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The Quantum Rabi Model: coupling regimes, analytic solutions and dynamics

Elena Lupo (University of Palermo)

Place: Sala de Videoconferencias
Time: 5.4.2017, 10:30
Title: The Quantum Rabi Model: coupling regimes, analytic solutions and dynamics

Despite the Quantum Rabi Model has been studied for years as model for the description of the light-matter interaction, the explicit expression of the static and dynamical solutions is not found yet, even if important progresses have been recently reported to award this objective. With the help of specific approximations, effective exactly solvable Hamiltonians are found in some coupling regimes (JC, BS or perturbative DSC Hamiltonian for instance), but it could be of interest analyzing a specific problem taking in account the whole Hamiltonian. Professors Messina and Napoli suggested to me to investigate the question of the instability of the vacuum state of the Quantum Rabi Hamiltonian, i.e they suggested to study the survival amplitude of the state with no excitation. Restricting ourselves to the subspace of defined excitation number parity, the problem can be reduced in finding the action of a generic power of the transformed Hamiltonian on the vacuum state. In my report I will try to explain how the projection in the vacuum state of the evolved initial condition is linked to the combinatorial problem of the Motzkin paths well studied in the number theory.