NonEquilibrium Phenomena of Bosons in the Presence of a Cavity Mode

Pati, Sohan (2025) NonEquilibrium Phenomena of Bosons in the Presence of a Cavity Mode. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Sohan Pati (20MS031)) 20MS031_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (5MB)

Abstract

This thesis investigates quantum phase transitions and dynamical behaviour in the Rabi and Dicke models, exploring both closed and dissipative systems. Beginning with the single-spin Rabi model, we employ a unitary transformation to demonstrate the closure of the energy gap, signaling crossover type of behaviour. Then, in the vanishing photon frequency limit we observe a phase transition from a photon-less regime to a superradiant phase characterised by coherent photon emission. Extending to the many-body Dicke model, we identify four dynamical phases: the normal phase (zero mode), the superradiant phase, and their excited counterparts. The phase space analysis highlights the normal phase as a stable attractor, while the superradiant phase exhibits persistent oscillatory dynamics. In the presence of photon loss, the excited phases lose their stability, and the critical coupling required for superradiance is increased. We then introduce the Coupled Top Dicke model, which is the extended Dicke system with two interacting spins. We use the symmetries to partition the phase space into symmetric and antisymmetric sectors, and we see that the antisymmetric sector decouples the spin and photonic dynamics, rendering it robust against photon loss. In contrast, the symmetric sector transitions to chaotic behaviour in the superradiant phase, whereas the normal and antiferromagnetic phases remain regular. Linear stability analysis confirms that antisymmetric fixed points are stable centres even in the presence of dissipation.

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