Xiaoyong Guo

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

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.

Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators

We have found the algebraic structure of the two-qubit quantum Rabi model behind the possibility of its novel exceptional eigenstates with finite photon numbers by analyzing the Hamiltonian in the photon number space. The exceptional solutions with at most 1 photon exist in the whole qubit?photon coupling regime with constant eigenenergy equal to single photon energy , which can be clearly demonstrated from the Hamiltonian structure. With a similar method, we find that these special dark-state-like eigenstates (the eigenenergy is coupling-independent, but the wave function is coupling-dependent) commonly exist for the two-qubit Jaynes?Cummings model, with (), and one of them is also the eigenstate of the two-qubit quantum Rabi model, which is interesting for application in a simpler way. Besides, using Bogoliubov operators, we analytically retrieve the solution of the general two-qubit quantum Rabi model. In this concise and physical way, we clearly see how the eigenvalues of the infinite-dimensional two-qubit quantum Rabi Hamiltonian are determined by a convergent power series, so that the solution can reach arbitrary accuracy conveniently because of the convergence property.