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.
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.
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.
We study the dynamics of open quantum systems driven by an external time-periodic force. Combining Floquet theory and the time-convolutionless projection operator technique we derive a time-local quantum master equation which exactly takes into account the periodic driving, while treating the system-environment interaction within second order in the coupling strength without performing the Markov approximation. The resulting equation of motion for the reduced density matrix is called Floquet time-convolutionless master equation. Employing the example of the driven spin-boson system, we demonstrate that this master equation is capable of describing strong non-Markovian effects, while yielding the Floquet-Lindblad master equation in the Markovian limit. A characteristic feature of memory effects in such driven dissipative systems is the emergence of sharp peaks of the trace-distance based non-Markovianity measure as a function of the driving amplitude, which can be traced back to quasienergy crossings leading to almost decoherence-protected subspaces through a quasienergy-induced dissipative decoupling mechanism.
Dynamical decoupling as a quantum control strategy aims at suppressing quantum decoherence adopting the popular philosophy that the disorder in the unitary evolution of the open quantum system caused by environmental noises should be neutralized by a sequence of ordered or well-designed external operations acting on the system. This work studies the solution of quantum-state-diffusion equations by mixing two channels of environmental noises, i.e., relaxation (dissipation) and dephasing. It is interesting to find in two-level and three-level atomic systems that a non-Markovian relaxation or dissipation process can be suppressed by a Markovian dephasing noise. The discovery results in an anomalous control strategy by coordinating relaxation and dephasing processes. Our approach opens an avenue of noise control strategy with no artificial manipulation over the open quantum systems.
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.
One of the fundamental problems of chemistry is the difficulty in determining full quantum mechanical descriptions of molecules. Molecules contain many degrees of freedom and as a result the classical description scales factorially with the number of electrons. One way to overcome this mismatch between quantum and classical pictures is to use one quantum system, a quantum computer, to simulate another. Quantum computation is based upon a two-level system, a qubit, which is analogous to a bit in classical computation. Unlike a classical bit, a qubit can exist in a superposition of quantum states. The interaction between a quantum system and its environment results in the decay of the superposition state of the system into a probability density of classical states [1]. This is known as decoherence. A realistic quantum computer requires qubits with long coherence times; with respect to the achievable gating times, for a formal relation refer to section 1.2.2. The spin echo effect in nuclear magnetic resonance (NMR) offers a way to increase the coherence time of a qubit and has been studied as a way to mitigate decoherence in quantum computation[2][3]. By applying an appropriate Π pulse to a system under the influence of a large external field, as in NMR, the interaction term of the Hamiltonian between the qubit and environment can be eliminated[3][4]. Periodic implementation of such pulses is known as periodic dynamic decoupling (PDD). Similar to PDD, concatenated dynamic decoupling (CDD) is a periodic pulse sequence which removes the interaction term of the Hamiltonian, however in CDD pulse sequences are recursively embedded within the overall pulse train. Such pulse sequences have been shown theoretically to work for model quantum systems such as GaAs quantum dots, and theoretically such pulse sequences vastly improve the coherence time of a qubit [5]. There have been many calculations showing that by progressively increasing the number of concatenated pulse sequences increasingly longer coherence times can be achieved [6][7]. These techniques have not been tested in the laboratory and experimental implementation of these promising techniques motivates current research. There also continues to be extensive work on developing novel pulse sequences which may improve coherence times even further. The goal of this research is to experimentally determine the coherence times which can be achieved with a trapped calcium atom by applying these pulse sequences.
An irreversible time evolution of a quantum system interacting with a surrounding environment is described by a quantum master equation. When an external field is applied to a quantum system, a non-Markovian master equation is derived in a rigorous way, where the relaxation terms in the quantum master equation include the effect of the external field that is ignored in the conventional treatment. It is shown that when the external field is a sequence of phase-modulation π-pulses, the decoherence of the quantum system can be suppressed. In particular, when the pulse separation is sufficiently short in comparison with the correlation time of the environmental system, dynamical decoupling takes place. To see the effect of the phase-modulation π-pulses, the time evolution of qubit entanglement is investigated in detail.