Quantum theory of the low-frequency linear susceptibility of interferometer-type superconducting qubits

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.Comment: 11 pages, 5 figures; the title and abstract are slightly changed; several typos are corrected; in order to make our argumentation more clear we added some comments in the introduction and other section

Magnetic flux noise in the three Josephson junctions superconducting ring

We analyze the influence of noise on magnetic properties of a su- perconducting loop which contains three Josephson junctions. This circuit is a classical analog of a persistent current (flux) qubit. A loop supercurrent induced by external magnetic field in the presence of thermal fluctuations is calculated. In order to get connection with experiment we calculate the impedance of the low-frequency tank cir- cuit which is inductively coupled with a loop of interest. We compare obtained results with the results in quantum mode - when the three junction loop exhibits quantum tunneling of the magnetic flux. We demonstrate that the tank-loop impedance in the classical and quan- tum modes have different temperature dependence and can be easily distinguished experimentally.Comment: 19 pages 9 figure

Radio-Frequency Method for Investigation of Quantum Properties of Superconducting Structures

We implement the impedance measurement technique (IMT) for characterization of interferometer-type superconducting qubits. In the framework of this method, the interferometer loop is inductively coupled to a high-quality tank circuit. We show that the IMT is a powerful tool to study a response of externally controlled two-level system to different types of excitations. Conclusive information about qubits is obtained from the read-out of the tank properties.Comment: 10 pages, 10 figures;to be published in Fizika Nizkikh Temperatur (Low Temperature Physics); v3: minor polishing; fina

Paramagnetic effect in YBaCuO grain boundary junctions

A detailed investigation of the magnetic response of YBaCuO grain boundary Josephson junctions has been carried out using both radio-frequency measurements and Scanning SQUID Microscopy. In a nominally zero-field-cooled regime we observed a paramagnetic response at low external fields for 45 degree asymmetric grain boundaries. We argue that the observed phenomenology results from the d-wave order parameter symmetry and depends on Andreev bound states.Comment: To be published in Phys. Rev.

Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit

Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a _continuously_ observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of_Rabi spectroscopy_ enabled a long coherence time of about 2.5 microseconds, corresponding to an effective qubit quality factor \~7000.Comment: REVTeX4, 4pp., 4 EPS figure files. v3: changed title, fixed typos; final, to appear in PR

Low-frequency characterization of quantum tunneling in flux qubits

We propose to investigate flux qubits by the impedance measurement technique (IMT), currently used to determine the current--phase relation in Josephson junctions. We analyze in detail the case of a high-quality tank circuit coupled to a persistent-current qubit, to which IMT was successfully applied in the classical regime. It is shown that low-frequency IMT can give considerable information about the level anticrossing, in particular the value of the tunneling amplitude. An interesting difference exists between applying the ac bias directly to the tank and indirectly via the qubit. In the latter case, a convenient way to find the degeneracy point in situ is described. Our design only involves existing technology, and its noise tolerance is quantitatively estimated to be realistic.Comment: 6 pages, 11 figures, to appear in Phys.Rev.

Quantum behaviour of a flux qubit coupled to a resonator

We present a detailed theoretical analysis for a system of a superconducting flux qubit coupled to a transmission line resonator. The master equation, accounting incoherent processes for a weakly populated resonator, is analytically solved. An electromagnetic wave transmission coefficient through the system, which provides a tool for probing dressed states of the qubit, is derived. We also consider a general case for the resonator with more than one photon population and compare the results with an experiment on the qubit-resonator system in the intermediate coupling regime, when the coupling energy is comparable with the qubit relaxation rate.Comment: 16 pages, 6 figure

Magnetic flux noise in the three Josephson junctions superconducting ring

We analyze the influence of noise on magnetic properties of a superconducting loop which contains three Josephson junctions. This circuit is a classical analog of a persistent current (flux) qubit. A loop supercurrent induced by external magnetic field at the presence of thermal fluctuations is calculated. In order to get connection with experiment we calculate the impedance of the low-frequency tank circuit which is inductively coupled with a loop of interest. We compare obtained results with the results in quantum mode — when the three junction loop exhibits quantum tunneling of the magnetic flux. We demonstrate that the tank-loop impedance in the classical and quantum modes have different temperature dependence and can be easily distinguished experimentally

Method for direct observation of coherent quantum oscillations in a superconducting phase qubit

Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems were so far restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a new method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop are detected by a high quality resonant tank circuit, inductively coupled to the phase qubit. Detailed calculation for zero and non-zero temperature are made for the case of persistent current qubit. According to the estimates for dephasing and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in MHz range.Comment: 5 pages, 1 figure, to appear in Phys.Rev.

Anomalous Periodicity of the Current-Phase Relationship of Grain-Boundary Josephson Junctions in High-Tc Superconductors

The current-phase relation (CPR) for asymmetric 45 degree Josephson junctions between two d-wave superconductors has been predicted to exhibit an anomalous periodicity. We have used the single-junction interferometer to investigate the CPR for this kind of junctions in YBCO thin films. Half-fluxon periodicity has been experimentally found, providing a novel source of evidence for the d-wave symmetry of the pairing state of the cuprates.Comment: 4 pages, 5 figure