Modelling non-Markovian quantum systems using tensor networks

Abstract

Accurately modelling the behaviour of quantum systems interacting with the environment is vital to the development of quantum technology. Open quantum systems are well understood when the influence of their environment is weak, but the problem of modelling general systems away from this limit remains difficult. Currently, all approaches to making this problem tractable require some assumption about the nature of the system and its environment. In this thesis a general and efficient numerical method for calculating observables of open quantum systems is presented. The method is to express the exact equations of motion that describe the evolution of a general open quantum system as a tensor network, whose structure allows for a decomposition in terms of matrix products that can be efficiently compressed in size. The power and versatility of the method is demonstrated by using it to study three contrasting models. The first of these is the Ohmic Spin-Boson model, in which the location of the localisation phase transition is identified by analysing the dissipative spin dynamics. This requires high precision numerical calculations, which are shown to be carried out with high efficiency. The second model is that of two spatially separated spins interacting with the same environment, for which no other exact results are available. Here the environment is seen to mediate interaction between the spins, which is intuitively found to be longer ranged for a lower spatial dimension. Finally, an experimentally relevant model of a driven quantum dot is considered. Calculations of the emission spectrum of the dot reveal complex interplay between the coherent driving and the dissipative influence of phonons. In particular the phonon sideband in the spectrum is found to be supressed as the driving of the dot is strengthened.