Time Evolving Matrix Product States

Abstract

Studying non-Markovian open quantum systems coupled strongly with their environments is essential for the development of future quantum technolo gies. Such systems are ubiquitous in real life but quite poorly understood. Here we develop a numerical approach to solve open quantum system coupled to a harmonic environment based on Feynman Vernon Influence Functional. The history of the system evolution is stored in an augmented density tensor (ADT) in order to study the non-Markovian behaviour. The ADT scheme, however, cannot account for non-Markovian effects that go far back in time. Here we represent the influence functional and the ADT as time-evolving ma trix product operators (TEMPO) and states (TEMPS), respectively. At each time step, the matrix product operator and state are contracted to give the time-evolved state which is decomposed using singular value decomposition and truncation. This method is very efficient and works for different coupling regimes. We demonstrate the robustness of the TEMPO algorithm by ex amining the phonon-induced damping of Rabi Oscillations in semiconductor Quantum Dots coupled to a cavity for different phonon-exciton couplings. The decay rates of Rabi Oscillations at different temperatures are also com pared.