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

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

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

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

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.

Resonant excitations of single and two-qubit systems coupled to a tank circuit

The interaction of flux qubits with a low frequency tank circuit is studied. It is shown that changes in the state of the interacting qubits influence the effective impedance of the circuit, which is the essence of the so-called impedance measurement technique. The multiphoton resonant excitations in both single flux qubits and pairs of coupled flux qubits are investigated. In particular, we compare our theoretical results with recent spectroscopy measurements, Landau-Zener interferometry, and multiphoton fringes.Comment: 11 pages, 11 figures; v.2: minor change

Multiphoton transitions in Josephson-junction qubits (Review Article)

Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator's state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent results for the driven superconducting qubit-resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau-Zener-St\"uckelberg interferometry, the multiphoton transitions of both direct and ladder- type character, and creation of the inverse population for lasing.Comment: 20 pages, 15 figure

Low-frequency measurement of the tunneling amplitude in a flux qubit

We have observed signatures of resonant tunneling in an Al three-junction qubit, inductively coupled to a Nb LC tank circuit. The resonant properties of the tank oscillator are sensitive to the effective susceptibility (or inductance) of the qubit, which changes drastically as its flux states pass through degeneracy. The tunneling amplitude is estimated from the data. We find good agreement with the theoretical predictions in the regime of their validity.Comment: REVTeX4, 3pp., 3 EPS figures. v2: new sample, textual clarifications. v3: minor polishing; final, to appear in PRB Rapid

Multiphoton excitations and inverse population in two-flux-qubit system

We study spectroscopy of artificial solid-state four-level quantum system. This system is formed by two coupled superconducting flux qubits. When multiple driving frequency of the applied microwaves matches the energy difference between any two levels, the transition to the upper level is induced. We demonstrate two types of the multi-photon transitions: direct transitions between two levels and ladder-type transitions via an intermediate level. For the latter transitions, in particular, the inverse population of the excited state with respect to the ground one is realized. These processes can be useful for the control of the level population for the multilevel scalable quantum systems.Comment: 4 pages, 2 figures; v.2: minor change

Weak continuous monitoring of a flux qubit using coplanar waveguide resonator

We study a flux qubit in a coplanar waveguide resonator by measuring transmission through the system. In our system with the flux qubit decoupled galvanically from the resonator, the intermediate coupling regime is achieved. In this regime dispersive readout is possible with weak backaction on the qubit. The detailed theoretical analysis and simulations give a good agreement with the experimental data and allow to make the qubit characterization.Comment: 4 pages, 3 figures, to be published in Phys. Rev.