The physics of open quantum systems, and therefore the phenomenon of decoherence, has become important in many branches of research. Within this thesis, we investigate the system--environment interaction in the context of different problems. The influence of decoherence is ubiquitous and, due to the scale independence of quantum theory, not limited to microscopic systems. One of the great open problems in theoretical physics is the appearance of a cosmological constant which differs by many orders of magnitude from the theoretical predicted value. In the first part of this thesis we will address this question within the framework of quantum mechanics. The considerations are based on a quantum mechanical model which explains the value of the cosmological constant without introducing extremely small numbers. Decoherence, based on the uncontrollable entanglement with the environment, can explain the localization of the vacuum energy to the classical observed value. The model mentioned above allows, in principle, the tunneling into a universe with a different vacuum energy. We investigate the modification of the tunneling rate due to dissipative effects which follow from the system--bath interaction. Closely related to the cosmological constant problem and subject of the second part of this thesis is the spontaneous decay of a quantum field vacuum. Using a semiclassical approximation it is possible to investigate this process within the framework of the path integral formalism. We discuss the quantum--to--classical transition of the spontaneously nucleated vacuum bubbles. Furthermore, we investigate the dependence of the decay rate on the space-time backgrounds. The third part of this thesis is dedicated to the interaction between quantum systems and their environment in a different context. We investigate the generation of entanglement between two systems which are interacting indirectly with each other through the coupling to a heat bath. The interaction--induced entanglement will be destroyed rapidly through decoherence and dissipation. We will show that it is possible to generate a significant amount of entanglement by imposing certain boundary conditions to the bath. Furthermore, the dependence of the entanglement generation on the spatial separation of the systems will be analyzed. Specifically we will examine the bathinduced entanglement of oscillators and spins.
The physics of open quantum systems, and therefore the phenomenon of decoherence, has become important in many branches of research. Within this thesis, we investigate the system--environment interaction in the context of different problems. The influence of decoherence is ubiquitous and, due to the scale independence of quantum theory, not limited to microscopic systems. One of the great open problems in theoretical physics is the appearance of a cosmological constant which differs by many orders of magnitude from the theoretical predicted value. In the first part of this thesis we will address this question within the framework of quantum mechanics. The considerations are based on a quantum mechanical model which explains the value of the cosmological constant without introducing extremely small numbers. Decoherence, based on the uncontrollable entanglement with the environment, can explain the localization of the vacuum energy to the classical observed value. The model mentioned above allows, in principle, the tunneling into a universe with a different vacuum energy. We investigate the modification of the tunneling rate due to dissipative effects which follow from the system--bath interaction. Closely related to the cosmological constant problem and subject of the second part of this thesis is the spontaneous decay of a quantum field vacuum. Using a semiclassical approximation it is possible to investigate this process within the framework of the path integral formalism. We discuss the quantum--to--classical transition of the spontaneously nucleated vacuum bubbles. Furthermore, we investigate the dependence of the decay rate on the space-time backgrounds. The third part of this thesis is dedicated to the interaction between quantum systems and their environment in a different context. We investigate the generation of entanglement between two systems which are interacting indirectly with each other through the coupling to a heat bath. The interaction--induced entanglement will be destroyed rapidly through decoherence and dissipation. We will show that it is possible to generate a significant amount of entanglement by imposing certain boundary conditions to the bath. Furthermore, the dependence of the entanglement generation on the spatial separation of the systems will be analyzed. Specifically we will examine the bathinduced entanglement of oscillators and spins.
We study, within a toy model, how a thermal bath of cosmological perturbations can decohere the minisuperspace degrees of freedom of the universe, treating the perturbations as an environment in the framework of open quantum systems. Instead of tracing out the perturbations from a semiclassical ansatz for the total wave function, as in earlier approaches, we incorporate their backreaction on the background through an effective second-order coupling and derive a master equation. The model describes a spatially flat semiclassical universe during slow-roll inflation with a dust clock field, while scalar cosmological perturbations in a phenomenologically assumed thermal state constitute the environment. The master equation is non-Markovian, since the bath correlation functions do not decay in time. Within this framework, we find that, for a representative set of parameter estimates, the characteristic decoherence timescale corresponding to the thermal contribution can be shorter than the Hubble timescale. In addition, we address the question of whether the pointer-state structure induced by the decoherence in such a framework could provide a criterion for the choice of semiclassical states in quantum cosmology.
In this Thesis we study the quantum to classical transition process in the context of quantum mechanics and quantum field theory. We shall analyze the effects that general environments, namely ohmic and non-ohmic, at zero and high temperature induce over a quantum Brownian particle. We state that the evolution of the system can be summarized in terms of two main environmental induced physical phenomena: decoherence and energy activation. In this Thesis, we shall show that the latter is a post-decoherence phenomenon. As the energy is an observable, the excitation process can be consider a direct indicator of the system-environment entanglement particularly useful at zero temperature. From other point of view, we shall study different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and for neutral particles with permanent dipole moments. In this context, we shall show that the interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. In this context, we shall apply our results to a real matter wave interferometry experiment. We shall also show under which general conditions the geometry phase of a quantum open system can be observed.Finally, we shall study the decoherence process during a quantum phase transition. In this framework, we shall show that it can be phrased easily in terms of the decoherence functional, without having to use the master equation. To demonstrate this, we shall consider the decohering effects due to the displacement of domain boundaries, with implications for the displacement of defects, in general. We shall see that decoherence arises so quickly in this event, that it is negligible in comparison to decoherence due to field fluctuations in the way defined in previous papers.
