Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

Memory Effects in the Dynamics of Open Quantum Systems

In this Thesis various aspects of memory effects in the dynamics of open quantum systems are studied. We develop a general theoretical framework for open quantum systems beyond the Markov approximation which allows us to investigate different sources of memory effects and to develop methods for harnessing them in order to realise controllable open quantum systems. In the first part of the Thesis a characterisation of non-Markovian dynamics in terms of information flow is developed and applied to study different sources of memory effects. Namely, we study nonlocal memory effects which arise due to initial correlations between two local environments and further the memory effects induced by initial correlations between the open system and the environment. The last part focuses on describing two all-optical experiment in which through selective preparation of the initial environment states the information flow between the system and the environment can be controlled. In the first experiment the system is driven from the Markovian to the non- Markovian regime and the degree of non-Markovianity is determined. In the second experiment we observe the nonlocal nature of the memory effects and provide a novel method to experimentally quantify frequency correlations in photonic environments via polarisation measurements.

Non-Markovian dynamics in quantum optical dephasing channels

Quantum computation and quantum communication are two of the most promising future applications of quantum mechanics. Since the information carriers used in both of them are essentially open quantum systems it is necessary to understand both quantum information theory and the theory of open quantum systems in order to investigate realistic implementations of such quantum technologies. In this thesis we consider the theory of open quantum systems from a quantum information theory perspective. The thesis is divided into two parts: review of the literature and original research. In the review of literature we present some important definitions and known results of open quantum systems and quantum information theory. We present the definitions of trace distance, two channel capacities and superdense coding capacity and give a reasoning why they can be used to represent the transmission efficiency of a communication channel. We also show derivations of some properties useful to link completely positive and trace preserving maps to trace distance and channel capacities. With the help of these properties we construct three measures of non-Markovianity and explain why they detect non-Markovianity. In the original research part of the thesis we study the non-Markovian dynamics in an experimentally realized quantum optical set-up. For general one-qubit dephasing channels we calculate the explicit forms of the two channel capacities and the superdense coding capacity. For the general two-qubit dephasing channel with uncorrelated local noises we calculate the explicit forms of the quantum capacity and the mutual information of a four-letter encoding. By using the dynamics in the experimental implementation as a set of specific dephasing channels we also calculate and compare the measures in one- and two-qubit dephasing channels and study the options of manipulating the environment to achieve revivals and higher transmission rates in superdense coding protocol with dephasing noise. Kvanttilaskenta ja kvanttikommunikaatio ovat kaksi puhutuimmista tulevaisuuden kvanttimekaniikan käytännön sovelluksista. Koska molemmissa näistä informaatio koodataan systeemeihin, jotka ovat oleellisesti avoimia kvanttisysteemejä, sekä kvantti-informaatioteorian, että avointen kvanttisysteemien tuntemus on välttämätöntä. Tässä tutkielmassa käsittelemme avointen kvanttisysteemien teoriaa kvantti-informaatioteorian näkökulmasta. Tutkielma on jaettu kahteen osioon: kirjallisuuskatsaukseen ja omaan tutkimukseen. Kirjallisuuskatsauksessa esitämme joitakin avointen kvanttisysteemien ja kvantti-informaatioteorian tärkeitä määritelmiä ja tunnettuja tuloksia. Esitämme jälkietäisyyden, kahden kanavakapasiteetin ja superdense coding -kapasiteetin määritelmät ja esitämme perustelun sille, miksi niitä voidaan käyttää kuvaamaan kommunikointikanavan lähetystehokkuutta. Näytämme myös todistukset kahdelle ominaisuudelle, jotka liittävät täyspositiiviset ja jäljensäilyttävät kuvaukset jälkietäisyyteen ja kanavakapasiteetteihin. Näiden ominaisuuksien avulla konstruoimme kolme epä-Markovisuusmittaa ja perustelemme, miksi ne havaitsevat dynamiikan epä-Markovisuutta. Oman tutkimuksen osiossa tutkimme epä-Markovista dynamiikkaa kokeellisesti toteutetussa kvanttioptisessa mittausjärjestelyssä. Yleisen yhden qubitin dephasing-kanavan tapauksessa laskemme molempien kanavakapasiteettien ja superdense coding -kapasiteetin eksplisiittiset muodot. Yleisen kahden qubitin korreloimattomien ympäristöjen dephasing-kanavan tapauksessa laskemme yhteisen informaation lausekkeen nelikirjaimisessa koodauksessa ja kvanttikanavakapasiteetin. Käyttämällä kokeellisen mittajärjestelyn dynamiikkoja esimerkki dephasing-kanavina me myös laskemme konstruoitujen epä-Markovisuusmittojen arvot ja vertailemme niitä yksi- ja kaksi-qubitti-dephasing-kanavissa. Lisäksi käyttäen kokeellisia esimerkkikanavia tutkimme, kuinka ympäristöä manipuloimalla superdense coding –skeemassa voidaan saada yhteinen informaatio ajoittain kasvamaan tai saavuttaa kaikenkaikkiaan korkeampi lähetystehokkuus.

