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.
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 compare decoherence induced in a simple 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 find that even a relatively compact oscillator bath (with the effective number of degrees of freedom of order ten), initially in a microcanonical state, will typically cause decoherence almost indistinguishable from that 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 qubit with the environment.
Decoherence is a quantum-mechanical phenomenon severely limiting quantum information processing and storage capability in quantum computers. Decoherence refers to mechanisms that cause transfer of information from a quantum system to its bath. Typically, in theoretical and experimental considerations of different systems containing superconducting qubits, the coupling strength between a qubit and its bath has been assumed to be constant in time. In this case, many standard results in the dynamics of two-level systems follow. For example, due to decoherence, driven Rabi oscillations in a qubit have a characteristic decay time. In addition, the oscillations may take place at any phase. However, by considering time-dependent coupling to the bath, these phenomena may be absent. In this thesis, we demonstrate with numerical simulations of a time-dependent Lindblad master equation persistent Rabi oscillations in a qubit driven by a coherent drive tone. The persistent Rabi oscillations are induced by modulating the coupling of the qubit to the bath with a sinusoidal temporal shape. We observe that the temporal modulation enforces a limit cycle on the evolution of the dressed qubit state with a fixed phase relative to the phase of the sinusoidal modulation regardless of the initial state of the system. Through a synchronization-like phenomenon, the frequency of the Rabi oscillation adapts to match the frequency of the modulation. We determine the effect of different system parameters on the limit cycle and study how the amplitude of the persistent oscillation depends on the coupling modulation parameters. We also observe a similar effect in the freely evolving qubit precession. In addition, the qubit acts as a non-linear mixer, resulting in different linear combinations of the original modulation waveform appearing in the bath-induced Rabi oscillations. We also introduce a design for a physical system where our simulations can be verified experimentally.
During the last decade the field of quantum information has seen considerable progress both
theoretically and experimentally. The building block of this theory is the so-called qubit,
the quantum counterpart of the classical bit. It turns out that spin degrees of freedom
of quantum particles are among the most promising candidates for quantum information
processing and computation. Thus, a deep understanding of the different processes that
govern the dynamics of these objects is of fundamental importance. For instance, the decoherence
process, caused the coupling of the qubits to their surrounding environment, is
the main obstacle to quantum information processing: it leads them to lose their quantum
coherence and thus behave classically. In addition, quantum systems exhibit correlations
that have no classical counterpart. This phenomenon is called entanglement and is the
vital resource for quantum teleportation and quantum computing. Decoherence and entanglement
dynamics were extensively studied within the framework of the Markovian
approximation using the master equation approach. However, due to the non-commuting
character of quantum observables, only few models are known to be exactly solvable.
Moreover, many spin systems display a strongly non-Markovian behavior. This thesis is
devoted to the development of new techniques for deriving the exact dynamics of spin
qubits, coupled through Heisenberg and/or Ising interactions to spin environments that
have internal dynamics. The basic idea behind these techniques is to use the underlying
symmetries exhibited by the Hamitonian operators of the composite systems. This allows
for the study of problems related to decoherence and entanglement.
A particular superconducting quantum interference device (SQUID) qubit, namely the double SQUID qubit, can be manipulated by rapidly modifying its potential with the application of fast flux pulses.In this system we observe coherent oscillations exhibiting non-exponential decay, indicating an unconventional decoherence mechanism.Moreover, via tuning the qubit in different conditions (different oscillation frequencies) by changing the pulse height, we observe a crossover between two distinct decoherence regimes and the existence of an 'optimal' point where the qubit is only weakly sensitive to intrinsic noise.We find that this behavior is in agreement with a model considering the decoherence caused essentially by low-frequency noise contributions, and we discuss the experimental results and possible issues.
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 are in the midst of a renaissance in the study and interpretation of fundamental quantum mechanics, from quantum coherence and quantum entanglement to the quantum measurement process. This stems partly from the impressive advances in experimental techniques that are making yesterday's gedanken experiment today's reality. Another reason quantum coherence and entanglement have come to the forefront is the emerging and tantalizing field of quantum information science. The ability to store information in quantum systems may someday yield devices that process quantum superpositions of inputs in parallel or improve communication through the `wiring' implicit in quantum entanglement. Indeed, quantum computing has the remote prospect of revolutionizing the way we store and process information. This has become particularly important in the face of impending limits on the miniaturization of conventional computers due to quantum effects. Of course, all real systems face limits imposed by decoherence, or the environmentally-induced destruction of quantum coherence. Here, superpositions of quantum states suddenly become probabilistic mixtures of states when they interact with the environment or when the system parameters are fluctuating. Decoherence theory is commonly interpreted as a way to quantify the elusive boundary between quantum and classical worlds and almost always precludes the existence of complex quantum superpositions, except at extremely short time scales. In practice, it is very important to study how decoherence appears in particular quantum systems and try to fight against it. In this special issue of Journal of Optics B: Quantum and Semiclassical Optics , we highlight recent results in the exciting area of quantum coherence and entanglement, including generating interesting and complex quantum states, characterizing coherence and entanglement in these systems, and triumphing over relevant decoherence processes. We hope this issue will not only act as a bookmark in the ongoing study of fundamental quantum mechanics, but will also help guide the rapid developments in quantum information science.