Phase Diagram for Ultracold Bosons in Optical Lattices and Superlattices

We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.Comment: 8 pages, 6 figures, submitted to Phys. Rev.

Dynamical density-matrix renormalization-group method

I present a density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems. The method is based on an exact variational principle for dynamical correlation functions and the excited states contributing to them. This dynamical DMRG is an alternate formulation of the correction vector DMRG but is both simpler and more accurate. The finite-size scaling of spectral functions is discussed and a method for analyzing the scaling of dense spectra is described. The key idea of the method is a size-dependent broadening of the spectrum.The dynamical DMRG and the finite-size scaling analysis are demonstrated on the optical conductivity of the one-dimensional Peierls-Hubbard model. Comparisons with analytical results show that the spectral functions of infinite systems can be reproduced almost exactly with these techniques. The optical conductivity of the Mott-Peierls insulator is investigated and it is shown that its spectrum is qualitatively different from the simple spectra observed in Peierls (band) insulators and one-dimensional Mott-Hubbard insulators.Comment: 16 pages (REVTEX 4.0), 10 figures (in 13 EPS files

Commensurate-incommensurate transition of cold atoms in an optical lattice

An atomic gas subject to a commensurate periodic potential generated by an optical lattice undergoes a superfluid--Mott insulator transition. Confining a strongly interacting gas to one dimension generates an instability where an arbitrary weak potential is sufficient to pin the atoms into the Mott state; here, we derive the corresponding phase diagram. The commensurate pinned state may be detected via its finite excitation gap and the Bragg peaks in the static structure factor.Comment: 4 pages, 2 figure

The Three-Magnon Contribution to the Spin Correlation Function in Integer-Spin Antiferromagnetic Chains

The exact form factor for the O(3) non-linear sigma model is used to predict the three-magnon contribution to the spin correlation function, S(q,w), near wavevector q=pi in an integer spin, one-dimensional antiferromagnet. The three-magnon contribution is extrememly broad and extremely weak; the integrated intensity is <2% of the single-magnon contribution.Comment: 4 pages, 1 figur

One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.Comment: 14 pages, 8 figure

Analysis of D Pellet Injection Experiments in the W7-AS Stellarator

A centrifugal injector was used to inject deuterium pellets (with 3--5 x 10{sup 19} atoms) at approx. equal 600 m/s into current-less, nearly shear-less plasmas in the Wendelstein 7-AS (W7-AS) stellarator. The D pellet was injected horizontally at a location where the non-circular and non-axisymmetric plasma cross section is nearly triangular. Visible-light TV pictures usually showed the pellet as a single ablating mass in the plasma, although the pellet occasionally broke in two or splintered into a cloud of small particles. The density evolution following pellet injection and the effect of pellet injection on energy confinement and fluctuations are discussed

Transport and Entanglement Generation in the Bose-Hubbard Model

We study entanglement generation via particle transport across a one-dimensional system described by the Bose-Hubbard Hamiltonian. We analyze how the competition between interactions and tunneling affects transport properties and the creation of entanglement in the occupation number basis. Alternatively, we propose to use spatially delocalized quantum bits, where a quantum bit is defined by the presence of a particle either in a site or in the adjacent one. Our results can serve as a guidance for future experiments to characterize entanglement of ultracold gases in one-dimensional optical lattices.Comment: 14 pages, 6 figure

Dynamical Correlation Functions using the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wavevectors using filter functions.Comment: minor revision, 10 pages, 15 figure

Fragmented superfluid due to frustration of cold atoms in optical lattices

A one dimensional optical lattice is considered where a second dimension is encoded in the internal states of the atoms giving effective ladder systems. Frustration is introduced by an additional optical lattice that induces tunneling of superposed atomic states. The effects of frustration range from the stabilization of the Mott insulator phase with ferromagnetic order, to the breakdown of superfluidity and the formation of a macroscopically fragmented phase.Comment: New version, more results, about 20 page