For the realistic theoretical descriptions of quantum devices, we have to take the unavoidable coupling to their surrounding environment into account. A lot of effort in theoretical physics has been made to describe decoherence effects and the corresponding quantum to classical transition in the past. In these studies, baths are coupled to certain observables making their behavior more classical. In the most general case, a quantum device is affected by environments coupled to different observables. In this thesis, we study the differences emerging from coupling the bath to different observables. In particular, we investigate the situation, where two baths are coupled simultaneously to two conjugate variables (e.g. xˆ and pˆ, denoted dissipative frustration). We study how the interplay of these two baths can lead to interesting effects. After an introduction of the topic, we discuss the results of this thesis in Part II and Part III. In Part II, we study the effect of quantum tunneling in presence of a dissipative interaction with two Ohmic environments to the position xˆ and/or to the momentum pˆ of a particle. In chapter 2, we consider a symmetric double well potential which is important in the context of coherent state preparation, as its ground state is a superposition of being in the left and in the right well. Using the semiclassical approximation to calculate instanton paths within the path integral method, we find that momentum dissipation enhances the coherent tunnel splitting. In presence of dissipative couplings to xˆ and pˆ, the momentum dissipation acts in favor of the delocalization of the particle shifting the critical coupling strength of the dissipative phase transition induced by the position dissipation. Chapter 3 contains a study of the escape rate out of a metastable well in presence of dissipation. Here we find that the incoherent tunneling rate is exponentially enhanced in presence of momentum dissipation. We further show that the influence of momentum dissipation depends on the slope of the part of barrier the particle escaping through. In presence of both dissipative couplings, we find a non-monotonic behavior of the escape rate as a function of the dissipative couplings strengths. In Part III, we show that it is possible to realize the situation of "dissipative frustration" in Josephson junction chains. In particular, we introduce charge dissipation as a physical realization of the afore introduced momentum coupling. After presenting the circuit elements needed for charge dissipation, we study a chain of Josephson junctions affected by Ohmic baths coupled to the charge and/or the phase. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a non-monotonic behavior as a function of the dissipative coupling strength. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that dissipative frustration increases the range in which the phase transition is second order. The non-monotonic behavior is also reflected in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.
Decoherence represents one of the most fundamental problems in quantum mechanics since its birth. Interest in decoherence has been primarily academic until recently when the advances in experimental techniques in different fields of physics such as superconducting quantum interferometers; quantum optics and neutron interferometry sparked the practical interest in this quantum mechanical phenomenon. One particular field where decoherence is of crucial role is quantum computing, where decoherence stands as one of the main obstacles toward realizing practical progress in the field. On the other hand, the ability to manipulate linear superpositions of quantum states is expected to lead to considerable advances in that field. The purpose of this dissertation is to present a study of decoherence in nonlinear quantum systems. We started by studying the coherent superposition of distinct basis states in a single-degree-of-freedom model of SQUID with a variable potential barrier between the basis flux states. We numerically integrated Schrödinger equation of the system. We found that linear superpositions of the basis states, with relatively little residual excitation, can be formed by pulsed modulation of the potential barrier, provided the pulse duration exceeds the period of small oscillations of the flux. Two pulses applied in sequence exhibit strong interference effects, which we propose to use for an experimental determination of the decoherence time in SQUIDS. In addition, we developed, using quantum field theory techniques, a general formalism to study decoherence in a quantum system due to coupling to a non-linear environment. This formalism can be used to investigate decoherence in many of the existing two state quantum systems proposed for quantum computing and reveals important information about them such as decoherence time. Moreover, we used this formalism to compare decoherence induced in a simple two-state quantum system (qubit) for two different initial states of the environment: canonical (fixed temperature) and microcanonical (fixed energy), for the general case of a fully interacting oscillator environment. We found that even a relatively compact oscillator bath (with effective number of degrees of freedom as low as 10), initially in a microcanonical state, will typically cause decoherence almost indistinguishable from that caused by a macroscopic, thermal environment, except possibly at singularities of the environment's specific heat (critical points). In the latter case the precise magnitude of the difference between the canonical and microcanonical results depends on the critical behavior of the dissipative coefficient, characterizing the interaction of the two-state quantum system with the environment.
We use numerically exact iterative path integral methods to investigate the decoherence and entanglement dynamics of a tunneling pair of two coupled qubits (spins) system interacting with a dissipative bath. We find that decoherence is generally accompanied by the destruction of entanglement, although the specifics of this destruction depend sensitively on the parameters of the Hamiltonian (qubit-qubit coupling and/or energy bias), the strength of dissipation, the temperature, and the choice of initial condition. We also observe that dissipation can in some cases generate a substantial amount of entanglement. Finally, if an entangled eigenstate exists which does not couple to the environment, the long-time entanglement can significantly exceed the value corresponding to the Boltzmann equilibrium state.
The search for methods to create and maintain entanglement has led to the idea of environmentally induced entanglement. Roughly speaking, the usually detrimental effect of coupling a non-interacting bipartite system to an environment is turned into an advantage by using the environment to mediate an indirect interaction, which can result in entanglement of the two parts of the system under certain conditions. Of course, care has to be taken to properly evaluate the conflicting influences of the environment. Only if the indirect interaction overcompensates for the decoherence, entanglement creation can be expected. \n \nIt has been suggested that entanglement creation can be achieved in bosonic heat baths even over finite spatial separations with only a moderate polynomial decay of entanglement with distance. In this work, we look more closely at the distance dependence, for the first time employing an oscillator model that is both exactly solvable and includes dissipation. We numerically prove that entanglement creation is, in fact, extremely distance-sensitive and it is not possible to entangle objects which are further apart than approximately their own size. \n \nAdditionally, we suggest an approach how to mitigate the distance dependence. It comes at the cost of geometrically modifying the bath modes by imposing physical boundary conditions resulting in a gap in the spectrum. This is implemented by placing the system inside of an infinitely long superconducting cavity. An experimental implementation of this could be feasible.