Dark-like states for the multi-qubit and multi-photon Rabi models

Abstract

Abstract. There are well-known dark states in the even-qubit Dicke models, which are the products of the two-qubit singlets and a Fock state, where the qubits are decoupled from the photon field. These spin singlets can be used to store quantum correlations since they preserve entanglement even under dissipation, driving and dipole-dipole interactions. One of the features for these dark states is that their eigenenergies are independent of the qubitphoton coupling strength. We have obtained a novel kind of dark-like states for the multi-qubit and multi-photon Rabi models, whose eigenenergies are also constant in the whole coupling regime. Unlike the dark states, the qubits and photon field are coupled in the dark-like states. Furthermore, the photon numbers are bounded from above commonly at 1, which is different from that for the one-qubit case. The existence conditions of the dark-like states are simpler than exact isolated solutions, and may be fine tuned in experiments. While the single-qubit and multi-photon Rabi model is well-defined only if the photon number M ≤ 2 and the coupling strength is below a certain critical value, the dark-like eigenstates for multi-qubit and multiphoton Rabi model still exist, regardless of these constraints. In view of these properties of the dark-like states, they may find similar applications like "dark states" in quantum information.

Symmetries in the Quantum Rabi Model

“…Otherwise, the single free integration constant c would not suffice to break off the series expansions forφ 1,2 at finite order. This is the reason a quasi-exact spectrum does not exist in the isotropic Dicke model [27] but is possible in the anisotropic Dicke models, where more parameters can be adjusted to eliminate the higher orders in expansions given by recurrence relations with more than three terms [43].…”

Digital-analog quantum simulation of generalized Dicke models with superconducting circuits

“… 10 , or in the inhomogeneous Dicke model wherever closed subspaces are produced in the dynamics, see ref. 53 . The numerical simulations we performed show that the protocol is feasible for the analyzed cases, where the number of bosonic excitations does not grow much.…”

Nonlinear two-photon Rabi-Hubbard model: Superradiance, photon, and photon-pair Bose-Einstein condensates

“…A lot of attention has been given to the two-photon Rabi model, its applications [32][33][34][35], and the spectral collapse [36][37][38][39][40][41][42][43] it undergoes in certain regions of its parameter space.…”

“…For example, it has been used to describe second-order processes in Rydberg atoms in cavities [32] and quantum dots [33,34], and mechanisms have been proposed to realize it in circuit QED [35]. The two-photon model undergoes spectral collapse where the Hamiltonian is no longer bounded when the coupling exceeds a certain value [36][37][38][39][40][41][42][43].…”