Generalized rotating-wave approximation to biased qubit-oscillator systems

The generalized rotating-wave approximation with counter-rotating interactions has been applied to a biased qubit-oscillator system. Analytical expressions are explicitly given for all eigenvalues and eigenstates. For a flux qubit coupled to superconducting oscillators, spectra calculated by our approach are in excellent agreement with experiment. Calculated energy levels for a variety of biases also agree well with those obtained via exact diagonalization for a wide range of coupling strengths. Dynamics of the qubit has also been examined, and results lend further support to the validity of the analytical approximation employed here. Our approach can be readily implemented and applied to superconducting qubit-oscillator experiments conducted currently and in the near future with a biased qubit and for all accessible coupling strengths

Entanglement creation in circuit QED via Landau-Zener sweeps

A qubit may undergo Landau-Zener transitions due to its coupling to one or several quantum harmonic oscillators. We show that for a qubit coupled to one oscillator, Landau-Zener transitions can be used for single-photon generation and for the controllable creation of qubit-oscillator entanglement, with state-of-the-art circuit QED as a promising realization. Moreover, for a qubit coupled to two cavities, we show that Landau-Zener sweeps of the qubit are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the qubit acting as the entanglement mediator. At the heart of our proposals lies the calculation of the exact Landau-Zener transition probability for the qubit, by summing all orders of the corresponding series in time-dependent perturbation theory. This transition probability emerges to be independent of the oscillator frequencies, both inside and outside the regime where a rotating-wave approximation is valid.Comment: 12 pages, 7 figure