When a quantum mechanical system interacts with its environment, the system and its environment can become entangled. This entanglement suppresses the interference effects between thedifferent states of the system. Thus, the system behaves more like a statistical mixture of statesrather than a superposition of states.Within quantum technologies, one aims to make use of a systems quantum mechanical properties. Thus, in the development of quantum technologies, it is important to get a better understanding of decoherence and how to prevent it. Furthermore, the decoherence effect due to quantumentanglement between a quantum system and its environment is often neglected in Materials Science. It is therefore important to determine if there are cases when the degree of decoherence is sohigh that it is not negligible.This project studies the variation of the degree of decoherence in a praseodymium-like modelsystem. The purpose of the project is to get a deeper understanding of which parameters of thesystem have a large impact on the degree of decoherence and why.The results show that there are many combinations of parameters where the degree of decoherence is significant. The results also show that certain parameters have a greater impact on thedegree of decoherence than others.It is important to note that certain approximations and restrictions have been used during theconstruction of the model system that may have made the model system less realistic.
When a quantum mechanical system interacts with its environment, the system and its environment can become entangled. This entanglement suppresses the interference effects between thedifferent states of the system. Thus, the system behaves more like a statistical mixture of statesrather than a superposition of states.Within quantum technologies, one aims to make use of a systems quantum mechanical properties. Thus, in the development of quantum technologies, it is important to get a better understanding of decoherence and how to prevent it. Furthermore, the decoherence effect due to quantumentanglement between a quantum system and its environment is often neglected in Materials Science. It is therefore important to determine if there are cases when the degree of decoherence is sohigh that it is not negligible.This project studies the variation of the degree of decoherence in a praseodymium-like modelsystem. The purpose of the project is to get a deeper understanding of which parameters of thesystem have a large impact on the degree of decoherence and why.The results show that there are many combinations of parameters where the degree of decoherence is significant. The results also show that certain parameters have a greater impact on thedegree of decoherence than others.It is important to note that certain approximations and restrictions have been used during theconstruction of the model system that may have made the model system less realistic.
This paper presents a comprehensive model for quantum decoherence, grounded in the principles of quantum field theory (QFT) and statistical mechanics. The core argument is that traditional decoherence models often oversimplify the process, failing to adequately capture the intricate interactions arising from the quantum effects of the surrounding environment. This work introduces a framework that explicitly incorporates the scattering of quantum states by the environment, treated as a QFT system, and then analyzes the resultant impact using statistical mechanics. The model aims to provide a more accurate and nuanced understanding of decoherence, particularly in scenarios involving strong environmental interactions. Specifically, the model utilizes the formalism of quantum scattering theory to describe the interaction between a quantum system and its environment. The resulting dynamics are then analyzed using the framework of statistical mechanics, allowing for the calculation of decoherence rates as a function of environmental parameters such as temperature and density. The key contributions of this work include a detailed mathematical description of the decoherence process, a clear separation of the quantum and classical aspects of the problem, and a framework for extending the model to more complex systems. The model predicts that decoherence is not simply a loss of quantum information, but rather a fundamental process of state transformation driven by the statistical properties of the environment. This work offers a significant step forward in our ability to understand and potentially mitigate the effects of decoherence in quantum technologies.
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.
Theory and experiment have not fully resolved the apparent dichotomy , which has agonized physics for the past eighty years: on the one hand, the description of microsystems by quantum mechanics and, on the other, the description of macrosystems by classical dynamics or statistical mechanics. Derivations of the time-irreversible Liouville equation for an open quantum system, based on projecting out its environment, have narrowed the gap between the quantum and classical descriptions. Yet our `classical' intuition continues to be confronted by quantum-mechanical results like the Einstein--Podolsky--Rosen paradox that challenges the classical notion of locality, or the quantum Zeno effect which suggests that the isolation of a system is not the only way to preserve its quantum state. There are two key concepts in any discussion of such issues. The first, which is responsible for the most salient nonclassical properties, is entanglement , that is partial or complete correlation or, more generally, inseparability of the elements comprising a quantum ensemble . Even after their interaction has ceased, this inseparability, originating from their past interaction, can affect the state of one element when another element is subject to a nonunitary action, such as its measurement, tracing- out, or thermalization. The second key concept is decoherence of open quantum systems, which is the consequence of their entanglement with their environment, a `meter' or a thermal `reservoir', followed by the tracing-out of the latter. Despite new insights into entanglement and decoherence, there are still no complete, unequivocal answers to the fundamental questions of the transition from quantal to classical behaviour: how do irreversibility and classicality emerge from unitarity as systems and their environments become increasingly complex ? At what stage does system--meter entanglement give rise to a classical readout of the meter? Is there an upper limit on the size or complexity of systems displaying entanglement? Major developments have opened new vistas into controlled