Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model

We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e. the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point.We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.Comment: 7 pages, 5 figures (endfloats used due to problems with figures and latex. Sorry about that); final version, similar to the published on

Excitations of Bose-Einstein condensates in optical lattices

In this paper we examine the excitations observable in atoms confined in an optical lattice around the superfluid-insulator transition. We use increases in the number variance of atoms, subsequent to tilting the lattice as the primary diagnostic of excitations in the lattice. We show that this locally determined quantity should be a robust indicator of coherence changes in the atoms observed in recent experiments. This was found to hold for commensurate or non-commensurate fillings of the lattice, implying our results will hold for a wide range of physical cases. Our results are in good agreement with the quantitative factors of recent experiments. We do, howevers, find extra features in the excitation spectra. The variation of the spectra with the duration of the perturbation also turns out to be an interesting diagnostic of atom dynamics.Comment: 6 pages, 7 figures, using Revtex4; changes to version 2: new data and substantial revision of tex

Connecting the one-band and three-band Hubbard models of cuprates via spectroscopy and scattering experiments

The one-band and three-band Hubbard models which describe the electronic structure of cuprates indicate very different values of effective electronic parameters (EPs), such as the Cu on-site Coulomb energy and the Cu-O hybridization strength. In contrast, a comparison of EPs of several cuprates with corresponding values from spectroscopy and scattering experiments indicates similar values in the three-band model and cluster model calculations used to simulate experimental results. To explore this relation in detail, a Cu$_2$O cluster model calculation was carried out to obtain an expression for the Heisenberg exchange coupling $J$ between Cu sites using a downfolding method, taking into account Cu and O on-site correlations ($U_d$ and $U_p$), the charge-transfer energy $\Delta$ and the hopping $t$ between Cu and O sites. A quantitative analysis provides a consistent description of $J$ from neutron scattering experiments, using the three-band model and spectroscopic EPs. In addition, $J$ can be expressed in the one-band Hubbard model form with $\tilde{U}$ and $\tilde{t}$, which denote renormalized $U$ and $t$ using $\Delta$ and $U_p$, and their values indicate a large $\tilde{U}/\tilde{t}$, in agreement with reported values. The large $\tilde{U}/\tilde{t}$ arising from a combination of $U_d$, $U_p$ and $\Delta$ is thus hidden in the effective one-band Hubbard model. The ground-state singlet weights obtained from an exact diagonalization show the importance of the Cu-O Zhang-Rice singlet in the effective one-band Hubbard model. The results provide a consistent method to connect EPs obtained from spectroscopy and the three-band model with values of $J$ obtained from scattering experiments, band dispersion measurements and the effective one-band Hubbard model.Comment: 9 pages, 2 figures (submitted to Physical Review B

Oscillating Superfluidity of Bosons in Optical Lattices

We follow up on a recent suggestion by C. Orzel et. al., Science, 291, 2386 (2001), whereby bosons in an optical lattice would be subjected to a sudden parameter change from the Mott to the superfluid phase. We analyze the Bose Hubbard model with a modified coherent states path integral which can escribe - both - phases. The saddle point theory yields collective oscillations of the uniform superfluid order parameter. These would be seen in time resolved interference patterns made by the released gas. We calculate the collective oscillation's damping rate by phason pair emission. In two dimensions the overdamped region largely overlaps with the quantum critical region. Measurements of critical dynamics on the Mott side are proposed.Comment: 4 pages 1 eps figures; Final version as appears in PRL. Added discussion on spontaneous generation of vortice

Stress-Mediated cis-Element Transcription Factor Interactions Interconnecting Primary and Specialized Metabolism in planta

Plant specialized metabolites are being used worldwide as therapeutic agents against several diseases. Since the precursors for specialized metabolites come through primary metabolism, extensive investigations have been carried out to understand the detailed connection between primary and specialized metabolism at various levels. Stress regulates the expression of primary and specialized metabolism genes at the transcriptional level via transcription factors binding to specific cis-elements. The presence of varied cis-element signatures upstream to different stress-responsive genes and their transcription factor binding patterns provide a prospective molecular link among diverse metabolic pathways. The pattern of occurrence of these cis-elements (overrepresentation/common) decipher the mechanism of stress-responsive upregulation of downstream genes, simultaneously forming a molecular bridge between primary and specialized metabolisms. Though many studies have been conducted on the transcriptional regulation of stress-mediated primary or specialized metabolism genes, but not much data is available with regard to cis-element signatures and transcription factors that simultaneously modulate both pathway genes. Hence, our major focus would be to present a comprehensive analysis of the stress-mediated interconnection between primary and specialized metabolism genes via the interaction between different transcription factors and their corresponding cis-elements. In future, this study could be further utilized for the overexpression of the specific transcription factors that upregulate both primary and specialized metabolism, thereby simultaneously improving the yield and therapeutic content of plants

Resonant Superfluidity in an Optical Lattice

We study a system of ultracold fermionic Potassium (40K) atoms in a three-dimensional optical lattice in the vicinity of an s-wave Feshbach resonance. Close to resonance, the system is described by a multi-band Bose-Fermi Hubbard Hamiltonian. We derive an effective lowest-band Hamiltonian in which the effect of the higher bands is incorporated by a self-consistent mean-field approximation. The resulting model is solved by means of Generalized Dynamical Mean-Field Theory. In addition to the BEC/BCS crossover we find a phase transition to a fermionic Mott insulator at half filling, induced by the repulsive fermionic background scattering length. We also calculate the critical temperature of the BEC/BCS-state and find it to be minimal at resonance.Comment: 19 pages, 3 figure

Density wave and supersolid phases of correlated bosons in an optical lattice

Motivated by the recent experiment on the Bose-Einstein condensation of $^{52}$Cr atoms with long-range dipolar interactions (Werner J. et al., Phys. Rev. Lett., 94 (2005) 183201), we consider a system of bosons with repulsive nearest and next-nearest neighbor interactions in an optical lattice. The ground state phase diagram, calculated using the Gutzwiller ansatz, shows, apart from the superfluid (SF) and the Mott insulator (MI), two modulated phases, \textit{i.e.}, the charge density wave (CDW) and the supersolid (SS). Excitation spectra are also calculated which show a gap in the insulators, gapless, phonon mode in the superfluid and the supersolid, and a mode softening of superfluid excitations in the vicinity of the modulated phases. We discuss the possibility of observing these phases in cold dipolar atoms and propose experiments to detect them