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Classical and Quantum Dynamics of the Dicke Model

Sarkar, Aakash (2016) Classical and Quantum Dynamics of the Dicke Model. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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    Abstract

    In this thesis, we explore the Dicke model, well-known for its explanation of the superradiant phase transition and signatures of Classical and Quantum Chaos. We then propose a variational approach to determine the semi-classical (SC) equations of motion, using coherent states. The SC dynamics exhibits signs of classical chaos both with increasing coupling and as the energy of the system is gradually increased, eventually leading to it completely engulfing the 2 dimensional phase space of the pseudospin, which we examine through Poincare sections. We then use numerical diagonalization to study the Quantum Dicke model - it is observed that at and after exactly the critical value of the coupling, the system shows a net macroscopic photon expectation value, and the pseudospin component in the z direction starts to steadily decline - implying a net fraction of the atoms are shifting to the excited state. We then study the dynamics of the Quantum Dicke Hamiltonian using coherent states and compare the expectation values of the dimensional with the classical trajectories from the semi-classical dynamics for stable and chaotic orbits. We then introduce a linear quench which drives the Dicke model across the Superradiant phase transition by changing the coupling strength. The quenched dynamics is simulated using both semi-classical and quantum dynamics - it is seen that dynamically varying quantities are periodically oscillating around their instantaneous steady-state coupling values.

    Item Type: Thesis (Masters)
    Additional Information: Supervisor: Dr. Subhasis Sinha
    Uncontrolled Keywords: Coherent States; Dicke Hamiltonian; Dicke Model; Linear Quench; Quantum Dynamics
    Subjects: Q Science > QC Physics
    Divisions: Department of Physical Sciences
    Depositing User: IISER Kolkata Librarian
    Date Deposited: 08 Aug 2016 16:26
    Last Modified: 08 Aug 2016 16:27
    URI: http://eprints.iiserkol.ac.in/id/eprint/378

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