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.
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.
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 derive the uncertainty relation for a quantum open system consisting of a Brownian particle interacting with a bath of quantum oscillators at finite temperature. We examine how the quantum and thermal fluctuations of the environment contribute to the uncertainty in the canonical variables of the system. We show that upon contact with the bath (assumed to be ohmic in this paper) the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is the same as the decoherence time in similar models in the discussion of quantum to classical transition. This offers some insight into the physical mechanisms involved in the environment-induced decoherence process. We obtain closed analytic expressions for this generalized uncertainty relation under the conditions of high temperature and weak damping, separately. We also consider under these conditions an arbitrarily squeezed initial state and show how the squeeze parameter enters in the generalized uncertainty relation. Using these results we examine the transition of the system from a quantum pure state to a nonequilibrium quantum statistical state and to an equilibrium quantum statistical state. The three stages are marked by the decoherence time and the relaxation time, respectively. With these observations we explicate the physical conditions under which the two basic postulates of quantum statistical mechanics become valid. We also comment on the inappropriate usage of the word “classicality” in many decoherence studies of quantum to classical transition.
Abstract. We study the effects of the environment at zero temperature on tunneling in an open system described by a static double-well potential. We show that the evolution of the system in an initial Schrödinger cat state, can be summarized in terms of three main physical phenomena, namely decoherence, quantum tunneling and noise-induced activation. Using large-scale numerical simulations, we obtain a detailed picture of the main stages of the evolution and of the relevant dynamical processes. The tunneling of a particle through a potential barrier is a fundamental effect in quantum mechanics. Macroscopic quantum tunneling can be associated with the tunneling of a many-body wavefunction through a potential barrier, and therefore provides a more stringent test of the validity of quantum mechanics than one particle case. One place where the study of macroscopic quantum tunneling is experimentally accesible is in the tunneling of a Bose-Einstein condensate (BEC) out of an optical trap. These systems have a controllable number of atoms and hence straddle the boundary between microscopic and macroscopic, and hence between quantum and classical systems. Proposals to perform interference experiments using confined atoms
Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature.
We review 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. Interference is studied when electrons or atomic systems are coupled to classical or quantum electromagnetic fields. The interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be almost as large as the corresponding one for coherent electrons and therefore can be observed. We analyse different trajectories in order to show the dependence of the decoherence factor on the velocity of the particles.
Decoherence of quantum signals is one of the main challenges of modern quantum information systems and technologies. This phenomenon is defined as the degradation of the coherent state of a quantum system as a result of environmental influences, which directly affects the information reliability of qubits, as well as the preservation of oscillations and superposition. Decoherence is a natural process of a quantum system when the system interacts with a thermally active or other quantum-mechanically active environment. This effect is important both in theoretical research and in practical quantum devices, including the development of quantum telecommunications, quantum computing, and high-precision quantum sensors. In cryogenic environments, where the temperature approaches zero Kelvin, the reduction of thermal excitations ensures the long-term preservation of the quantum signal. Under such conditions, zero-point fluctuations remain the only source of decoherence, which significantly increases the coherence of qubits and the possibility of performing complex quantum operations. At relatively high temperatures, bosonic and color spectrum excitations significantly increase the decoherence rate, which leads to rapid degradation of the quantum signal and a rapid transition of the system state towards the classical paradigm.