We analyze a system composed of a superconducting flux qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonators harmonics. The first strong signal is used for exciting the system to a high energeti
c state while a second weak signal is applied for probing effective eigenstates of the system. In the framework of doubly dressed states we showed the possibility of amplification and attenuation of the probe signal by direct transitions at the Rabi frequency. We present a brief review of theoretical and experimental works where a direct resonance at Rabi frequency have been investigated in superconducting flux qubits. The interaction of the qubit with photons of two harmonics has prospects to be used as a quantum amplifier (microwave laser) or an attenuator.
A system of a two-level atom of an impurity (qubit) inserted into a periodic chain coupled to the continuum is studied with the use of the effective non-Hermitian Hamiltonian. Exact solutions are derived for the quasistationary eigenstates, their com
plex energies, and transport properties. Due to the presence of the qubit, two long-lived states corresponding to the ground and excited states of the qubit emerge outside the Bloch energy band. These states remain essentially localized at the qubit even in the limit of sufficiently strong coupling between the chain and the environment when the super-radiant states are formed. The transmission through the chain is studied as a function of the continuum coupling strength and the chain-qubit coupling; the perfect resonance transmission takes place through isolated resonances at weak and strong continuum coupling, while the transmission is lowered in the intermediate regime.
We report measurements of transfer functions and flux shifts of 20 on-chip high T$_C$ DC SQUIDs half of which were made purposely geometrically asymmetric. All of these SQUIDs were fabricated using standard high T$_C$ thin film technology and they we
re single layer ones, having 140 nm thickness of YBa$_2$Cu$_3$O$_{7-x}$ film deposited by laser ablation onto MgO bicrystal substrates with 24$^0$ misorientation angle. For every SQUID the parameters of its intrinsic asymmetry, i. e., the density of critical current and resistivity of every junction, were measured directly and independently. We showed that the main reason for the on-chip spreading of SQUIDs voltage-current and voltage-flux characteristics was the intrinsic asymmetry. We found that for SQUIDs with a relative large inductance ($L>120 $ pH) both the voltage modulation and the transfer function were not very sensitive to the junctions asymmetry, whereas SQUIDs with smaller inductance ($Lsimeq 65-75 $ pH) were more sensitive. The results obtained in the paper are important for the implementation in the sensitive instruments based on high T$_C$ SQUID arrays and gratings.
We use the density matrix formalism to analyze the interaction of interferometer-type superconducting qubits with a high quality tank circuit, which frequency is well below the gap frequency of a qubit. We start with the ground state characterization
of the superconducting flux and charge qubits. Then, by making use of a dressed state approach we describe the qubits spectroscopy when the qubit is irradiated by a microwave field which is tuned to the gap frequency. The last section of the paper is devoted to continuous monitoring of qubit states by using a DC SQUID in the inductive mode.
