Abstract
Quantum mechanics has provided the theoretical foundations which have allowed for the design and development of new technologies that have revolutionised the modern world. By further developing our understanding of condensed matter and solid state systems, we have been able to create novel quantum technologies that directly exploit the archetypal properties of quantum physics, associated with superpositions of states, tunnelling and entanglement. However, due to this reliance on key quantum aspects, such systems are vulnerable to decoherence, a loss of information to the environment, limiting their utility. This has led to the rapid increase in interest in the field of open quantum systems. Studying open quantum systems enriches our understanding of the decoherence processes that impede current quantum technologies. Furthermore, non-Markovian effects allow for a bi-directional flow of information to and from the environment and may give rise to new avenues to control the quantum dynamics of the systems of interest. For example, these effects can lead to extensions of coherence lifetimes and understanding them is integral to developing new quantum technologies.
This thesis explores the influence of non-Markovian effects associated with structured environments on the dynamics of embedded quantum systems. We unveil a series of remarkable traits enabled by the non-Markovian evolution, from pairwise entanglement generation between atomic systems, superradiant decay, and the extension of the coherence lifetimes in green fluorescent proteins to demonstrating the ability of artificial neural networks and quantum physical reservoir computers for solving both classical and quantum problems.
We begin with exploring the dynamics of atomic ensembles in structured photonic reservoirs associated with photonic band-gap materials and photonic cavity systems. We demonstrate that by carefully structuring the electromagnetic environment, we can achieve a high degree of control over the evolution of the quantum system of interest. The new effects unveiled by our study include super-radiance, enhancements of energy transfer and reduction of decoherence, which pave the way for enhancing our understanding of the dynamics of open quantum systems and for the development of future quantum technologies.
Subsequently, we develop novel machine-learning approaches capable of efficiently determining the dynamics of open quantum systems and allowing for the full exploration of the parameter hyperspace, inaccessible with conventional methods. Our formalism employs recurrent neural networks able to maintain long-range temporal correlations, and hence ideally suited for modelling non-Markovian dynamics. The formalism is validated for a strongly non-Markovian system associated with a divergent density of states found in photonic band gap materials, a system that is numerically prohibitive to solve by conventional approaches. However, we show that the complex quantum dynamics can be inexpensively determined by deploying recurring neural network architectures. By exploiting the relationship between the architecture of recurrent neural networks and the non-Markovian dynamics of open quantum systems, we then address the inverse task of utilising these quantum systems to instantiate a recurrent neural network by employing the theory of physical reservoir computation. The proposed quantum physical reservoir computer is shown to be capable of solving both classical image recognition tasks and to unveil the dynamics of open quantum systems. Remarkably, it outperformed an identical neural network without the reservoir computing layer.
Next, we explore the dynamical decoherence and memory effects in green fluorescent proteins enabled by their interaction with a frequency-depended dielectric reservoir. Working within the spin-boson model and the Hierarchical Equations of Motion formalism, we demonstrate that the effects of dielectric relaxation in the finite-temperature dielectric environment induce a highly nonMarkovian behaviour. The resulting dynamical features can extend the coherence lifetime of the system and generate transient reductions in entropy, a striking feature of the non-Markovian nature of the system-environment interaction.
Finally, we derive a novel master equation and employ it to explore the physics of quantum permanent dipoles. We utilise here the polaron transformation which allows for non-perturbative insights into the nature of these systems. We find that permanent dipoles introduce exciton pumping, multiple photon processes, photon sidebands, and substantial modifications to single-photon transition dipole processes. We identify experimentally accessible regimes where the new effects predicted, including energy level driving and photonic sidebands, can be explored.