Rabi model and spin-boson model

Jorge Casanova, Ricardo Puebla, Hector Moya-Cessa +1 more

Abstract We establish an approximate equivalence between a generalised quantum Rabi model and its nth order counterparts, where spin-boson interactions are nonlinear as they comprise a simultaneous exchange of n bosonic excitations. Although there exists no unitary transformation between these models, we demonstrate their equivalence to a good approximation in a wide range of parameters. This shows that nonlinear spin-boson couplings, i.e., nth order quantum Rabi models, are accessible to quantum systems with only linear coupling between boson and spin modes by simply adding spin rotations and after an appropriate transformation. Furthermore, our result prompts novel approximate analytical solutions to the dynamics of the quantum Rabi model in the ultrastrong coupling regime improving previous approaches.

Fumio Hiroshima

Jorge Casanova, Ricardo Puebla, H. M. Moya-Cessa +1 more

We establish an approximate equivalence between a generalised quantum Rabi model and its nth order counterparts, where spinboson interactions are nonlinear as they comprise a simultaneous exchange of n bosonic excitations. Although there exists no unitary transformation between these models, we demonstrate their equivalence to a good approximation in a wide range of parameters. This shows that nonlinear spin-boson couplings, i.e., nth order quantum Rabi models, are accessible to quantum systems with only linear coupling between boson and spin modes by simply adding spin rotations and after an appropriate transformation. Furthermore, our result prompts novel approximate analytical solutions to the dynamics of the quantum Rabi model in the ultrastrong coupling regime improving previous approaches.

Juan José García‐Ripoll

Thomas Hamlyn, Chi Zhang, Igor Lesanovsky +1 more

We investigate a tripartite quantum Rabi model (TQRM) wherein a bosonic mode concurrently couples to two spin- 1/2 particles through a spin-spin interaction, resulting in a spin-spin-boson coupling—a departure from conventional quantum Rabi models featuring bipartite spin-boson couplings. The symmetries of the TQRM depend on the detuning parameter, representing the energy difference between the spin states. At zero detuning a parity symmetry renders the TQRM reducible to a quantum Rabi model. A subradiant-to-superradiant transition in the ground state is predicted as the tripartite coupling strength increases. For nonzero detuning the total spin emerges as the sole conserved quantity in the TQRM. It is found that superradiance prevails in the ground state as long as the tripartite coupling remains nonzero. We derive the Braak G function of the TQRM analytically, with which the eigenspectra are obtained. The TQRM can be realized in a viable trapped Rydberg ion quantum simulator, where the required tripartite couplings and single-body interactions in the TQRM are naturally present. Our study opens opportunities to explore and create correlations and entanglement in the spin and motional degrees of freedoms with the TQRM. Published by the American Physical Society 2024

Abraham Klein