ETD

Archivio digitale delle tesi discusse presso l'Università di Pisa

Tesi etd-09012015-204712


Tipo di tesi
Tesi di laurea magistrale
Autore
CUSUMANO, STEFANO
URN
etd-09012015-204712
Titolo
Thermodynamics and correlations in quantum cascade systems
Dipartimento
FISICA
Corso di studi
FISICA
Relatori
relatore Prof. Giovannetti, Vittorio
Parole chiave
  • thermodynamics
  • quantum physics
  • cascade systems
  • open systems
  • correlations
Data inizio appello
23/09/2015
Consultabilità
Completa
Riassunto
Interest in quantum cascaded systems first arose in the 80’, when new exotic
forms of light, like squeezed light, were discovered. This led to a strong demand
for a new quantum formalism able to describe the evolution of a total system in
which one subsystem is driven with the light from another quantum subsystem
(e.g. two atoms). Gardiner and Collet [15] and Charmichael [6] first developed
the so-called input-output formalism which allowed to describe the evolution
of the system’s operator through Langevin’s equations, and moreover led to
a standard method to derive from these equations a master equation for the
density matrix. This formalism has been subsequently developed for various
case of interests [14, 16], up to become a well-based theory presented in books
[17].
In recent years the interest towards cascaded system has undergone a revival
due to important application in quantum information theory and many-body
physics. In general quantum cascaded systems are studied in the wider context
of quantum open systems: while in the past the noise from an external environ-
ment was seen only as a detrimental feature causing decoherence [37], nowadays
it is considered as a tool to control system’s evolution [29, 34] in order to obtain
states of interest, like entangled states [24, 33] or particular many-body states
[32, 35].
In this thesis a quantum cascaded system composed of bosonic subsystems
will be studied, mainly focusing on his thermodynamics and on the correlations
arising during the evolution.
Thermodynamics has been since its dawn in the 19th a quite difficult sub-
ject: it started as a purely phenomenological science, until the atomic theory
became popular. It was then that Boltzmann made a first attempt to derive
thermodynamics entirely from classical mechanics. Even if his theory clarified
some points of thermodynamics, nonetheless it was still unsatisfactory from a
foundational point of view, because it relied on unproven assumptions like the
ergodicity postulate or the a priori probabilities hypothesis. Many other sci-
entists tried to solve this problem, but none of them gave a fully satisfactory
answer.
With the emergence of quantum theory the old image of a gas as a set of
balls in a box started to seem just a sketch of reality, so that many efforts were
given to establish the theory of quantum thermodynamics [18]. On one side it
is necessary to reconcile quantum mechanics and classical thermodynamics [36,
38], while on the other side the main thermodynamical quantities like work,
heat and entropy have to be redefined in the quantum framework [2–4, 22, 25].
Concerning cascaded systems the interest in thermodynamics is due to the
peculiar features that heat flux showed in the case of a quantum system com-
posed by two subsystem, as analyzed in [26], so that it is interesting to know
what happens if there are more subsystems, if the features remain unchanged
or they are sensible to the number of subsystems. Moreover one asks if it would
be possible to engineer these systems in order to create heat cells able to release
energy slower, faster or in another desired way. Moreover it is interesting to see
if it is possible to create a heat interferometer with this kind of systems [19, 27].
The interest in correlations is mainly due the importance that they have
in several information theory protocols: it is well known that entanglement is
considered the main source for many quantum computation tasks [9, 10, 30],
and one of the most striking feature of quantum mechanics [37]. Many efforts
have been given all over the years to find methods for generating [24, 33, 35]
and distributing [5, 23] entangled states.
Moreover in recent years correlations have been analyzed in the new frame-
work of quantum discord [21, 31], a quantity that allows to measure all quantum
correlations of a state beyond entanglement. One of the most striking feature
of quantum discord is that while every entangled state has a non-null discord,
there exist non-entangled states also with non-zero discord [11, 13]. In recent
years several studies have been done to understand quantum discord [8, 12], to
define it operationally [7], to quantify it [28] and at least in some cases to find
closed formulas for its evaluation [1, 11, 20].
The first chapters of this thesis are focused on the basic arguments necessary
to understand the following chapters, such as open systems dynamics, cascaded
systems definition and Gaussian states. The last chapters are instead focused
on deriving and explaining all the results obtained about thermodynamics and
correlations. Here it is a detailed outline of the thesis.
In the second chapter a brief introduction about quantum mechanics and
open system dynamics is given. Dynamical semigroups and the concept of mas-
ter equation are introduced, together with the assumptions usually made in the
analysis of such systems.
The third chapter is focused on cascade systems, how they are defined and
which are the physical assumption made. The collisonal model used to find the
master equation is explained, and then the master equation is derived under
different physical assumptions.
Chapter four deals with Gaussian states and the formalism used to describe
them. The covariance matrix formalism is introduced and the dynamics of the
covariance matrix is derived through the master equation.
In the fifth chapter the thermodynamics of the system is analyzed, focusing
on the behaviour of the heat flux. First all the quantities used, such as heat
flux and transferred heat, are defined. Then, using the master equation, it is
studied how heat flux is affected by the system’s characteristics, like the number
of subsystems or their temperature.
Fynally in the sixth chapter correlations in the system are studied, observing
how they can arise during the transient dynamics. All the necessary formulas
to compute the amount of correlations in the system are explained and then
correlations dynamics is examined.

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