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Physical Review A

Entanglement of alkaline-earth-metal fermionic atoms confined in optical lattices

Jereson Silva-Valencia, André M. C. Souza

Published Mar 7, 2012• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.85.033612

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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.
We studied the ground state of alkaline-earth-metal atoms confined in one-dimensional optical lattices with an effective hybridization generated by a suitable laser field. This system is modeled by the periodic Anderson model plus a quadratic confining potential, and we adopted the density-matrix renormalization group to calculate its ground state. We found a one-to-one correspondence between the local variance, the local von Neumann entropy, and the on-site spin-spin correlation. For low global densities, we observed the formation of local singlets between delocalized and localized atoms and found Kondo spin-liquid domains that can be tuned with the confining potential, the hybridization, and the local repulsion. Band insulator, metallic, phase separation, and Kondo spin-liquid regions coexist in the ground state.
We study the ground-state properties of spin-1/2 fermionic atoms confined in a one-dimensional optical superlattice with harmonic confinement by using the density-matrix renormalization group method. For this purpose, we consider an ionic Hubbard model that has superlattice potentials with two-site periodicity. We find that several different types of insulating regimes coexist even if the number of atoms at each site is not an integer, but its average within the unit cell is an integer or half integer. This is contrasted to the coexisting phase of the metallic and Mott-insulating regimes known for the ordinary Hubbard model in an optical lattice. The phase characteristics are elucidated by investigating the profiles of the atom density, the local density (spin) fluctuations, the double occupation probability, and the spin correlations in detail.
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.
Using the White�s density matrix renormalization group, we study a strongly correlated system of fermions confined in an external potential. This system can be modelled by the one-dimensional Hubbard model with a quadratic confining potential. This model describe 6Li or 40K atoms trapped in an optical lattice, which has been studied experimentally and theoretically since the realization of Bose-Einstein condensation of alkali atoms. The fermion density profiles and their variance were computed. We observe coexistence of insulating and metallic regions in the system, this evidence a quantum critical behavior.