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.
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.
The irreversible time evolution of a quantum system interacting with a large environmental system can be described by a quantum master equation. When an external field is applied to a quantum system, a non-Markovian mater equation is derived in a rigorous way, where the relaxation terms in the quantum master equation include the effects of the external field. It is shown that, when the external field is a sequence of phase-modulation pulses, the decoherence of the quantum system can be suppressed under certain conditions. To see the effects of phase-modulation pulses, the irreversible time evolutions of qubit and photon systems are investigated in detail.
We study the time evolution of a qubit linearly coupled with a quantum environment under a sequence of short π pulses.Our attention is focused on the case where qubit-environment interactions induce the decoherence with population decay.We assume that the environment consists of a set of bosonic excitations.The time evolution of the reduced density matrix for the qubit is calculated in the presence of periodic short π pulses.We confirm that the decoherence is suppressed if the pulse interval is shorter than the correlation time for qubit-environment interactions.
The decoherence of entanglement of two-qubit states is investigated by means of the non-Markovian quantum master equation. It is assumed that the decoherence is caused by environmental systems in non-stationary states, which evolve from initial states into equilibrium states. In this case, the non-Markovian nature of the environmental systems is of essential importance. It is shown that the disentanglement time after which there is no qubit entanglement is determined by the non-Markovian effect and the thermal effect of the environmental systems.
The pulse control of decoherence in a qubit interacting with a quantum environment is studied with focus on a general case where decoherence is induced by both pure dephasing and population decay. To observe how the decoherence is suppressed by periodic pi pulses, we present a simple method to calculate the time evolution of a qubit under arbitrary pulse sequences consisting of bit-flips and/or phase-flips. We examine the effectiveness of the two typical sequences: bb sequence consisting of only bit-flips, and bp sequence consisting of both bit- and phase-flips. It is shown that the effectiveness of the pulse sequences depends on a relative strength of the two decoherence processes especially when a pulse interval is slightly shorter than qubit-environment correlation times. In the short-interval limit, however, the bp sequence is always more effective than, or at least as effective as, the bb sequence.
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 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.