In this report, we have studied exceptional spectra of the two-qubit quantum Rabi model in two situations. Firstly, an exceptional spectra is achieved in resonant condition, in which the frequencies of two qubit and photon field satisfy resonant relation. With transformed rotating-wave approximation (TRWA) method, the Rabi model can be mapped into the solvable formation in qubit-photon Fock states space. Based on the quantum supperconducting circuits experiment setup, the best value range of the system parameters are discussed. In the resonant station working window, the energy spectrums are calculated. Secondly, a special quasi-exact solution of two qubits Rabi model in reservoir is achieved. The algebraic structure of Hamiltonian is analyzed in the photon number space, a closed quasi-exact eigenstates space is found, and the quasi-exact solution can be clearly found from the algebraic structure of Hamiltonian. The results could be used to test quantum Rabi model.In this report, we have studied exceptional spectra of the two-qubit quantum Rabi model in two situations. Firstly, an exceptional spectra is achieved in resonant condition, in which the frequencies of two qubit and photon field satisfy resonant relation. With transformed rotating-wave approximation (TRWA) method, the Rabi model can be mapped into the solvable formation in qubit-photon Fock states space. Based on the quantum supperconducting circuits experiment setup, the best value range of the system parameters are discussed. In the resonant station working window, the energy spectrums are calculated. Secondly, a special quasi-exact solution of two qubits Rabi model in reservoir is achieved. The algebraic structure of Hamiltonian is analyzed in the photon number space, a closed quasi-exact eigenstates space is found, and the quasi-exact solution can be clearly found from the algebraic structure of Hamiltonian. The results could be used to test quantum Rabi model.

arXiv:1609.01847Sep 7, 20160 citations

Solution of the two-qubit quantum Rabi model and its exceptional eigenstates

Jie Peng, Zhongzhou Ren, Daniel Braak +4 more

We have studied the two-qubit quantum Rabi model in the asymmetric case and its generalizations with dipole and Heisenberg-type qubit-qubit interactions. The solutions are obtained analytically with eigenstates given in terms of the extended coherent states or photon number states. For identical qubit-photon couplings, a novel type of quasi-exact solution which exists for all coupling values with constant eigenenergy is found, leading to level crossings within the same parity subspace even for non-identical qubits. In contrast to the quasi-exact eigenstates of the single-qubit model, these exceptional eigenstates are formed by just a few Fock states (photon number bounded from above at one or three), and the condition for them depends only on a fine-tuning of the qubit level splittings with respect to the photon energy, but not on the coupling to the photon field if the qubit-qubit interaction is not taken into consideration. This makes them excellent candidates for direct experimental observation within circuit quantum electrodynamics (QED) and application in single photon experiments. Besides, exceptional solutions with finite photon numbers N are also found.We have studied the two-qubit quantum Rabi model in the asymmetric case and its generalizations with dipole and Heisenberg-type qubit-qubit interactions. The solutions are obtained analytically with eigenstates given in terms of the extended coherent states or photon number states. For identical qubit-photon couplings, a novel type of quasi-exact solution which exists for all coupling values with constant eigenenergy is found, leading to level crossings within the same parity subspace even for non-identical qubits. In contrast to the quasi-exact eigenstates of the single-qubit model, these exceptional eigenstates are formed by just a few Fock states (photon number bounded from above at one or three), and the condition for them depends only on a fine-tuning of the qubit level splittings with respect to the photon energy, but not on the coupling to the photon field if the qubit-qubit interaction is not taken into consideration. This makes them excellent candidates for direct experimental observation within circuit quantum electrodynamics (QED) and application in single photon experiments. Besides, exceptional solutions with finite photon numbers N are also found.

Journal of Physics A Mathematical and TheoreticalJun 12, 201460 citations

Multi-photon Rabi model: Generalized parity and its applications

Bartłomiej Gardas, Jerzy Dajka

Physics Letters AOct 10, 201310 citations

Analytical Solutions to Asymmetric Two-Photon Rabi Model

Marzieh Baradaran, Luis Miguel Nieto, S. Zarrinkamar

Jan 1, 20260 citations

N-photon solutions to the two-qubit quantum Rabi model

Qiang Lin, Junlong Tian, Pinghua Tang +1 more

We studied the two-qubit quantum Rabi model and found its dark state solutions with at most N photons. One peculiar case presents when $N=3$ , which has constant eigenenergy in the whole coupling regime and leads to level crossings within the same parity subspace. We also discovered asymptotic solutions with at most $N=2i+3$ $(i=1,2,3,\dots)$ photons, and constant eigenenergy $N\hbar ω$ when coupling $g$ becomes much larger than photon frequency $ω$ . Although generally all photon number states are involved in the two-qubit quantum Rabi model, such $N$ -photon solutions exist and may have applications in quantum information processing with ultrastrong couplings.We studied the two-qubit quantum Rabi model and found its dark state solutions with at most N photons. One peculiar case presents when $N=3$, which has constant eigenenergy in the whole coupling regime and leads to level crossings within the same parity subspace. We also discovered asymptotic solutions with at most $N=2i+3$ $(i=1,2,3,\dots)$ photons, and constant eigenenergy $N\hbar ω$ when coupling $g$ becomes much larger than photon frequency $ω$. Although generally all photon number states are involved in the two-qubit quantum Rabi model, such $N$-photon solutions exist and may have applications in quantum information processing with ultrastrong couplings.

arXiv:2406.02418Jun 4, 20240 citations

We studied the two-qubit quantum Rabi model and found its dark state solutions with at most N photons. One peculiar case presents when

N=3

, which has constant eigenenergy in the whole coupling regime and leads to level crossings within the same parity subspace. We also discovered asymptotic solutions with at most

N=2i+3

(i=1,2,3,\dots)

photons, and constant eigenenergy

N\hbar ω

when coupling

g

becomes much larger than photon frequency

ω

. Although generally all photon number states are involved in the two-qubit quantum Rabi model, such

N

-photon solutions exist and may have applications in quantum information processing with ultrastrong couplings.