Majorana sphere representation for the time evolution of one qubit-spin coherent state model

Abstract

The interaction between qubit – field has attracted many researchers’ curiosity as it sparked the development of quantum technologies such as quantum computing, quantum cryptography, and quantum metrology. There is a need to study the behavior of the qubit – field interaction system especially with a consideration of realistic errors to simulate the practical system for experimental purposes. This dissertation investigated the interaction system between a single qubit with a collection of N qubits or known as the spin coherent state, where the event of collapse and revival in the time evolution of the qubit state was focused. In this study, the time evolution of the qubit state in the one qubit – spin coherent state model was reproduced, and the dynamics of the qubit state probabilities was transformed into the little known Majorana Sphere representation. The dynamics in the Majorana Sphere was then analysed by considering three different initial state of the qubit. The results demonstrated that for the case of the qubit initially in the excited state and ground state, the dynamics started at a point on the surface of the Majorana Sphere at the north pole and south pole respectively, and we observed the oscillations of the dynamics in the sphere as time evolves. On the other hand, for the case of an equal probability between the excited state and ground state, we cannot see the same type of oscillations like in the previous case, and the dynamics just moved around in circle at the center of the sphere. The research was extended by considering the effect of having an off-resonant frequencies attributes to the system, then the frequency differences with distributions of varying width were averaged over to address the decoherence effects. It was found that for the case of qubit initially in excited state, the dynamics is more squished towards the north pole of the Majorana Sphere with increasing value of detuning. However, with an increasing width of ‘error’ distribution, the amplitude of the oscillations in the Majorana Sphere decreased and the dynamics remain averaged at the center of the sphere, which shows the suppression of the collapse and revival activity in the interaction system.