Nonlinear Dynamics of Multiple Quantum Well Lasers: Chaos and Multistability

This thesis presents analytical and numerical results from studies based on the multiple quantum well laser rate equation model. We address the problem of controlling chaos produced by direct modulation of laser diodes. We consider the delay feedback control methods for this purpose and study their performance using numerical simulation. Besides the control of chaos, control of other nonlinear effects such as quasiperiodicity and bistability using delay feedback methods are also investigated.A number of secure communication schemes based on synchronization of chaos semiconductor lasers have been successfully demonstrated theoretically and experimentally. The current investigations in these field include the study of practical issues on the implementations of such encryption schemes. We theoretically study the issues such as channel delay, phase mismatch and frequency detuning on the synchronization of chaos in directly modulated laser diodes. It would be helpful for designing and implementing chaotic encryption schemes using synchronization of chaos in modulated semiconductor lasers.

Electronic properties of liquid hydrogen fluoride: A sequential quantum mechanical/Born-Oppenheimer molecular dynamics approach

The electronic properties of liquid hydrogen fluoride (HF) were investigated by carrying out sequential quantum mechanics/Born-Oppenheimer molecular dynamics. The structure of the liquid is in good agreement with recent experimental information. Emphasis was placed on the analysis of polarisation effects, dynamic polarisability and electronic excitations in liquid HF. Our results indicate an increase in liquid phase of the dipole moment (similar to 0.5 D) and isotropic polarisability (5%) relative to their gas-phase values. Our best estimate for the first vertical excitation energy in liquid HF indicates a blue-shift of 0.4 +/- 0.2 eV relative to that of the gas-phase monomer (10.4 eV). (C) 2010 Elsevier B.V. All rights reserved.

A study of the relaxation dynamics in a quadrupolar NMR system using Quantum State Tomography

This article reports a relaxation study in an oriented system containing spin 3/2 nuclei using quantum state tomography (QST). The use of QST allowed evaluating the time evolution of all density matrix elements starting from several initial states. Using an appropriated treatment based on the Redfield theory, the relaxation rate of each density matrix element was measured and the reduced spectral densities that describe the system relaxation were determined. All the experimental data could be well described assuming pure quadrupolar relaxation and reduced spectral densities corresponding to a superposition of slow and fast motions. The data were also analyzed in the context of Quantum Information Processing, where the coherence loss of each qubit of the system was determined using the partial trace operation. (C) 2008 Elsevier Inc. All rights reserved.

Nonequilibrium dynamics of quantum fields

The nonequilibrium effective equation of motion for a scalar background field in a thermal bath is studied numerically. This equation emerges from a microscopic quantum field theory derivation and it is suitable to a Langevin simulation on the lattice. Results for both the symmetric and broken phases are presented.

Quantum discrete phase space dynamics and its continuous limit

The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.

