# Dissipative Bose-Josephson junction coupled to bosonic baths

## TL;DR

This paper explores how dissipation affects a Bose-Josephson junction coupled to bosonic baths, revealing quantum phase transitions, stability changes, and decay of oscillations, with implications for experimental observation.

## Contribution

It introduces a detailed analysis of dissipation effects in BJJ, including phase transitions, stability analysis, and dynamics, using spin model mapping and variational methods, which is novel in this context.

## Key findings

- Quantum phase transition induced by bath coupling
- Damping and decay of Josephson oscillations
- Instability of steady states at resonance conditions

## Abstract

We investigate the effect of dissipation in a Bose-Josephson junction (BJJ) coupled to bath of bosons at two sites. 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 exhibit 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 damping of Josephson oscillations and transition to symmetry broken state for strong coupling we observe 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 experiment. Finally we discuss the experimental setup to study the observable effects of dissipation in BJJ.