We investigate the influence of environmental noise on spin networks and spin chains. In addition to the common model of an independent bath for each spin in the system we also consider noise with a finite spatial correlation length. We present the emergence of decoherence-free subspaces and different dynamics with increasing correlation length for both dephasing and dissipating environments. This leads to relaxation blocking of one spin by uncoupled surrounding spins. We then consider perfect state transfer through a spin chain in the presence of decoherence and discuss the dependence of the transfer quality on spatial noise correlation length. We identify qualitatively different features for dephasing and dissipative environments in spin-transfer problems.
We investigate the influence of environmental noise on spin networks and spin chains. In addition to the common model of an independent bath for each spin in the system we also consider noise with a finite spatial correlation length. We present the emergence of decoherence-free subspaces and different dynamics with increasing correlation length for both dephasing and dissipating environments. This leads to relaxation blocking of one spin by uncoupled surrounding spins. We then consider perfect state transfer through a spin chain in the presence of decoherence and discuss the dependence of the transfer quality on spatial noise correlation length. We identify qualitatively different features for dephasing and dissipative environments in spin-transfer problems.
The challenge of making nano-scale quantum systems experimentally accessible is being overcome for an increasing diversity of systems by improved fabrication techniques and experimental control. Despite rapid progress, one of the main hindrances in all experiments is the difficulty of isolating the quantum system from the surrounding environment and its fluctuations. This experimental “noise” perturbs the quantum system, a process that is generally referred to as decoherence: the system slowly loses its distinguishing quantum features. In this thesis the effects of spatial correlations in the noise environment with a finite correlation length are investigated. The consequences for the experimental design of controlled quantum systems as well as the dynamics of solid state systems are presented. We utilize the Bloch-Redfield formalism, a Markovian master equation approach, which gives a close connection to the underpinning system-environment model. We show how to use this formalism to model any spatial correlation function of the noise environment. Using microscopic environmental models, several correlation functions are derived and their properties connected to the environmental parameters. Several phenomenological correlation functions are also studied and a mapping to the Lindblad master equation is presented, which provides a test of positivity for phenomenological models. For quantum transport through spin chains and networks, noise is generally detrimental. Spatial correlations however reduce the effect of dephasing noise and can reinstate the transport dynamics. The critical correlation length proves to be closely connected to the maximal packet width of one excitation in the transfer process. For dissipation noise, relaxation-free states emerge with spatial correlations. The decay of an excitation is therefore fundamentally modified into a fast decay towards an intermediate relaxation-reduced state and a subsequent decay to the ground state on a much longer time scale. In quantum metrology noise correlations have been observed in experiments with trapped ions, in which they limit the use of such experiments for metrology. Quantum advantage, i.e. a better precision scaling than the standard quantum limit has been proven impossible in the presence of uncorrelated Markovian noise only. We show that for certain optimized states the best possible quantum advantage, Heisenberg scaling, can be achieved in the presence of noise with a finite spatial decay of correlations. We furthermore identify how dephasing effects change and a topology dependence arises in strength with increasing correlation length for entangled states in a general way. Biological photosynthetic complexes have recently been found to potentially include quantum coherent dynamics, particularly in the process of transmitting an exciton from the point of creation to the reaction centre. We show how the formalism of spatially correlated decoherence adapts to this significantly different energy regime. Typical effects of decoherence in this field are presented and we show how the light-harvesting efficiency is influenced by spatial correlations in the noise. This thesis highlights the fundamental relevance of noise correlations to several fields of quantum physics and the importance of the efficient and comprehensive modelling techniques presented.
Abstract Transmission of a quantum state is essential for performing quantum information processing tasks. The communication channel will be inevitably immersed in its surrounding environment under realistic conditions. In this paper, we investigate the influence of environment noise on the transmission fidelity when transferring a quantum state through a spin chain. The non-Markovian open system dynamics is systematically analyzed by using the quantum state diffusion equation method. With each spin immersed in its own finite temperature and non-Markovian heat bath, we consider three types of system–bath interaction: dephasing, dissipation and spin-boson. The transmission fidelity is found to decrease with the increasing bath temperature and system–bath coupling strength. Interestingly, we find that the bath non-Markovianity can help enhancing the transmission fidelity.
We analyze the decoherence dynamics of a central spin coupled to a spin chain with a time-dependent noisy magnetic field, focusing on how noise influences the system's decoherence. Our results show that decoherence due to the nonequilibrium critical dynamics of the environment is amplified in the presence of uncorrelated and correlated Gaussian noise. We demonstrate that decoherence factor consistently signals the critical points, and exhibits exponential scaling with the system size, the square of noise intensity, and the noise correlation time at the critical points. We find that strong coupling between the qubit and the environment leads to partial revivals of decoherence, which diminish with increasing noise intensity or decreasing noise correlation time. In contrast, weak coupling leads to monotonic enhanced decoherence. The numerical results illustrate that, the revivals decay and scale exponentially with noise intensity. Moreover, the revivals increase and indicate linear or power law scaling with noise correlation time depending on how the correlated noise is fast or slow. Additionally, we explore the non-Markovianity of the dynamics, finding that it decays in the presence of noise but increases as the noise correlation time grows.
Quantum decoherence arises due to uncontrollable entanglement between a system and its environment. However, the effects of decoherence are often thought of and modeled through a simpler picture in which the role of the environment is to introduce classical noise in the system's degrees of freedom. Here, we establish necessary conditions that the classical noise models need to satisfy to quantitatively model the decoherence. Specifically, for pure-dephasing processes, we identify well-defined statistical properties for the noise that are determined by the quantum many-point time correlation function of the environmental operators that enter into the system-bath interaction. In particular, for the exemplifying spin-boson problem with a Lorentz-Drude spectral density, we show that the high-temperature quantum decoherence is quantitatively mimicked by colored Gaussian noise. In turn, for dissipative environments, we show that classical noise models cannot describe decoherence effects due to relaxation through spontaneous emission of photons/phonons. These developments provide a rigorous platform to assess the validity of classical noise models of decoherence.
Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths and pronounced separation of dynamical timescales. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: strong internal hybridization generates an effective detuning that suppresses transfer to other weakly coupled sites, yielding a parametrically enhanced relaxation time in the weak-dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.
We study excitation transfer in a spin chain in presence of noise. To model noise, we assume that each qubit of the spin chain is interacting with a Bosonic environment and has Markovian evolution. We derive the explicit form of master equation both in global and local approaches. Comparing the results of each approach, we discuss the noise effect on excitation transfer and in addition to that we show that the results of local approach are not a limiting case of global approach.