Açık kuantum sistemlerinde ve kuantum faz geçişlerinde kuantum korelasyonları

In this thesis, we, first, study the dynamics of different quantumness measures, such as entanglement and beyond~(quantum discord and measurement induced disturbance) as well as Bell non-locality under decoherence. We, second, focus the ability of the considered quantum correlation measures to detect the critical points of quantum phase transitions.First, we have studied the dynamics of quantum correlations such as entanglement, Bell non-locality and quantum discord between identical and unidentical atoms interacting with a single-mode cavity field and subject to cavity decay. The effect of single atom detuning, cavity decay rate and initial preparation of the atoms on the corresponding correlation measures have been investigated under rotating wave approximation by numerically solving the standard Lindblad quantum optical master equation. High quantum discord is found to be induced regardless of the magnitude of the cavity decay rate, while entanglement and Bell non-locality stay zero for an initially product states. Quantum discord is found to increase in a certain time period under dissipation, while entanglement decreases for the initial state that both atoms are in their excited states. For some type of initial states and identical atom case, cavity decay is shown to drive the system to a stationary state with high entanglement and quantum discord.Second, we have investigated the dynamics of entanglement and quantum discord between two identical qubits resonantly interacting with a common single mode leaky cavity field beyond the rotating wave approximation (RWA) for general Werner-like initial states. The dynamics have been numerically investigated by using recently derived Lindblad type quantum optical master equation [F.~Beaudoin, J.M.~Gambetta, A.~Blais, Phys. Rev. A {\bf 84} (2011) 043832] and compared with the dynamics investigated by {\it ad hoc} master equation, the so-called standard Lindblad quantum optical master equation. Contrary to previous investigations of the same model in the dissipative regime by using thestandard Lindblad quantum optical master equation at ultrastrong coupling regime, we have found that the atom-field steady states are cavity decay rate independent and have a very simple structure determined solely by the overlap of initial atomic state with the decoherence free state which is valid for all coupling regimes. Non-RWA dynamics are found to have remarkable effects on the steady state quantum discord and entanglement that cannot be achieved under RWA conditions, for instance, they can induce steady state entanglement even for the initial states that have no overlap with the decoherence free state.Finally, we have investigated the quantum phase transitions in the ground states of several critical systems, including transverse field Ising and XY models as well as XY with multiple spin interactions, XXZ and the collective system Lipkin-Meshkov-Glick models, by using different quantumness measures, such as entanglement, quantum discord, measurement-induced disturbance and Bell non-locality. We have basically analyzed the performance of different quantumness measures, especially measurement-induced disturbance and Bell non-locality to detect the critical points of quantum phase transitions. Measurement-induced disturbance is found to detect the first and second order phase transitions present in these critical systems, while it is found to fail to signal the infinite-order phase transition present in the XXZ model. Remarkably, Bell non-locality is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.Keywords: Quantum Correlations; Open Quantum Systems; Quantum Phase Transitions.