Exact dynamics of single-qubit-gate fidelities under the measurement-based quantum computation scheme

Measurement-based quantum computation is an efficient model to perform universal computation. Nevertheless, theoretical questions have been raised, mainly with respect to realistic noise conditions. In order to shed some light on this issue, we evaluate the exact dynamics of some single-qubit-gate fidelities using the measurement-based quantum computation scheme when the qubits which are used as a resource interact with a common dephasing environment. We report a necessary condition for the fidelity dynamics of a general pure N-qubit state, interacting with this type of error channel, to present an oscillatory behavior, and we show that for the initial canonical cluster state, the fidelity oscillates as a function of time. This state fidelity oscillatory behavior brings significant variations to the values of the computational results of a generic gate acting on that state depending on the instants we choose to apply our set of projective measurements. As we shall see, considering some specific gates that are frequently found in the literature, the fast application of the set of projective measurements does not necessarily imply high gate fidelity, and likewise the slow application thereof does not necessarily imply low gate fidelity. Our condition for the occurrence of the fidelity oscillatory behavior shows that the oscillation presented by the cluster state is due exclusively to its initial geometry. Other states that can be used as resources for measurement-based quantum computation can present the same initial geometrical condition. Therefore, it is very important for the present scheme to know when the fidelity of a particular resource state will oscillate in time and, if this is the case, what are the best times to perform the measurements.

Quantum-Critical Spin Dynamics in Quasi-One-Dimensional Antiferromagnets

By means of nuclear spin-lattice relaxation rate T-1(-1), we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2-4SC(NH2)(2) and the spin-ladder system (C5H12N)(2)CuBr4. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, T-1(-1) exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T-1(-1), compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

Exact dynamics of single-qubit-gate fidelities under the measurement-based quantum computation scheme

Measurement-based quantum computation is an efficient model to perform universal computation. Nevertheless, theoretical questions have been raised, mainly with respect to realistic noise conditions. In order to shed some light on this issue, we evaluate the exact dynamics of some single-qubit-gate fidelities using the measurement-based quantum computation scheme when the qubits which are used as a resource interact with a common dephasing environment. We report a necessary condition for the fidelity dynamics of a general pure N-qubit state, interacting with this type of error channel, to present an oscillatory behavior, and we show that for the initial canonical cluster state, the fidelity oscillates as a function of time. This state fidelity oscillatory behavior brings significant variations to the values of the computational results of a generic gate acting on that state depending on the instants we choose to apply our set of projective measurements. As we shall see, considering some specific gates that are frequently found in the literature, the fast application of the set of projective measurements does not necessarily imply high gate fidelity, and likewise the slow application thereof does not necessarily imply low gate fidelity. Our condition for the occurrence of the fidelity oscillatory behavior shows that the oscillation presented by the cluster state is due exclusively to its initial geometry. Other states that can be used as resources for measurement-based quantum computation can present the same initial geometrical condition. Therefore, it is very important for the present scheme to know when the fidelity of a particular resource state will oscillate in time and, if this is the case, what are the best times to perform the measurements.

Quantum effects and dynamics in hydrogen-bonded systems: a first-principles approach to spectroscopic experiments

