Occupation number and fluctuations in the finite-temperature Bose-Hubbard model

We study the occupation numbers and number fluctuations of ultra-cold atoms in deep optical lattices for finite temperatures within the Bose-Hubbard model. Simple analytical expressions for the mean occupation number and number fluctuations are obtained in the weak-hopping regime using an interpolation between results from different perturbation approaches in the Mott-insulator and superfluid phases. These analytical results are compared to exact one dimensional numerical calculations using a finite temperature variant of the Density-Matrix Renormalisation Group (DMRG) method and found to have a high degree of accuracy. We also find very good agreement in the crossover ``thermal'' region. With the present approach the magnitude of number fluctuations under realistic experimental conditions can be estimated and the properties of the finite temperature phase diagram can be studied.Comment: 4 pages, 1 eps figure, submitted to PR

Quantum-field-theoretical techniques for stochastic representation of quantum problems

We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck equation and hence fail to produce a stochastic representation, the QFT techniques nevertheless yield stochastic difference equations in discretised time

Stochastic Simulation of a finite-temperature one-dimensional Bose-Gas: from Bogoliubov to Tonks-Girardeau regime

We present an ab initio stochastic method for calculating thermal properties of a trapped, 1D Bose-gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard-like Hamiltonian, whose imaginary time evolution is made computationally accessible by stochastic factorization of the kinetic energy. To achieve convergence for low enough temperatures such that quantum fluctuations are essential, the stochastic factorization is generalized to blocks, and ideas from density-matrix renormalization are employed. We compare our numerical results for density and first-order correlations with analytic predictions.Comment: 5 pages, 3 figures;text added;accepted in Physical Review

Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions

We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with non-randon, finite-range interactions. We show that the criticality of the system as well as validity or break-down of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bi-partite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strog evidence for the multi-dimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest neighbor coupling is analyzed.Comment: 4 pages, one figure, revised versio

Sagnac interferometry based on ultra-slow polaritons in cold atomic vapors

The advantages of light and matter-wave Sagnac interferometers -- large area on one hand and high rotational sensitivity per unit area on the other -- can be combined utilizing ultra-slow light in cold atomic gases. While a group-velocity reduction alone does not affect the Sagnac phase shift, the associated momentum transfer from light to atoms generates a coherent matter-wave component which gives rise to a substantially enhanced rotational signal. It is shown that matter-wave sensitivity in a large-area interferometer can be achieved if an optically dense vapor at sub-recoil temperatures is used. Already a noticeable enhancement of the Sagnac phase shift is possible however with much less cooling requirements.Comment: 4 pages, 3 figure

Discovery and characterizatopn of small molecular weight metallocarboxypeptidase inhibitors

