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arXiv:0812.4381 · Journal of Physics Condensed Matter

Entanglement and the Mott insulator–superfluid phase transition in bosonic atom chains

R. J. Costa Farias, M. C. de Oliveira

Published Jun 2, 2010• 7 citations
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Abstract

We analyze the developing of bipartite and multipartite entanglement through the Mott insulator-superfluid quantum phase transition. Starting from a Mott insulator state, where a filling factor ν = N/M = 1 per lattice site is considered, we derive an expression for a completely connected graph configuration of bosons and show how bipartite and multipartite entanglement evolve through the phase transition predicted in previous works. We show how, in the transition, bipartite entanglement is distributed through the system respecting monogamous relations.

DOI
10.1088/0953-8984/22/24/245603

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We analyze the developing of bipartite and multipartite entanglement through the Mott insulator-superfluid quantum phase transition. Starting from a Mott insulator state, where a filling factor ν = N/M = 1 per lattice site is considered, we derive an expression for a completely connected graph configuration of bosons and show how bipartite and multipartite entanglement evolve through the phase transition predicted in previous works. We show how, in the transition, bipartite entanglement is distributed through the system respecting monogamous relations.
"We studied the one-dimensional Bose-Hubbard model, by means of the Density Matrix Renormalization Group (DMRG). The U parameter, which contains the Coulombian repulsion information, is fixed to U = 1 and it is performed a swept over the hopping parameter t. The entanglement is investigated by implementing the one-site, two-site and block von Neumann entropy looking for which of these measures give account of the quantum phase transition from Mott insulator to superfluid. The one-site and two-site entropy do not give information of the phase transition of the system. In contrast, the block entropy shows, in the Mott insulator phase a behavior that saturates rapidly to a finite value and in the superfluid phase shows a logarithmic behavior that agrees with the mean field theory. From the derivative of the block entropy average as a function of t we found the phase transition takes place at tc =0.15."
An optical lattice with cold trapped atoms represents a quantum system of fundamental importance as it enables the study of quantum many-body system in a controllable way. It is thus necessary to develop theoretical and experimental tools to explore quantum correlation in such systems to advance our understanding of many-body physics. While previous works have identified some profound aspects of quantum entanglement using e.g. entanglement entropy, there exists a critical demand to have an experimentally accessible tool to investigate many-body quantum entanglement in a broad context. We present an entanglement criterion characterizing collective entanglement in Boson lattice systems and enabling experimental observation readily. On applying our approach to the extended Bose-Hubbard model, we show that our criterion witnesses phase transitions such as Mott insulator--superfluid and Mott insulator--charge density wave transitions. Remarkably, it also makes it possible to detect multipartite entanglement among boson lattice sites in a rigorous sense. Our criterion can be experimentally tested via Raman scattering or time-of-flight methods, which are within the reach of current technology.
We study the quantum phase transition between superfluid and Mott-insulator states for ultracold bosons with two internal states forming two bands of an optical lattice. The two atomic states are resonantly coupled by a coherent field enclosed in a single cavity mode, which mediates transitions between the two bosonic particle modes via absorption or emission of cavity photons. As nonlocal atomic coherence can build up via photon assisted tunneling, this coupling shifts the transition to the Mott-insulator phase toward deeper lattice potentials and stronger on-site interaction. Varying the intra and interband on-site interactions leads to several different atomic phase configurations. There are even parameter regions, where a mean-field approach predicts concurrence of a Mott-insulator state in one band and a superfluid in the other band.
We study, using quantum Monte Carlo simulations, the bosonic Kondo-Hubbard model in a two-dimensional square lattice. We explore the phase diagram and analyze the mobility of particles and magnetic properties. At unit filling, the transition from a paramagnetic Mott insulator to a ferromagnetic superfluid appears continuous, contrary to what was predicted with mean field. For double occupation per site, both the Mott insulating and superfluid phases are ferromagnetic and the transition is still continuous. Multiband tight-binding Hamiltonians can be realized in optical lattice experiments, which offer not only the possibility of tuning the different energy scales over wide ranges, but also the option of loading the system with either fermionic or bosonic atoms.
The superfluid--Mott-insulator phase transition of dipolar bosons in optical lattice is analyzed. By using the Bogoliubov approach and decoupling approximation, the energy spectrum and zero-temperature phase diagram of dipolar bosonic atoms in an optical lattice are obtained analytically. The results show that in these systems the superfluid--Mott-insulator phase transition can be induced by tuning the dipole-dipole interaction and the position of the phase boundary can be moved when the on-site interaction is varied. Corresponding to a large on-site interaction, the dipole-dipole interaction is attractive near the critical point of the superfluid--Mott-insulator phase transition.
We study a bosonic ladder with two coupled chains using the finite-size density-matrix renormalization group method. We show that in a commensurate bosonic ladder the critical on-site interaction (UC)({U}_{C})(UC​) for the superfluid to Mott insulator transition gets larger as the interchain hopping $({t}_{\ensuremath{\perp}})$ increases. We analyze this quantum phase transition and obtain the phase diagram in the ${t}_{\ensuremath{\perp}}\ensuremath{-}U$ plane. We also consider the asymmetric case where the on-site interactions are different in the two chains and have shown that the system as a whole will not be in the Mott insulator phase unless both the chains have on-site interactions greater than the critical value.