entanglement , which is the resource of quantum information processing. However, these developments have mainly focused on ensembles of simple two- and three-level systems that are thoroughly isolated from their environments. Treatments of coherence in quantum computing have mostly assumed that only a single or a few the elements of the quantum ensemble may simultaneously undergo an uncontrolled intervention---a quantum error. Decoherence-control protocols for more general types of errors are still incomplete. In order to resolve the outstanding issues of the quantum--classical transition, and study the control of entanglement and decoherence without the foregoing restrictions, we must venture into the domain of Quantum Complex Systems (QUACS), either consisting of a large number of inseparable elements or having many coupled degrees of freedom. Our conviction is that fundamental understanding and manipulation of entanglement within QUACS or their entanglement with the environment or a meter, call for the creation of a new conceptual framework or paradigm, that would encompass phenomena common to cold atoms in laser fields, large molecules, Josephson junctions, quantum gases and solids, with the view of employing these systems for quantum information processing and computing. Progress within this paradigm should allow us to answer the questions: does entanglement play an essential role in the evolution of large collections of complex systems? What are the size and complexity limits of systems and ensembles still controllable by an external intervention? What are the most appropriate decoherence protection schemes and control algorithms? This special issue addresses the challenge of understanding in depth and manipulating the basic quantum properties of optical, atomic, molecular and condensed-matter QUACS, and large ensembles thereof. In view of the interdisciplinary character of this issue, we find it expedient to look at the presented articles not only according to the physical objects they describe, but also from a unifying standpoint. Several unifying themes may be discerned: memory effects in dephasing and relaxation; protection of quantum information by its distribution throughout the ensemble; control of decoherence and entanglement by time-dependent interventions or measurements; manifestations of entanglement in scattering off statistical ensembles; measurment-induced dynamics. The concerted discussion of the topics outlined above should help us advance the new paradigm that addresses our abilities to diagnose and manipulate the entangled states of complex quantum objects and their robustness against decoherence. These abilities are required for quantum information (QI) applications in matter--wave interferometry in molecular, semiconducting or superconducting systems. On the fundamental level, this book may help establish the notion of dynamical information exchange between quantum systems and chart in detail the route from unitarity to classicality. Further developments within the outlined paradigm should yield novel, advantageous QI processing schemes and high-sensitivity interferometers, owing to decoherence suppression and effective control of many degrees of freedom. In the long run, these strategies may prove to be the first step towards the (hitherto unattempted) use of entanglement in nanotechnology, metrology and chemistry, with potentially remarkable novel applications.
The entanglement properties of two-electron atomic systems have been the subject of considerable research activity in recent years. These studies are still somewhat fragmentary, focusing on numerical computations on particular states of systems such as helium, or on analytical studies of model systems such as the Moshinsky atom. Some general trends are beginning to emerge from these studies: the amount of entanglement tends to increase with energy and, in the case of excited states, entanglement does not necessarily tend to zero in the limit of vanishing interaction between the two constituting particles. A physical explanation of these properties, shared by the different two-electron models investigated so far, is still lacking. As a first step towards this goal, we perform here, via a perturbative approach, an analysis of entanglement in two-electron models that sheds new light on the physical origin of the aforementioned features and on their universal character.
Quantum information science is a rapidly growing research area for that it provides new insights to the fundamentals of quantum mechanics and offers a platform for the architecture of novel quantum technologies. The successfulness and practicality of this important scientific field rely on the controllability of a quantum system subject to a realistic noisy environment. The environment always leads to unintended dynamics of the system, and thus destroys its coherence and limits its applications. It is therefore important to understand these decoherence mechanisms from first principles, in order to minimize, or even remove, its adverse effect on the quantum system. The study of this open quantum system problem is usually based on some effective paradigms, where the environment is assumed to be "large", such that it can affect the quantum system without any back action. However, due to the demand for a high precision in quantum computation, such an approximate framework becomes questionable. We provide a new theoretical approach to treat this type of open quantum system problem, including the correlated dynamics between the system and the environment, by using a diagrammatic technique in the same spirit as the Keldysh non-equilibrium Green's function. In this formalism, both the environment and the photonic control are quantized. The dynamics of the system can be evaluated accurately for a time scale of small decoherence, but arbitrary quantum control, relevant to the need for quantum technologies. This offers a way of precise quantum noise calculations. We find how fundamental quantum correlations between the quantum control and quantum environment can arise, and are missing in the existing Master equation approximations. On the other hand, the study of the environment not only provides a better understanding of the decoherence, it also allows applicable designs of quantum operations between different qubit systems. In particular, we engineer a new protocol to entangle two qubits at a distance by projection measurements of their environments, the resonance fluorescence photons. We find exceptional improvements on the probability of success and the rate of entanglement based on the multiphoton environment approach, in comparison with the existing single photon entanglement scheme