Generalized Spin-Boson model and its application to dissipative Bose-Josephson Junction

Sinha, Sudip (2019) Generalized Spin-Boson model and its application to dissipative Bose-Josephson Junction. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

We investigate the effect of dissipation in a Bose Josephson junction (BJJ) coupled to bath of bosons at two sites as an application of the generalized spin-boson model. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within Holstein-Primakoff approximation, which exhibits vanishing of energy gap and enhanced quantum fluctuations at the critical coupling. We study the dynamics of BJJ using time-dependent variational method and analyze stability of different types of steady states. As a special case, we study in details the phase space dynamics of BJJ coupled to a single-mode, which reveals diffusive and incoherent behaviour with increasing coupling to the bath mode. The dynamical steady states corresponding to the Pi-oscillation and self-trapped state become unstable in the region where their oscillation frequencies are in resonance with the bath modes. We investigate the time evolution of number imbalance and relative phase in presence of Ohmic bath with Gaussian noise to incorporate thermal fluctuations. Apart from the damping of Josephson oscillations and transition to symmetry broken state for strong coupling, we observe the decay of Pi-oscillation and self-trapped state to the ground state as a result of dissipation. Variation of phase fluctuation with temperature of the bath shows similar behaviour as observed in the experiments.

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