Quantum Simulation of the Periodic Quantum Rabi Model at Deep Strong Coupling

Abstract

The quantum Rabi model (QRM) stands as perhaps the most fundamental framework describing qubit-light interaction. While observations of many experiments can already be described within the Jaynes-Cummings model, which represents the limit of the quantum Rabi model in the weak coupling regime, establishing experimental investigations for high coupling strengths, where the full Hamiltonian has is applicable, remains a challenge. This is most prominent for the case of deep strong coupling, where the coupling strength between the qubit and the light field is the dominating energy in the system, giving rise to counter-intuitive effects such as creating excitations out of the vacuum. <br /> In this work, experiments realizing a quantum simulation of the periodic quantum Rabi model (pQRM), which is a generalization of the original quantum Rabi model applicable to cold atoms in a periodic lattice potential, are reported. A bosonic field mode is realized by the harmonic trapping potential of an optical dipole trap for ultra-cold rubidium atoms, and a qubit two-level system is encoded in the Bloch band structure of a superimposed optical lattice potential. Overlaying these two potentials onto a rubidium Bose-Einstein condensate induces a coupling strength equivalent to 6.5 times the characteristic energies within the system. The mapping between the two systems becomes evident through the introduction of the Bloch ansatz, where the experimentally simulated system within the first Brillouin zone fully reflects the dynamics of the quantum Rabi model. However, stepping beyond this range gives rise to a quantum simulation of a periodic variant of the quantum Rabi model (pQRM), which constitutes the central focus of this thesis. At long interaction times, collapse and revival of the excitation number, as well as a revival of the initial state are experimentally observed. <br /> The reported quantum simulation of the periodic quantum Rabi model demonstrates the phase-coherence of Schrödinger cat-like states far in the deep strong coupling regime. Interestingly, the realized Hamiltonian maps onto superconducting fluxonium qubit systems. Further prospects of this work include applications in atom-based quantum information processing.