Abstract An open quantum system is now attracting much attention because a quantum device such as quantum computers and quantum sensors is an emerging technology. Here, we present a model of the open system that shows either time-homogeneous Markovian relaxations or non-Markovian relaxations depending on its parameters that we can control. This model is fully described with the master equation that is analytically solvable. More importantly, this model can be easily realized with molecules in isotropic liquids and measured with NMR techniques.
Abstract An open quantum system is now attracting much attention because a quantum device such as quantum computers and quantum sensors is an emerging technology. Here, we present a model of the open system that shows either time-homogeneous Markovian relaxations or non-Markovian relaxations depending on its parameters that we can control. This model is fully described with the master equation that is analytically solvable. More importantly, this model can be easily realized with molecules in isotropic liquids and measured with NMR techniques.
We are interested in dynamics of a system in an environment, or an open system. Such phenomena as crossover from Markovian to non-Markovian relaxation and thermal equilibration are of our interest. Open systems have experimentally been studied with ultra cold atoms, ions in traps, optics, and cold electric circuits because well-isolated systems can be prepared here and thus the effects of environments can be controlled. We point out that some molecules solved in isotropic liquid are well isolated and thus they can also be employed for studying open systems in Nuclear Magnetic Resonance (NMR) experiments. First, we provide a short review on related phenomena of open systems that helps readers to understand our motivation. We, then, present two experiments as examples of our approach with molecules in isotropic liquids. Crossover from Markovian to non-Markovian relaxation was realized in one NMR experiment, while relaxation-like phenomena were observed in approximately isolated systems in the other.
Abstract Recently remarkable progress in quantum technology has been witnessed. In view of this it is important to investigate an open quantum system as a model of such quantum devices. Quantum devices often require extreme conditions for the devices to operate: dynamics can be non-Markovian here. This observation necessitates us to investigate a non-Markovian open quantum system, both theoretically and experimentally. In this paper, we report two important results: (1) exact solution of a simple but non-trivial theoretical model and (2) demonstration of this model by NMR experiments, where non-Markovianity is continuously controllable. We observe qualitative agreement between theory and experiment.
The theory of open quantum systems represents one of the major developments of quantum mechanics over the last 50 years. Its central object of study is constituted by quantum systems that cannot be regarded as fully isolated, but instead interact with additional degrees of freedom, giving rise to irreversible phenomena such as dissipation and decoherence. The tools provided by this framework are nowadays of paramount importance across many active areas of research, including quantum computation, thermodynamics, metrology and biology. In this thesis, we investigate three main topics within the field. The first contribution concerns the microscopic derivation of the evolution equations, socalled quantum master equations, for open systems which are also subject to external driving fields. Standard techniques developed for time-independent Hamiltonians encounter several difficulties in the time-dependent case, largely restricting their applicability to specific instances, such as periodic or adiabatic drivings. In contrast, a core result of the derivation presented in the thesis is that, when the environment is sufficiently Markovian (essentially, memoryless), the non-adiabatic contributions to the driving field can be neglected in a controlled fashion, yielding an accurate master equation with time-dependent generator, capable of correctly reproducing the open dynamics even for strong drivings. This result is further supported by benchmarks against numerically exact simulations. The second contribution addresses the long-time behavior of general types of (Markovian) quantum master equations, including those of the form introduced above. While this problem has been extensively analyzed in the time-independent setting, virtually no results are known for time-dependent generators. In particular, we establish the foundations of a general theory of relaxation, that is, convergence towards an asymptotic trajectory in the long-time limit, independently of the initial state. The main results include a theorem guaranteeing sufficient conditions for relaxation and the derivation of a rate function governing the convergence to the asymptotic trajectory. The analysis is further extended to a simple non-Markovian case. Moreover, we treat in detail the specific master equation derived in the first part, connecting the aforementioned relaxation property directly to the underlying microscopic dynamics. The third contribution investigates chirality-induced spin selectivity (CISS) effects from the perspective of open quantum systems. Although the majority of theoretical studies aiming to model CISS are based on a coherent description of the spin dynamics, such effects have been observed also for electrons subject to incoherent transport across molecular networks. In this regard, we provide a rigorous ab initio derivation of the microscopic Hamiltonian describing the electronic transport, incorporating electron spin effects and contributions stemming from the nuclear vibrations. Within this result, we critically revise a master equation approach aiming to explain the origin of CISS effects observed in photosynthetic complexes. Taken together, these contributions offer fresh insights and original results on the interplay between driving fields and dissipation, relaxation phenomena, and electronic spin transport in the presence of incoherent dynamics. More broadly, these results provide new theoretical tools with several potential applications in quantum technologies, from modeling of control pulses in noisy environments to quantum reservoir engineering, and contribute to a deeper understanding of the role of quantum effects in biological systems.
The recently developed formalism of Markovian master equations for quantum open systems with external periodic driving is applied to the theory of dynamical decoupling by periodic control. This new approach provides a more detailed quantitative picture of this phenomenon applicable both to traditional NMR spectroscopy and to recent attempts of decoherence reduction in quantum devices. For popular choices of bath spectral densities and a two-level system, exact formulas for the relaxation rates are available. In the context of NMR imaging, the obtained formulas allow the extraction of a new parameter describing bath relaxation time from the experimental data.
[Abstract] A quantum computer, that is able to calculate much faster than a conventional one, has been attracting a lot of attentions, recently. The largest obstacle against its realization is a decoherence of a system. We implement a model system with NMR technique of which decoherence can be controlled by varying the concentration of magnetic impurity and apply a dynamical decoupling technique on it. [概要] 量子コンピュータは,通常のコンピュータでは事実上不可能な計算を実行できる可能性を秘めており注目されている. この量子コンピュータの実現を阻む最大の原因は位相緩和である. NMRを用いて磁性不純物濃度を変えることにより位相緩和を制御できるモデルを実装し, さらにそのモデルに対して動的位相緩和抑制を試みた.
The precise characterization of dynamics in open quantum systems often presents significant challenges, leading to the introduction of various approximations to simplify a model. One commonly used strategy involves Markovian approximations, assuming a memoryless environment. In this study, such approximations are not used and an analytical dynamical depiction of an open quantum system is provided. The system under consideration is an oscillator that is surrounded by a bath of oscillators. The resulting dynamics are characterized by a second-order complex coefficient linear differential equation, which may be either homogeneous or inhomogeneous. Moreover, distinct dynamical regions emerge, depending on certain parameter values. Notably, the steady-state average excitation number (AEN) of the system shows rapid escalation with increasing non-Markovianity, reflecting the intricacies of real-world dynamics. In cases where there is detuning between the system frequency and the environmental central frequency within a non-Markovian regime, the AEN maintains its initial value for an extended period. Furthermore, the application of pulse control can effectively protect the quantum system from decoherence effects without using approximations. The pulse control can not only prolong the relaxation time of the oscillator, but can also be used to speed up the relaxation process, depending on the specifications of the pulse. By employing a kick pulse, the Mpemba effect can be observed in the non-Markovian regime in a surprisingly super-cooling-like effect.