The engineering of quantum devices has reached the stage where we now have small scale quantum processors containing multiple interacting qubits within them. Simple quantum circuitshave been demonstrated and scaling up to larger numbers is underway. However as the number of qubits in these processors increases, it becomes challenging to implement switchable or tunable coherent coupling among them. The typical approach has been to detune each qubit from others or the quantum bus it connected to, but as the number of qubits increases this becomes problematic to achieve in practice due to frequency crowding issues. Here, we demonstrate that by applying a fast longitudinal control field to the target qubit, we can turn off its couplings to other qubits or buses (in principle on/off ratio higher than 100 dB). This has important implementations in superconducting circuits as it means we can keep the qubits at their optimal points, where the coherence properties are greatest, during coupling/decoupling processing. Our approach suggests a new way to control coupling among qubits and data buses that can be naturally scaled up to large quantum processors without the need for auxiliary circuits and yet be free of the frequency crowding problems.
With the assistance of a single cyclic three-level system, which can be realized by a superconducting flux qubit, we study theoretically the degenerate microwave parametric down-conversion(PDC) in the superconducting transmission line resonator with the fundamental and second harmonic modes involved. By adiabatically eliminating the excited states of the three-level system, we obtain an effective microwave PDC Hamiltonian for the two modes in the resonator. In our system, the PDC efficiency can be much larger than that in the case of two-level system interacting with two-mode transmission line resonator [K. Moon and S. M. Girvin, Phys. Rev. Lett. {\bf 95}, 140504 (2005)]. With the effective coupling between those two resonator modes, a coherent driving of the second harmonic mode can lead to the squeezing and bunching effect of the fundamental one.
In order to examine whether or not the quantum phase transition of Dicke type
exists in realistic systems, we revisit the model setup of the superconducting
circuit QED from a microscopicmany-body perspective based on the BCS theory
with pseudo-spin presentation. By deriving the Dicke model with the correct
charging terms from the minimum coupling principle, it is shown that the
circuit QED system can exhibit superradiant quantum phase transition in the
limit Nrightarrowinfty. The critical point could be reached at easiness by
adjusting the extra parameters, the ratio of Josephson capacitance C_{J} to
gate capacitance C_{g}, as well as the conventional one, the ratio of Josephson
energy E_{J} to charging energy E_{C}.