JultikaUniversity of Oulu repository

With the recent advancements made in the coupling of quantum systems, reaching the (ultra)strong coupling regime, where the coupling constant exceeds the dissipation rate and approaches the frequencies of the coupled systems, is getting closer. In this regime, the much used semiclassical model is no longer valid, and the solving of the full quantum master equation can be computationally too demanding. Thus, we must develop a new approach to be able to simulate the system. One solution is to use the semiquantum approximation. In this thesis, we present a systematic way of employing the semiquantum approximation and compare it to the full master equation. Our aim is to determine the range for the coupling strength where the semiquantum model is applicable. We chose to do the comparison of the semiquantum approximation and the master equation within the Rabi model, which can be used to describe e.g. the interaction of light and matter. The Rabi model describes a system with a coupled two-level system and a harmonic oscillator. It was chosen because its behaviour is reasonably well known. We compared the semiquantum approximation to the quantum master equation in two cases. First we studied the steady state results from the two models, and then moved on to the spectral properties. The results show that the steady state and the spectrum obtained from the semiquantum model agree with the ones obtained by using the master equation, until the coupling reaches a considerable fraction of the resonant frequency of the oscillator, while still exceeding the experimentally reasonable dissipation rate by an order of magnitude. In the future, one could use the semiquantum approximation in the field of cavity optomechanics. There a mechanical oscillator is coupled to optical radiation confined in a cavity, e.g. a Fabry-Pérot cavity. Especially in optomechanics, the solving of the master equation can turn out to be a formidable task, and by using the semiquantum approximation one could reduce the computation time considerably.