Direct Josephson coupling between superconducting flux qubits

We have demonstrated strong antiferromagnetic coupling between two three-junction flux qubits based on a shared Josephson junction, and therefore not limited by the small inductances of the qubit loops. The coupling sign and magnitude were measured by coupling the system to a high-quality superconducting tank circuit. Design modifications allowing to continuously tune the coupling strength and/or make the coupling ferromagnetic are discussed.Comment: REVTeX 4, 4 pages, 5 figures; v2: completely rewritten, added finite-temperature results and proposals for ferromagnetic galvanic couplin

Metastable Voltage States of Coupled Josephson Junctions

We investigate a chain of capacitively coupled Josephson junctions in the regime where the charging energy dominates over the Josephson coupling, exploiting the analogy between this system and a multi-dimensional crystal. We find that the current-voltage characteristic of the current-driven chain has a staircase shape, beginning with an (insulating) non-zero voltage plateau at small currents. This behavior differs qualitatively from that of a single junction, which should show Bloch oscillations with vanishing dc voltage. The simplest system where this effect can be observed consists of three grains connected by two junctions. The theory explains the results of recent experiments on Josephson junction arrays.Comment: 5 pages, 4 figures include

Four-qubit device with mixed couplings

We present the first experimental results on a device with more than two superconducting qubits. The circuit consists of four three-junction flux qubits, with simultaneous ferro- and antiferromagnetic coupling implemented using shared Josephson junctions. Its response, which is dominated by the ground state, is characterized using low-frequency impedance measurement with a superconducting tank circuit coupled to the qubits. The results are found to be in excellent agreement with the quantum-mechanical predictions.Comment: REVTeX 4, 5pp., 7 EPS figure files. N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. v2: final published version, with changed title, different sample micrograph, and several clarification

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.

Theory of weak continuous measurements in a strongly driven quantum bit

Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector, namely, a spectrum of voltage fluctuations and an impedance, are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating wave approximations. Backaction effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about a frequency and a decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behaviour as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.Comment: 28 page

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

A Fully Quantum Mechanical Model of a SQUID Ring Coupled to an Electromagnetic Field

A quantum system comprising of a monochromatic electromagnetic field coupled to a SQUID ring with sinusoidal non-linearity, is studied. A magnetostatic flux $\Phi_{x}$ is also threading the SQUID ring, and is used to control the coupling between the two systems. It is shown that for special values of $\Phi_{x}$ the system is strongly coupled. The time evolution of the system is studied. It is shown that exchange of energy takes place between the two modes and that the system becomes entangled. A second quasi-classical model that treats the electromagnetic field classically is also studied. A comparison between the fully quantum mechanical model with the electromagnetic field initially in a coherent state and the quasi-classical model, is made.Comment: 7 pages, 9 figures. Uploaded as implementing a policy of arXiving old paper