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Abstract:  The Sine-Gordon Hamiltonian is ubiquitous in low-dimensional physics, with applications that range from cold atom systems and strongly correlated systems to quantum impurity systems. We study here its non-equilibrium dynamics using the quantum quench protocol, following time evolution the Sine Gordon system from initial  Mott type  states with large potential barriers.    By means of the Bethe Ansatz we calculate exactly the Loschmidt amplitude, the fidelity and work distribution characterizing these quenches for different values of the interaction strength. Some universal features are noted as well as an interesting duality relating  quenches in different parameter regimes of the model.