Manipulating the dynamics of open quantum systems is a crucial requirement for large-scale quantum computers. Finding ways to overcome or extend decoherence times is a challenging task. Already at the level of a single two-level atom, its reduced dynamics with respect to a larger environment can be very complex. Structured environments, for instance, can lead to various regimes other than memoryless Markovian spontaneous emission. Here, we consider an atom coupled to an array of coupled cavities in the presence of on-site correlated disorder. The correlation is long-ranged and associated with the trace of a fractional Brownian motion following a power-law spectrum. With the cavity modes playing the role of the environment, we study the dynamics of the spontaneous emission. We observe a change from non-Markovian to Markovian decay in the presence of disorder by tuning the correlation parameter. This is associated with a localization-delocalization transition involving the field modes. Two dissipative models that effectively reproduce the behavior of the non-Markovianity are discussed. The dissipation dynamics of the atom can thus be used to extract information about the phase of the environment. Our results provide a direction in the engineering of disordered quantum systems to function as controllable reservoirs.
Manipulating the dynamics of open quantum systems is a crucial requirement for large-scale quantum computers. Finding ways to overcome or extend decoherence times is a challenging task. Already at the level of a single two-level atom, its reduced dynamics with respect to a larger environment can be very complex. Structured environments, for instance, can lead to various regimes other than memoryless Markovian spontaneous emission. Here, we consider an atom coupled to an array of coupled cavities in the presence of on-site correlated disorder. The correlation is long-ranged and associated with the trace of a fractional Brownian motion following a power-law spectrum. With the cavity modes playing the role of the environment, we study the dynamics of the spontaneous emission. We observe a change from non-Markovian to Markovian decay in the presence of disorder by tuning the correlation parameter. This is associated with a localization-delocalization transition involving the field modes. Two dissipative models that effectively reproduce the behavior of the non-Markovianity are discussed. The dissipation dynamics of the atom can thus be used to extract information about the phase of the environment. Our results provide a direction in the engineering of disordered quantum systems to function as controllable reservoirs.
Controlling the non-Markovian dynamics of open quantum systems is essential in quantum information technology since it plays a crucial role in preserving quantum memory. Albeit in many realistic scenarios the quantum system can simultaneously interact with composite environments, this condition remains little understood, particularly regarding the effect of the coupling between environmental parts. We analyze the non-Markovian behavior of a qubit interacting at the same time with two coupled single-mode cavities which in turn dissipate into memoryless or memory-keeping reservoirs. We show that increasing the control parameter, that is the two-mode coupling, allows for triggering and enhancing a non-Markovian dynamics for the qubit starting from a Markovian one in the absence of coupling. Surprisingly, if the qubit dynamics is non-Markovian for the zero control parameter, increasing the latter enables multiple transitions from non-Markovian to Markovian regimes. These results hold independently on the nature of the reservoirs. This work highlights that suitably engineering the coupling between parts of a compound environment can efficiently harness the quantum memory, stored in a qubit, based on non-Markovianity.
Understanding the non-Markovian dynamics of dissipative processes induced by memory effects of the environment is a fundamental subject of open quantum systems. Because of the complexity of open quantum systems, e.g., the multiple energy scales involving that of the system, the environment, and their mutual coupling, it is generally a challenging task to characterize the relationship among the parameters of the system dynamics and the reservoir spectra. For the two-level spontaneous emission model within structured environments, it was shown in a recent literature (Opt. Lett. 38, 3650) that a functional relation could be established between the asymptotically non-decaying population and the spectral density of the reservoir as the system undergoes a long-time evolution. It hence renders a distinct perspective to look into the character of long-lived quantum coherence in the corresponding non-Markovian process. This article is devoted to further investigate the phenomena of limit cycle oscillations possibly occurring in such non-Markovian dissipative systems in a long-time evolution. For a two-level system subjected to an environment with Ohmic class spectra, due to the presence of a unique bound-state mode of the system, the evolution trajectory of the given initial states will converge to a limit cycle in the Bloch space. The dependence of the radius and the location of the limit cycle on the spectral density function of the reservoir are manifested by virtue of the described functional relation. For the model subjected to a photonic crystal environment with multiple bands, our studies reveal that, owing to the presence of two or more bound states, the evolution trajectory of the system will converge to a toric curve of a paraboloid in the Bloch space and the phenomena of periodic or quasi-periodic oscillations could exhibit. While the equation of the parabolic curve is fully determined by the initial values of the state vector in the Bloch space, our results reveal that the scope of the evolution trajectory inside the toric curve is related to the spectral density of the reservoir and their quantified relation is distinctly characterized. Finally, the asymptotic dynamics of the correlations of a two-qubit system is discussed when it is subjected locally to the non-Markovian dissipative process.
As discovered by P. W. Anderson, excitations do not propagate freely in a disordered lattice, but, due to destructive interference, they localise. As a consequence, when an atom interacts with a disordered lattice, one indeed observes a non-trivial excitation exchange between atom and lattice. Such non-trivial atomic dynamics will in general be characterised also by a non-trivial quantum information backflow, a clear signature of non-Markovian dynamics. To investigate the above scenario, we consider a quantum emitter, or atom, weakly coupled to a uniform coupled-cavity array (CCA). If initially excited, in the absence of disorder, the emitter undergoes a Markovian spontaneous emission by releasing all its excitation into the CCA (initially in its vacuum state). By introducing static disorder in the CCA the field normal modes become Anderson-localized, giving rise to a non-Markovian atomic dynamics. We show the existence of a functional relationship between a rigorous measure of quantum non-Markovianity and the CCA localization. We furthermore show that the average non-Markovianity of the atomic dynamics is well-described by a phenomenological model in which the atom is coupled, at the same time, to a single mode and to a standard - Markovian - dissipative bath.
We demonstrate how a time-dependent dissipative environment may be used as a tool for controlling the quantum state of a two-level atom. In our model system the frequency and coupling strength associated with microscopic reservoir modes are modulated, while the principal features of the reservoir structure remain fixed in time. Physically, this may be achieved by containing a static atom-cavity system inside an oscillating external bath. We show that it is possible to dynamically decouple the atom from its environment, despite the fact that the two remain resonant at all times. This can lead to Markovian dynamics, even for a strong atom-bath coupling, as the atomic decay becomes inhibited into all but a few channels; the reservoir occupation spectrum consequently acquires a sideband structure, with peaks separated by the frequency of the environmental modulation. The reduction in the rate of spontaneous emission using this approach can be significantly greater than could be achieved with an oscillatory atom-bath detuning using the same parameters.
This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.
Non-Markovian evolution of an open quantum system can be induced by the memory effects of a reservoir. Although a reservoir with stronger memory effects may seem like it should cause stronger non-Markovian effects on the system of interest, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a qubit (a two-level atom) that is coupled to a hierarchical environment, which contains a single-mode cavity and a reservoir consisting of an infinite number of modes. We show how the non-Markovian character of the system is influenced by the coupling strength between the qubit and cavity and the correlation time of the reservoir. In particular, we found a phenomenon whereby the qubit Markovian and non-Markovian transition exhibits a anomalous pattern in a parameter space depicted by the coupling strength and the correlation time of the reservoir.