Computer simulations have become an important tool in physics. Especially systems in the solid state have been investigated extensively with the help of modern computational methods. This thesis focuses on the simulation of hydrogen-bonded systems, using quantum chemical methods combined with molecular dynamics (MD) simulations. MD simulations are carried out for investigating the energetics and structure of a system under conditions that include physical parameters such as temperature and pressure. Ab initio quantum chemical methods have proven to be capable of predicting spectroscopic quantities. The combination of these two features still represents a methodological challenge. Furthermore, conventional MD simulations consider the nuclei as classical particles. Not only motional effects, but also the quantum nature of the nuclei are expected to influence the properties of a molecular system. This work aims at a more realistic description of properties that are accessible via NMR experiments. With the help of the path integral formalism the quantum nature of the nuclei has been incorporated and its influence on the NMR parameters explored. The effect on both the NMR chemical shift and the Nuclear Quadrupole Coupling Constants (NQCC) is presented for intra- and intermolecular hydrogen bonds. The second part of this thesis presents the computation of electric field gradients within the Gaussian and Augmented Plane Waves (GAPW) framework, that allows for all-electron calculations in periodic systems. This recent development improves the accuracy of many calculations compared to the pseudopotential approximation, which treats the core electrons as part of an effective potential. In combination with MD simulations of water, the NMR longitudinal relaxation times for 17O and 2H have been obtained. The results show a considerable agreement with the experiment. Finally, an implementation of the calculation of the stress tensor into the quantum chemical program suite CP2K is presented. This enables MD simulations under constant pressure conditions, which is demonstrated with a series of liquid water simulations, that sheds light on the influence of the exchange-correlation functional used on the density of the simulated liquid.

Classical and quantum aspects of black hole dynamics

Il contenuto fisico della Relatività Generale è espresso dal Principio di Equivalenza, che sancisce l'equivalenza di geometria e gravitazione. La teoria predice l'esistenza dei buchi neri, i più semplici oggetti macroscopici esistenti in natura: essi sono infatti descritti da pochi parametri, le cui variazioni obbediscono a leggi analoghe a quelle della termodinamica. La termodinamica dei buchi neri è posta su basi solide dalla meccanica quantistica, mediante il fenomeno noto come radiazione di Hawking. Questi risultati gettano una luce su una possibile teoria quantistica della gravitazione, ma ad oggi una simile teoria è ancora lontana. In questa tesi ci proponiamo di studiare i buchi neri nei loro aspetti sia classici che quantistici. I primi due capitoli sono dedicati all'esposizione dei principali risultati raggiunti in ambito teorico: in particolare ci soffermeremo sui singularity theorems, le leggi della meccanica dei buchi neri e la radiazione di Hawking. Il terzo capitolo, che estende la discussione sulle singolarità, espone la teoria dei buchi neri non singolari, pensati come un modello effettivo di rimozione delle singolarità. Infine il quarto capitolo esplora le ulteriori conseguenze della meccanica quantistica sulla dinamica dei buchi neri, mediante l'uso della nozione di entropia di entanglement.

Structure and thermodynamics of H3O+(H2O)8 clusters: A combined molecular dynamics and quantum mechanics approach

We have studied the structure and stability of (H3O+)(H2O)8 clusters using a combination of molecular dynamics sampling and high-level ab initio calculations. 20 distinct oxygen frameworks are found within 2 kcal/mol of the electronic or standard Gibbs free energy minimum. The impact of quantum zero-point vibrational corrections on the relative stability of these isomers is quite significant. The box-like isomers are favored in terms of electronic energy, but with the inclusion of zero-point vibrational corrections and entropic effects tree-like isomers are favored at higher temperatures. Under conditions from 0 to 298.15 K, the global minimum is predicted to be a tree-like structure with one dangling singly coordinated water molecule. Above 298.15 K, higher entropy tree-like isomers with two or more singly coordinated water molecules are favored. These assignments are generally consistent with experimental IR spectra of (H3O+)(H2O)8 obtained at 150 K.

Real-time dynamics of open quantum spin systems driven by dissipative processes

We study the real-time evolution of large open quantum spin systems in two spatial dimensions, whose dynamics is entirely driven by a dissipative coupling to the environment. We consider different dissipative processes and investigate the real-time evolution from an ordered phase of the Heisenberg or XY model towards a disordered phase at late times, disregarding unitary Hamiltonian dynamics. The corresponding Kossakowski-Lindblad equation is solved via an efficient cluster algorithm. We find that the symmetry of the dissipative process determines the time scales, which govern the approach towards a new equilibrium phase at late times. Most notably, we find a slow equilibration if the dissipative process conserves any of the magnetization Fourier modes. In these cases, the dynamics can be interpreted as a diffusion process of the conserved quantity.