM), where local electron orbitals interplay with itinerant electronic carriers, plays an essential role in our understanding of heavy fermion materials. Motivated by recent proposals for simulating the Kondo lattice model (KLM) in terms of alkaline-earth metal atoms, we take another step toward the simulation of PAM, which includes the crucial charge/valence fluctuation of local f-electrons beyond purely low-energy spin fluctuation in the KLM. To realize PAM, a transition induced by a suitable laser between the electronic excited and ground state of alkaline-earth metal atoms (1 S 0⇌3 P 0) is introduced. This leads to effective hybridization between local electrons and conduction electrons in PAM. Generally, the SU(N) version of PAM can be realized by our proposal, which gives a unique opportunity to detect large-N physics without complexity in realistic materials. In the present work, high-temperature physical features of standard [SU(2)] PAM with harmonic trapping potential are analyzed by quantum Monte Carlo and dynamic mean-field theory, where the Mott/orbital-selective Mott state was found to coexist with metallic states. Indications for near-future experiments are provided. We expect our theoretical proposal and (hopefully) forthcoming experiments will deepen our understanding of heavy fermion systems. At the same time, we hope these will trigger further studies on related Mott physics, quantum criticality, and non-trivial topology in both the inhomogeneous and nonequilibrium realms.
We study the ground-state properties of the SU(NNN) generalization of the Kondo lattice model in one dimension when the Kondo coupling JK{J}_{\text{K}}JK​ (both ferromagnetic and antiferromagnetic) is sufficiently strong. Both cases can be realized using alkaline-earth-metal-like cold gases in optical lattices. Specifically, we first carry out the strong-coupling expansion and identify two insulating phases [one of which is the SU(NNN) analog of the well-known gapped Kondo singlet phase]. We then rigorously establish that the ground state in the low-density (for JK<0{J}_{\text{K}}<0JK​<0) or the high-density (for JK>0{J}_{\text{K}}>0JK​>0) region is ferromagnetic. The results are accounted for by generalizing the double-exchange mechanism to SU(NNN) ``spins.'' Possible realizations of Bose-Fermi supersymmetry SU(N∣1N|1N∣1) in the (generalized) SU(NNN) Kondo lattice model are discussed as well.
Real materials are extremely complicated, and any attempt to understand their bulk properties must begin with the appropriate choice of an idealized model, or Hamiltonian. There are many situations where such models have furnished a decisive understanding of complex quantum phenomena, such as BCS superconductivity and quantum magnetism. There are also cases, for instance the unconventional superconductivity of doped cuprates or heavy-fermion metals, where even the simplest conceivable models are intractable to current theoretical techniques. A promising route toward understanding the physics of such models is to simulate them directly with a highly controlled quantum system. Ultracold neutral atoms, polar molecules, and ions are in many ways ideally suited to this task.\nIn this thesis, we emphasize how the unique features of particular atomic and molecular sys- tems can be leveraged to access interesting physics in experimentally feasible temperature regimes. In chapter 3, we consider prospects for simulation of the Kondo lattice model using alkaline- earth atoms. In particular, we show how groundstate properties--for instance anomalous mass enhancement--can be probed by looking at far-from equilibrium dynamics, which are a standard diagnostic tool in ultracold atom experiments. Chapter 4 describes a realistic implementation of a bosonic version of the Kondo lattice model, and we show how the Kondo interaction qualitatively changes the superfluid to Mott insulator phase transition. Chapters 5, 6, and 7 are unified through an attempt to understand the effects of dissipation in many-body quantum systems. In chapter 5, our goal is mainly to understand the detrimental effects of two-body reactive collisions on dipolar molecules in a 3D optical lattice. Chapter 6 takes a rather different perspective, and shows that this type of loss naturally induces quantum correlations in the steady state of reactive fermionic molecules or alkaline earth atoms. In chapter 7, we develop an exact analytic solution for the non-equilibrium dynamics of long-ranged Ising models with Markovian decoherence. We apply our solution to the benchmarking of dynamics in an existing trapped-ion quantum simulator, which due to its large size and long-ranged, frustrated, interactions is well beyond the reach of a brute force numerical description.