Analytical mean-field approach to the phase-diagram of ultracold bosons in optical superlattices

We report a multiple-site mean-field analysis of the zero-temperature phase diagram for ultracold bosons in realistic optical superlattices. The system of interacting bosons is described by a Bose-Hubbard model whose site-dependent parameters reflect the nontrivial periodicity of the optical superlattice. An analytic approach is formulated based on the analysis of the stability of a fixed-point of the map defined by the self-consistency condition inherent in the mean-field approximation. The experimentally relevant case of the period-2 one-dimensional superlattice is briefly discussed. In particular, it is shown that, for a special choice of the superlattice parameters, the half-filling insulator domain features an unusual loophole shape that the single-site mean-field approach fails to capture.Comment: 7 pages, 1 figur

Strong-coupling expansions for the topologically inhomogeneous Bose-Hubbard model

We consider a Bose-Hubbard model with an arbitrary hopping term and provide the boundary of the insulating phase thereof in terms of third-order strong coupling perturbative expansions for the ground state energy. In the general case two previously unreported terms occur, arising from triangular loops and hopping inhomogeneities, respectively. Quite interestingly the latter involves the entire spectrum of the hopping matrix rather than its maximal eigenpair, like the remaining perturbative terms. We also show that hopping inhomogeneities produce a first order correction in the local density of bosons. Our results apply to ultracold bosons trapped in confining potentials with arbitrary topology, including the realistic case of optical superlattices with uneven hopping amplitudes. Significant examples are provided. Furthermore, our results can be extented to magnetically tuned transitions in Josephson junction arrays.Comment: 5 pages, 2 figures,final versio

Cooperative Spectrum Sensing based on the Limiting Eigenvalue Ratio Distribution in Wishart Matrices

Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. Most of such techniques use the ratio between the largest and the smallest eigenvalues of the received signal covariance matrix to infer the presence or absence of the primary signal. The results derived so far in this field are based on asymptotical assumptions, due to the difficulties in characterizing the exact distribution of the eigenvalues ratio. By exploiting a recent result on the limiting distribution of the smallest eigenvalue in complex Wishart matrices, in this paper we derive an expression for the limiting eigenvalue ratio distribution, which turns out to be much more accurate than the previous approximations also in the non-asymptotical region. This result is then straightforwardly applied to calculate the decision threshold as a function of a target probability of false alarm. Numerical simulations show that the proposed detection rule provides a substantial performance improvement compared to the other eigenvalue-based algorithms.Comment: 7 pages, 2 figures, submitted to IEEE Communications Letter

On the Structure of the Bose-Einstein Condensate Ground State

We construct a macroscopic wave function that describes the Bose-Einstein condensate and weakly excited states, using the su(1,1) structure of the mean-field hamiltonian, and compare this state with the experimental values of second and third order correlation functions.Comment: 10 pages, 2 figure

Quantum signatures of self-trapping transition in attractive lattice bosons

We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice, and compare the relevant ground-state properties with those of the corresponding symmetry-breaking semiclassical nonlinear theory. The introduction of a suitable measure allows us to highlight many correspondences between the nonlinear theory and the inherently linear quantum theory, characterized by the well-known self-trapping phenomenon. In particular we demonstrate that the localization properties and bifurcation pattern of the semiclassical ground-state can be clearly recognized at the quantum level. Our analysis highlights a finite-number effect.Comment: 9 pages, 8 figure

Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping

The zero-temperature phase diagram for ultracold Bosons in a random 1D potential is obtained through a site-decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose-glass phase. The different phases -i.e. Mott insulator, superfluid, Bose-glass- are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes are related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.Comment: 7 pages, 6 figures. Submitted to Laser Physic

Strong-field tidal distortions of rotating black holes: III. Embeddings in hyperbolic 3-space

In previous work, we developed tools for quantifying the tidal distortion of a black hole's event horizon due to an orbiting companion. These tools use techniques which require large mass ratios (companion mass $\mu$ much smaller than black hole mass $M$), but can be used for arbitrary bound orbits, and for any black hole spin. We also showed how to visualize these distorted black holes by embedding their horizons in a global Euclidean 3-space, ${\mathbb{E}}^3$. Such visualizations illustrate interesting and important information about horizon dynamics. Unfortunately, we could not visualize black holes with spin parameter $a_* > \sqrt{3}/2 \approx 0.866$: such holes cannot be globally embedded into ${\mathbb{E}}^3$. In this paper, we overcome this difficulty by showing how to embed the horizons of tidally distorted Kerr black holes in a hyperbolic 3-space, ${\mathbb{H}}^3$. We use black hole perturbation theory to compute the Gaussian curvatures of tidally distorted event horizons, from which we build a two-dimensional metric of their distorted horizons. We develop a numerical method for embedding the tidally distorted horizons in ${\mathbb{H}}^3$. As an application, we give a sequence of embeddings into ${\mathbb{H}}^3$ of a tidally interacting black hole with spin $a_*=0.9999$. A small amplitude, high frequency oscillation seen in previous work shows up particularly clearly in these embeddings.Comment: 10 pages, 6 figure