Qubit-oscillator dynamics in the dispersive regime: Analytical theory beyond the rotating-wave approximation

We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive qubit readout is possible. If several qubits are coupled to one resonator, an effective qubit-qubit interaction of Ising type emerges, whereas RWA leads to isotropic $XY$ interaction. This impacts on the entanglement characteristics of the qubits.

Figure 1

(Color online) Oscillator frequency shift as function or the qubit splitting $ϵ=\omega +\Delta$ for the spin state $|\downarrow ⟩$ obtained (a) within RWA [Eq. (10)] and (b) beyond RWA [Eq. (17)]. The lines mark the analytical results, while the symbols refer to the numerically obtained splitting between the ground state and the first-excited state in the subspace of the qubit state $|\downarrow ⟩$.