Quantum Phase Transition And Quantum Fisher Information Of Cavity QED

The real interaction between matter and electromagnetic radiation is too complicated for a complete theoretical investigation. However, in some cases, considering interesting phenomena in the framework of rather simple models having even exact solutions would lead one to deeper physical comprehension.The single-mode Dicke model is well known to undergo a quantum phase transition from the so-called normal phase to the superradiant phase (hereinafter called the "superradiant quantum phase transition"). Normally, quantum phase transitions can be identified by the critical behavior of quantities such as entanglement, quantum fluctuations, and fidelity. In this paper, we study the role of quantum Fisher information (QFI) of both the field mode and the atoms in the ground state of the Dicke Hamiltonian. For a finite but large number of atoms, our numerical results show that near the critical atom-field coupling, the QFIs of the atomic and the field subsystems can surpass their classical limits, due to the appearance of non-classical quadrature squeezing. As the coupling increases far beyond the critical point, each subsystem becomes highly mixed state, which degrades the QFI and hence the ultimate phase sensitivity. In the thermodynamic limit, we present analytical results of the QFI and their relationship with the reduced variance of the field mode and the atoms. For each subsystem, we find that there is a singularity in the derivative of the QFI at the critical point, a clear signature of the quantum criticality in the Dicke model.Our paper is organized as follows. In chapter1and chapter2, we introduce some fundamental concepts of Quantum mechanics, Quantum optics, and Quantum metrology. In chapter3, we present numerical results of the QFI and variance for the atomic and the field subsystems by exactly diagonalizing the finite-N Dicke Hamiltonian. In section4, analytical results of the QFI and its relationship with the reduced variance for each subsystem are derived in the thermodynamic limit.