Mott Insulator Lobes Research Articles

Phase diagram and momentum distribution of an interacting Bose gas in a bichromatic lattice

We determine the phase diagram and the momentum distribution for a one-dimensional Bose gas with repulsive short-range interactions in the presence of a two-color lattice potential, with an incommensurate ratio among the respective wavelengths, by using a combined numerical (density matrix renormalization group) and analytical (bosonization) analysis. The system displays a delocalized (superfluid) phase at small values of the intensity of the secondary lattice ${\mathit{V}}_{2}$ and a localized (Bose-glasslike) phase at larger intensity ${\mathit{V}}_{2}$. We analyze the localization transition as a function of the height ${\mathit{V}}_{2}$ beyond the known limits of free and hard-core bosons. We find that weak repulsive interactions disfavor the localized phase, i.e., they increase the critical value of ${\mathit{V}}_{2}$ at which localization occurs. In the case of integer filling of the primary lattice, the phase diagram at fixed density displays, in addition to a transition from a superfluid to a Bose glass phase, a transition to a Mott-insulating state for not too large ${\mathit{V}}_{2}$ and large repulsion. We also analyze the emergence of a Bose-glass phase by looking at the evolution of the Mott-insulator lobes when increasing ${\mathit{V}}_{2}$. The Mott lobes shrink and disappear above a critical value of ${\mathit{V}}_{2}$. Finally, we characterize the superfluid phase by the momentum distribution, and show that it displays a power-law decay at small momenta typical of Luttinger liquids, with an exponent depending on the combined effect of the interactions and of the secondary lattice. In addition, we observe two side peaks that are due to the diffraction of the Bose gas by the second lattice. This latter feature could be observed in current experiments as characteristics of pseudo-random Bose systems.

Quantum phase transitions of light in the Dicke-Bose-Hubbard model

We extend the idea of quantum phase transitions of light in an atom-photon system with a Dicke-Bose-Hubbard model for an arbitrary number of two-level atoms. The formulations of eigenenergies, effective Rabi frequencies, and critical chemical potentials for two atoms are derived. With a self-consistent method, we obtain a complete phase diagram for two two-level atoms on resonance, which indicates the transition from Mott insulator to superfluidity and with a mean excitations diagram for confirmation. We illustrate the generality of the method by constructing the dressed-state basis for an arbitrary number of two-level atoms. In addition, we show that the Mott insulator lobes in the phase diagrams will smash out with the increase of atom numbers. The results of this work provide a step for studying the effects with combinations of Dicke-like and Hubbard-like models to simulate strongly correlated electron systems using photons.

Quantum phase transition in a multicomponent Bose-Einstein condensate in optical lattices

We present a general lattice model for a multicomponent atomic Bose-Einstein system in an optical lattice. Using the model, we analytically study the quantum phase transition between the Mott insulator and a superfluid. A mean-field theory is developed from the Mott-insulator ground state. When the interspecies interactions are strong enough, the Mott insulator demonstrates the phase separation behavior. For weak interspecies interactions, the multispecies system is miscible. Finally, the phase diagram is discussed with emphasis on the role of interspecies interactions. The tip and the shape of the Mott insulator lobes do not depend on the interspecies interactions, but the latter indeed modify the position of the phase boundaries.

Lattice boson systems with a finite maximum number of bosons in a site

We study a quantum spin-$S$ Heisenberg Hamiltonian which can describe a system of bosons hopping over the sites of a lattice with intrasite repulsion restricted to at most $N=2S$ bosons in a site. The phase diagram displays a series of $2S\ensuremath{-}1$ Mott-insulating lobes and a superfluid phase. In the limit $\stackrel{\ensuremath{\rightarrow}}{S}\ensuremath{\infty},$ the Hamiltonian reduces to the Bose-Hubbard Hamiltonian with an infinite number of lobes. The case $S=1,$ which possesses just one lobe, is studied in one dimension by the Lanczos method for chains of sizes up to 12 sites.

Response of Josephson-junction arrays near the quantum phase transition.

We study the superconductor-insulator transition of a two-dimensional Bose-Hubbard model, considering as a specific example, an array of Josephson junctions. Within a coarse-graining approach we derive an effective free-energy functional from which we determine the phase diagram. At zero temperature it consists of a superconducting phase and Mott-insulating lobes. The phase boundaries of some of these lobes display reentrant behavior as a function of temperature. Next, we evaluate the electromagnetic-response functions of the system. The real part of the longitudinal conductivity is characterized by an excitation gap, whereas the imaginary part describes a capacitor. In an ideal system, under certain conditions a universal conductance is found at the transition. If we add low-frequency dissipation to the model a different value of the universal conductance is found, but still it is independent of the strength of the dissipation. Qualitatively differing results are obtained for frustrated and unfrustrated systems. We also discuss the Hall conductance of the system.