We propose a protocol to simulate the evolution of a non-Markovian open quantum system by considering a collisional process with a many-body system, which plays the role of an environment. As a result of our protocol, the environment spatial correlations are mapped into the time correlations of a noise that drives the dynamics of the open system. Considering the weak coupling limit, the open system can also be considered as a probe of the environment properties. In this regard, when preparing the environment in its ground state, a measurement of the dynamics of the open system allows to determine the length of the environment spatial correlations and therefore its critical properties. To illustrate our proposal we simulate the full system dynamics with matrix-product-states and compare this to the reduced dynamics obtained with an approximated variational master equation.
We propose a protocol to simulate the evolution of a non-Markovian open quantum system by considering a collisional process with a many-body system, which plays the role of an environment. As a result of our protocol, the environment spatial correlations are mapped into the time correlations of a noise that drives the dynamics of the open system. Considering the weak coupling limit, the open system can also be considered as a probe of the environment properties. In this regard, when preparing the environment in its ground state, a measurement of the dynamics of the open system allows to determine the length of the environment spatial correlations and therefore its critical properties. To illustrate our proposal we simulate the full system dynamics with matrix-product-states and compare this to the reduced dynamics obtained with an approximated variational master equation.
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational principle for its nonequilibrium steady state. We successfully apply our variational method to study dissipative Rydberg gases, finding very good quantitative agreement with small-scale simulations of the full quantum master equation. We observe that correlations related to non-Markovian behavior play a significant role during the relaxation dynamics towards the steady state. We further quantify this non-Markovianity and find it to be closely connected to an information-theoretical measure of quantum and classical correlations.
The stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex colored noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating colored noises of this kind that are built on a noise amplitude reduction procedure [Imai et al., Chem. Phys. 446, 134 (2015)CMPHC20301-010410.1016/j.chemphys.2014.11.014], including two analytically optimized schemes. In doing so, we pay close attention to the properties of the correlation functions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realization that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well-controlled method for doing so. We compare the ability of these schemes, along with an alternative optimized scheme [Schmitz and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)1951-635510.1140/epjst/e2018-800094-y], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimizing an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.
We report the development of an efficient many-body algorithm for simulating open quantum system dynamics that utilizes a time-dependent variational principle for matrix product states to evolve large system-environment states. Capturing all system-environment correlations, we reproduce the nonperturbative, quantum-critical dynamics of the zero-temperature spin-boson model, and then exploit the many-body information to visualize the complete time-frequency spectrum of the environmental excitations. Our ``environmental spectra'' reveal correlated vibrational motion in polaronic modes which preserve their vibrational coherence during incoherent spin relaxation, demonstrating how environment information could yield valuable insights into complex quantum dissipative processes.
Quantum mechanics has both deepened our understanding of the physical reality and allowed development of quantum technologies beating their classical counterparts in efficiency, security, and sensitivity. As a major downside, the quantum properties behind these technologies are very sensitive to the effects the system’s interaction with its environment. The theory of open quantum systems describes how such interaction influences the system, and as a consequence, how the quantum features are lost, controlled, and possibly returned by manipulating the environment. This thesis begins with a short description of the most relevant features and results of the open quantum system theory. We continue by presenting some commonly used measures to quantify the information encoded in quantum systems and the correlations between spatially or temporally separated parties. The literature review ends with discussion of non-Markovianity and memory effects which combine the fields of open quantum systems and quantum information in a natural way. The rest of the thesis presents the main results of Publications I – VII. We study the memory effects and physicality conditions of open system dynamics described by the vast family of phase-covariant master equations. We show how the open quantum system picture can be exploited to design probing protocols to extract information without knowing how the probe and system interact. Such protocols are considered also from the point-of view of efficiently obtaining the information required in the probing, both in theory and by experimental implementation. The experiment serves also as evidence for applicability of recently developed geometric tools to design informationally incomplete measurements for solving so-called membership problems. We present and experimentally realize a protocol where control over intial correlations between polarization and frequency gives full freedom to implement any dephasing dynamics in the open system polarization, thus dictating how its information content changes in time. We study the two-qubit memory effects of dephasing dynamics and compare them to the effect of such noise in the transmission efficiency in superdense coding. Optimal noise configurations in different situations are found. Finally, we characterize the families of initial states for which the decay of quantum correlations depends or does not depend on the noise location.
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.
One of the main goals of the theory of open quantum systems is to devise methods which help preserve the quantum properties of a system interacting with its environment.One possible pathway to achieve this goal is to use non-Markovian reservoirs, characterized by information backflows and revivals of certain quantum properties.These reservoirs usually require advanced engineering techniques, which may turn their implementation impractical.In this dissertation we propose an alternative technique: the injection of a classical colored noise, which induces the desired quantum non-Markovianity.In order to do that, we investigate the dynamics of a quantum system interacting with its surrounding environment and under the injection of a classical stochastic colored noise.A time-local master equation for the system is derived by using the stochastic wave function formalism and functional calculus.Afterwards, the non-Markovianity of the evolution is detected by using the Andersson, Cresser, Hall and Li measure, which is based on the decay rates of the master equation in canonical Lindblad-like form.Finally, we evaluate the measure for three different colored noises and study the interplay between environment and noise pump necessary to induce quantum non-Markovianity, as well as the energy balance of the system.