Mutual information and Bose-Einstein condensation

In the present work we are studying a bosonic quantum field system at finite temperature, and at zero and non-zero chemical potential. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures the total amount of information of one of the parts about the other. In order to find it, we first derive the geometric entropy corresponding to the specific partition and then we substract its extensive part which coincides with the thermal entropy of the system. In the case of non-zero chemical potential, we examine the influence of the underlying Bose-Einstein condensation on the behavior of the mutual information, and we find that its thermal derivative possesses a finite discontinuity at exactly the critical temperature

Beyond Mean-Field Dynamics in Closed and Open Bosonic Systems

The present thesis is devoted to the dynamics in open or closed many-body bosonic systems, with the use of beyond mean-field methods. In the first part, inspired by the state-of-the-art experiments, we study the dynamics of a Bose-Einstein condensation which is loaded in an optical lattice with localized loss channels for the atoms. We prove that the particular form of the dissipation can help us to control the many-body dynamics. The loss allows the local manipulation of the system’s coherence properties and creates attractive fixed points in the classical (mean-field) phase space. We predict the dynamical creation of stable nonlinear structures like discrete bright and dark solitons. Furthermore, for specific initial states, the systems produces highly entangled and long-living states, which are of high relevance for practical applications. The first part of this thesis ends with the study of non-equilibrium bosonic transport across optical one-dimensional lattices. In the second part, we present techniques for bosonic many-body systems which are based on path integrals. We analyze the Bose-Einstein condensation phenomenon by using tools from quantum information theory and field theory. Finally, we introduce a coherent state path integral formalism in the continuum, which allows us the systematic development of approximate methods for the study of bosons in optical lattices

Beyond mean-field dynamics in closed and open bosonic systems

Η παρούσα διδακτορική διατριβή πραγματεύεται τη μελέτη της δυναμικής ανοικτών ή κλειστών μποζονικών συστημάτων πολλών σωμάτων, με τη χρήση μεθόδων πέραν της προσέγγισης μέσου πεδίου. Στο πρώτο μέρος, εμπνεόμαστε από τα πειράματα αιχμής και μελετάμε τη δυναμική ενός συμπυκνώματος Bose-Einstein παγιδευμένο σε ένα οπτικό πλέγμα που υπόκεινται σε εντοπισμένες απώλειες μεμονωμένων ατόμων. Αποδεικνύεται ότι οι συγκεκριμένου τύπου απώλειες μπορούν να μας βοηθήσουν να ελέγξουμε τη δυναμική πολλών σωμάτων, αφού επιτρέπουν τον τοπικό έλεγχο της συνεκτικότητας του συστήματος και δημιουργούν ελκτικά σημεία στον κλασσικό χώρο φάσεων. Χρησιμοποιούμαι αυτό το μηχανισμό για να δημιουργήσουμε εντοπισμένες μη γραμμικές δομές όπως φωτεινά και σκοτεινά διακριτά σολιτόνια. Επιπλέον, για συγκεκριμένες αρχικές καταστάσεις, το σύστημα παράγει εναγκαλισμένες μακρόβιες καταστάσεις, εξαιρετικής σημασίας για πρακτικές εφαρμογές. Το πρώτο μέρος τελειώνει με τη μελέτη της εκτός ισορροπίας μεταφοράς μποζονίων σε ένα οπτικό πλέγμα. Στο δεύτερο μέρος παρουσιάζουμε τεχνικές ολοκληρωμάτων διαδρομών που επιτρέπουν τη μελέτη μποζονικών συστημάτων. Αναλύουμε το φαινόμενο της συμπύκνωσης Bose-Einstein χρησιμοποιώντας εργαλεία από την κβαντική θεωρία πεδίου και τη θεωρία της κβαντικής πληροφορίας. Η εργασία καταλήγει με την εισαγωγή ενός φορμαλισμού ολοκληρωμάτων διαδρομών συνεκτικών καταστάσεων στο συνεχές που επιτρέπει τη συστηματική ανάπτυξη προσεγγιστικών μεθόδων για τη μελέτη μποζονίων παγιδευμένων σε οπτικά πλέγματαThe present thesis is devoted to the dynamics in open or closed many-body bosonic systems, with the use of beyond mean-field methods. In the first part, inspired by the state-of-the-art experiments, we study the dynamics of a Bose-Einstein condensation which is loaded in an optical lattice with localized loss channels for the atoms. We prove that the particular form of the dissipation can help us to control the many-body dynamics. The loss allows the local manipulation of the system's coherence properties and creates attractive fixed points in the classical (mean-field) phase space. We predict the dynamical creation of stable nonlinear structures like discrete bright and dark solitons. Furthermore, for specific initial states, the systems produces highly entangled and long-living states, which are of high relevance for practical applications. The first part of this thesis ends with the study of non-equilibrium bosonic transport across optical one-dimensional lattices. In the second part, we present techniques for bosonic many-body systems which are based on path integrals. We analyze the Bose-Einstein condensation phenomenon by using tools from quantum information theory and field theory. Finally, we introduce a coherent state path integral formalism in the continuum, which allows us the systematic development of approximate methods for the study of bosons in optical lattices

Mutual information and bose-einstein condensation

In this work we study an ideal bosonic quantum field system at finite temperature, and in a canonical and a grand canonical ensemble. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures the total amount of information of one of the parts about the other. In order to find it, we first derive the von Neumann entropy that corresponds to the spatially separated subsystem (i.e. the geometric entropy) and then we subtract its extensive part which coincides with the thermal entropy of the subsystem. In the framework of the grand canonical description, we examine the influence of the underlying Bose-Einstein condensation on the behaviour of the mutual information, and we find that its derivative with respect to the temperature possesses a finite discontinuity at exactly the critical temperature. © 2013 World Scientific Publishing Company