Self-consistent Keldysh approach to quenches in weakly interacting Bose-Hubbard model

We present a non-equilibrium Green's functional approach to study the dynamics following a quench in weakly interacting Bose Hubbard model (BHM). The technique is based on the self-consistent solution of a set of equations which represents a particular case of the most general set of Hedin's equations for the interacting single-particle Green's function. We use the ladder approximation as a skeleton diagram for the two-particle scattering amplitude useful, through the self-energy in the Dyson equation, for finding the interacting single-particle Green's function. This scheme is then implemented numerically by a parallelized code. We exploit this approach to study the correlation propagation after a quench in the interaction parameter, for one (1D) and two (2D) dimensions. In particular, we show how our approach is able to recover the crossover from ballistic to diffusive regime by increasing the boson-boson interaction. Finally we also discuss the role of a thermal initial state on the dynamics both for 1D and 2D Bose Hubbard models, finding that surprisingly at high temperature a ballistic evolution is restored.Comment: 13 figure

Spreading of correlations and Loschmidt echo after quantum quenches of a Bose gas in the Aubry-Andr\'e potential

We study the spreading of density-density correlations and the Loschmidt echo, after different sudden quenches in an interacting one dimensional Bose gas on a lattice, also in the presence of a superimposed aperiodic potential. We use a time dependent Bogoliubov approach to calculate the evolution of the correlation functions and employ the linked cluster expansion to derive the Loschmidt echo.Comment: 10 pages, 14 figures, a section on momentum distribution function is include

Protein synthesis in Archaea. mechanism of dissociation from ribosomes of the conserved translation factor aIF6; development of an in vitro transcription/translation system from the thermophilic archaeon Sulfolobus solfataricus

This work describes two experimental studies performed for my doctoral thesis. The general subject is the analysis of the features and mechanisms of protein synthesis in extremely thermophilic Archaea. The subject is interesting and relevant from different points of view. Firstly, it has long been known that archaeal translation shares several features and components with the corresponding eukaryal process. Investigating the common themes between archaeal and eukaryal protein synthesis may help to shed light on the evolutionary origin thereof and to reconstruct the pathways whereby Eukarya emerged from the common tree of life. Secondly, extremely thermophilic Archaea have a lot of potential for biotechnological development, for instance as a source of thermostable enzymes to be used for both medical and industrial purposes. In the first part of my work, I shall describe a functional analysis of the archaeal translation factor aIF6, a protein shared by the Archaea and the Eukarya but not found in Bacteria. Although the eukaryal factor (eIF6) has been studied extensively, its function in translation is still imperfectly understood. It is established that it acts as a ribosome anti-association factor, binding to the large subunit and preventing its premature joining with the small subunit. To allow the 60S ribosome to enter the translation cycle, eIF6 must be actively released, a process that depends on the action of another factor, Sdo1/SBDS, which is also found in Archaea, and of a GTPase, EFL1, that instead does not have an archaeal homologue. In my work, I studied the mechanism of aIF6 release from archaeal large ribosomal subunits, using as the model organism the thermophilic archaeon Sulfolobus solfataricus. The results I obtained show that detachment of aIF6 from ribosomes requires the GTPase activity of elongation factor 2 (aEF2), while the Sdo1/SBDS homologue apparently inhibits rather than promoting aIF6 release. The function of archaeal Sdo1 remains therefore to be understood and must be studied further. In the second part of work, I developed a coupled in vitro transcription/translation system for cell-free protein synthesis from cell lysates of S. solfataricus. The essential element in this expression system is a strong promoter derivedfrom 16S/23S rRNA-encoding DNA promoter from the archaebacterium Sulfolobus sp. P2 that produces, with high efficiency, specific mRNAs. I show that this method permits the efficient synthesis in vitro at high temperature of biologically active proteins

Criticality, factorization and long-range correlations in the anisotropic XY-model

We study the long-range quantum correlations in the anisotropic XY-model. By first examining the thermodynamic limit we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Further, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.Comment: 8 pages, 8 figures. Close to published versio

Exact spectral function of a Tonks-Girardeau gas in a lattice

The single-particle spectral function of a strongly correlated system is an essential ingredient to describe its dynamics and transport properties. We develop a general method to calculate the exact spectral function of a strongly interacting one-dimensional Bose gas in the Tonks-Girardeau regime, valid for any type of confining potential, and apply it to bosons on a lattice to obtain the full spectral function, at all energy and momentum scales. We find that it displays three main singularity lines. The first two can be identified as the analogs of Lieb-I and Lieb-II modes of a uniform fluid; the third one, instead, is specifically due to the presence of the lattice. We show that the spectral function displays a power-law behaviour close to the Lieb-I and Lieb-II singularities, as predicted by the non-linear Luttinger liquid description, and obtain the exact exponents. In particular, the Lieb-II mode shows a divergence in the spectral function, differently from what happens in the dynamical structure factor, thus providing a route to probe it in experiments with ultracold atoms.Comment: 10 pages, 3 figure

Vortex entanglement in Bose-Einstein condensates coupled to Laguerre-Gauss beams

We study the establishment of vortex entanglement in remote and weakly interacting Bose Einstein condensates. We consider a two-mode photonic resource entangled in its orbital angular momentum (OAM) degree of freedom and, by exploiting the process of light-to-BEC OAM transfer, demonstrate that such entanglement can be efficiently passed to the matter-like systems. Our proposal thus represents a building block for novel low-dissipation and long-memory communication channels based on OAM. We discuss issues of practical realizability, stressing the feasibility of our scheme and present an operative technique for the indirect inference of the set vortex entanglement.Comment: 10 pages, 7 figures, RevTex

Decoherence in a fermion environment: Non-Markovianity and Orthogonality Catastrophe

We analyze the non-Markovian character of the dynamics of an open two-level atom interacting with a gas of ultra-cold fermions. In particular, we discuss the connection between the phenomena of orthogonality catastrophe and Fermi edge singularity occurring in such a kind of environment and the memory-keeping effects which are displayed in the time evolution of the open system