Descripció del recurs: el 02 de novembre de 2010Las hidrolasas son enzimas que catalizan la ruptura del enlace amida o peptódico, y por lo tanto son denominadas también proteasas o peptidasas. Las proteasas constituyen cerca del 2 % del genoma humano, lo que representa unos 600 productos génicos. De acuerdo con el residuo catalóticamente activo, existen seis grandes grupos de peptidasas. En este trabajo nos centraremos en la familia M14 de peptidasas, también denominadas metalocarboxipeptidasas (CPs) debido a que su actividad catalótica reside en el ion zinc presente en el sitio activo de la enzima. En el genoma humano, se han identificado al menos 26 genes que codifican carboxipeptidasas. Las peptidasas de la familia M14 que actúan en el tracto gastrointestinal son las principales metaloproteasas responsables de la obtención de aminoácidos libres de la proteína de la dieta. En otros compartimientos corporales, las CPs pueden llevar a cabo tareas especializadas y altamente reguladas como ser la maduración de neuropéptidos, citokinas y hormonas peptódicas. En algunos casos, una actividad catalótica fuera de control puede conducir a enfermedades. Cada vez existe una mayor evidencia experimental que demuestra la actividad carboxipeptidasa en procesos como la pancreatitis aguda, la diabetes, la inflamación, la fibrinólisis y el cáncer. A pesar de ciertos avances en algunos aspectos, la actividad específica de las CPs es pobremente conocida. Además, las carboxipeptidasas son blancos terapéuticos interesantes para el desarrollo de fármacos, y por lo tanto se ha decidido emplear una aproximación multi-disciplinaria para la identificación y caracterización de nuevas moléculas de bajo peso molecular capaces de interferir la actividad carboxipeptidasa. Así, en este trabajo se han combinado modernas herramientas computacionales, screening in vitro, modelado molecular y cristalografía de rayos X con el fin de obtener nuevas entidades quφmicas como base para el desarrollo de fármacos. Con base en herramientas computacionales, aplicando el método de Optimal Docking Areaö, se han caracterizado sitios de unión proteína-proteína y proteína-ligando en la superficie de las peptidasas de la familia M14. A partir de aquí, se identificó una nueva clase de compuestos químicos capaces de explotar las diferencias existentes entre enzimas de la familia por unión a regiones hidrofóbicas. Otros inhibidores fueron identificados mediante un screening in silico de grandes colecciones de compuestos. Ensayos in vitro demostraron que los compuestos líderes inhibieron de manera potente a las carboxipeptidasas blanco con otras características interesantes como la posibilidad de coordinación del ion zinc catalítico por intermedio de un anillo oxadiazol. A través de una colaboración con el Departamento de Química Orgánica se obtuvieron y caracterizaron nuevos compuestos químicos con conectividades atómicas novedosas que, inesperadamente, demostraron ser potentes inhibidores de carboxipeptidasas. Una clase adicional de molécula de bajo peso molecular caracterizada corresponde a inhibidores que se unen covalentemente al enzima blanco. En este caso, se logró obtener la estructura tridimensional del complejo a resolución atómica mediante cristalografφa de rayos X, lo que ha permitido el dise±o basado en la estructura de una nueva generación de compuestos. Basados en otros datos de cristalografía de rayos X y análisis computacional, se ha revisado y ampliado el mecanismo de acción catalítica de las peptidasas de la familia M14 a partir de una nueva forma cristalina de CPB a alta resolución. En conjunto, nuestro trabajo ha permitido la obtención de nuevas moléculas líderes de bajo peso molecular que podrían servir como base para futuros desarrollos en el diseño de fármacos y agentes de diagnóstico o imaginería dirigidos a metalocarboxipeptidasas fisiológicamente activas.Hydrolases are enzymes catalyzing the breakdown of the amide or peptide bond, and are therefore called proteases or peptidases as well. In the human genome, proteases made up about 2% of the genome, or about 600 gene products. There are six major groups of peptidases according to the catalytic residue. In our work we focused on the M14 family of peptidases, also called metallocarboxypeptidases (CPs) because of their catalytic activity hinges on the zinc ion present in the active site of the enzyme. In the human genome there are identified at least 26 genes encoding for CPs. M14 peptidases in the gastrointestinal tract are the main metalloproteases responsible of the liberation of free aminoacids from the protein content of the diet. In other compartments of the body, CPs may perform specialized and tightly controlled tasks such as neuropeptide, cytokine and hormone maturation. In some instances an imbalance in their activity leads to disease states in man. Increasing evidence shows carboxypeptidase involvement in acute pancreatitis, diabetes, inflammation, fibrinolysis and cancer. Although some aspects have become clearer, much of their activity remain poorly understood. Besides, carboxypeptidases are interesting targets for drug development, and therefore we pursued a multidisciplinary approach to identify and characterize novel small molecular weight compounds able to interfere carboxypeptidase activity. In this work we combined modern computational tools, in vitro screening, molecular modelling and X-ray crystallography to obtain new chemical entities useful as scaffolds for drug design. Based on a bioinformatics tools, the Optimal Docking Area method, we identified protein-protein and protein-ligand binding sites over the surface of M14 peptidases. This knowledge was employed to find out a new class of small molecular weight inhibitors which exploit the differential binding provided by hydrophobic patches. A further class of inhibitors was identified from in silico screening of collections of compounds. In vitro analysis revealed that the leads were potent inhibitors against the target proteases with interesting features like an oxadiazole zinc-chelating moiety. Compounds obtained from the Organic Chemistry Department were also screened, and unexpectedly, afforded some good inhibitors with unprecedented atomic bonding. One further class involved inhibitors that attach covalently to the target enzyme. In this case the structure of the complex obtained at high resolution by X-ray crystallography allowed the structure-guided design of new generation of compounds. The catalytic mechanism of M14 peptidases was also revisited based on our crystallographic and computational analysis of a new CPB crystal form at high resolution. Overall, our study provided new lead small molecular weight inhibitors which can be the foundation for further developments in the design of drugs and bioimaging or diagnostic agents targeted to physiologically-relevant metallocarboxypeptidases

Quantum-theoretical treatments of three-photon processes

We perform and compare different analyses of triply degenerate four-wave mixing in the regime where three fields of the same frequency interact via a nonlinear medium with a field at three times the frequency. As the generalized Fokker-Planck equation (GFPE) for the positive-P function of this system contains third-order derivatives, there is no mapping onto genuine stochastic differential equations. Using techniques of quantum field theory, we are able to write stochastic difference equations that we may integrate numerically. We compare the results of this method with those obtained by the use of approximations based on semiclassical equations, and on truncation of the GFPE leading to stochastic differential equations. In the region where the difference equations converge, the stochastic methods agree for the field intensities, but give different predictions for the quantum statistics

Many-body effects on adiabatic passage through Feshbach resonances

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate alpha, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $Gamma\propto alpha$ is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law $Gamma\propto alpha^{1/3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.Comment: 9 pages, 9 figure

Nonlinear adiabatic passage from fermion atoms to boson molecules

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction $\Gamma$ on the sweep rate $\alpha$ varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number $N$. The power-law is linear, $\Gamma \propto \alpha$, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and $\Gamma \propto \alpha^{1/3}$ when it is larger. Experimental data agree better with a linear dependence than with an exponential Landau-Zener fit, indicating that many-body effects are significant in the atom-molecule conversion process.Comment: 5 pages, 4 figure