We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation ͑RWA͒ 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.

We present a theoretical treatment for the dissipative two-resonator circuit quantum electrodynamics setup referred to as quantum switch. There, switchable coupling between two superconducting resonators is mediated by a superconducting qubit operating in the dispersive regime, where the qubit transition frequency is far detuned from those of the resonators. We derive an effective Hamiltonian for the quantum switch beyond the rotating wave approximation and provide a detailed study of the dissipative dynamics. As a central finding, we derive analytically how the qubit affects the quantum switch even if the qubit has no dynamics, and we estimate the strength of this influence. The analytical results are corroborated by numerical calculations, where coherent oscillations between the resonators, the decay of coherent and Fock states, and the decay of resonator-resonator entanglement are studied. Finally, we suggest an experimental protocol for extracting the damping constants of qubit and resonators by measuring the quadratures of the resonator fields.

We propose a startling hybrid quantum architecture for simulating a localization-delocalization transition. The concept is based on an array of superconducting flux qubits which are coupled to a diamond crystal containing nitrogen-vacancy (NV) centers. The underlying description is a Jaynes-Cummings-lattice in the strong-coupling regime. However, in contrast to well-studied coupled cavity arrays the interaction between lattice sites is mediated here by the qubit rather than by the oscillator degrees of freedom. Nevertheless, we point out that a transition between a localized and a delocalized phase occurs in this system as well. We demonstrate the possibility of monitoring this transition in a non-equilibrium scenario, including decoherence effects. The proposed scheme allows the monitoring of localization-delocalization transitions in Jaynes-Cummings-lattices by use of currently available experimental technology. Contrary to cavity-coupled lattices, our proposed recourse to stylized qubit networks facilitates (i) to investigate localization-delocalization transitions in arbitrary dimensions and (ii) to tune the inter-site coupling in-situ.

We propose a generalisation of dispersive qubit readout which provides the time evolution of a flux qubit observable. Our proposal relies on the non-linear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc-SQUID. Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection. The measurement process is simulated for the example of coherent qubit oscillations. This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.

We propose a scheme for monitoring coherent quantum dynamics with good time-resolution and low backaction, which relies on the response of the considered quantum system to high-frequency ac driving. An approximate analytical solution of the corresponding quantum master equation reveals that the phase of an outgoing signal, which can directly be measured in an experiment with lock-in technique, is proportional to the expectation value of a particular system observable. This result is corroborated by the numerical solution of the master equation for a charge qubit realized with a Cooper-pair box, where we focus on monitoring coherent oscillations.