We have realized controllable coupling between two three-junction flux qubits by inserting an additional coupler loop between them, containing three Josephson junctions. Two of these are shared with the qubit loops, providing strong qubit-coupler interaction. The third junction gives the coupler a nontrivial current-flux relation; its derivative (i.e., the susceptibility) determines the coupling strength J, which thus is tunable in situ via the coupler's flux bias. In the qubit regime, J was varied from approximately 45 (antiferromagnetic) to approximately -55 mK (ferromagnetic); in particular, J vanishes for an intermediate coupler bias. Measurements on a second sample illuminate the relation between two-qubit tunable coupling and three-qubit behavior.

Laser cooling of the atomic motion paved the way for remarkable achievements in the fields of quantum optics and atomic physics, including Bose-Einstein condensation and the trapping of atoms in optical lattices. More recently superconducting qubits were shown to act as artificial two-level atoms, displaying Rabi oscillations, Ramsey fringes, and further quantum effects 1,2,3 . Coupling such qubits to resonators 4,5,6,7 brought the superconducting circuits into the realm of quantum electrodynamics (circuit QED). It opened the perspective to use superconducting qubits as micro-coolers or to create a population inversion in the qubit to induce lasing behavior of the resonator 8,9,10,11 . Furthering these analogies between quantum optical and superconducting systems we demonstrate here Sisyphus cooling 12 of a low frequency LC oscillator coupled to a near-resonantly driven superconducting qubit. In the quantum optics setup the mechanical degrees of freedom of an atom are cooled by laser driving the atom's electronic degrees of freedom. Here the roles of the two degrees of freedom are played by the LC circuit and the qubit's levels, respectively. We also demonstrate the counterpart of the Sisyphus cooling, namely Sisyphus amplification.For red-detuned high-frequency driving of the qubit the low-frequency LC circuit performs work in the forward and backward part of the oscillation cycle, always pushing the qubit up in energy, similar to Sisyphus who always had to roll a stone uphill. The oscillation cycle is completed with a relaxation process, when the work performed by the oscillator together with a quantum of energy of the high-frequency driving is released by the qubit to the environment via spontaneous emission. For blue-detuning the same mechanism creates excitations in the LC circuit with a tendency towards lasing and the characteristic line-width narrowing. In this regime "lucky Sisyphus" always rolls the stone downhill. Parallel to the experimental demonstration we analyze the system theoretically and find quantitative agreement, which supports the interpretation and allows us to estimate system parameters.The system considered is shown in the inset of Fig. 1. It consists of a three-junction flux qubit 13 , with the two qubit FIG. 1: (a) The energy levels of the qubit as a function of the energy bias of the qubit ε(fx) = 2Φ0Ipfx. The sinusoidal current in the tank coil, indicated by the wavy line, drives the bias of the qubit. The starting point of the cooling (heating) cycles is denoted by blue (red) dots. The resonant excitation of the qubit due to the high-frequency driving, characterized by ΩR0, is indicated by two green arrows and by the Lorentzian depicting the width of this resonance. The relaxation of the qubit is denoted by the black dashed arrows. The inset shows a schematic of the qubit coupled to an LC circuit. The high frequency driving is provided by an on-chip microwave antenna. (b) SEM picture of the superconducting flux qubit prepared by shadow evaporation technique.

We compare the results of ground state and spectroscopic measurements carried out on superconducting flux qubits which are effective two-level quantum systems. For a single qubit and for two coupled qubits we show excellent agreement between the parameters of the pseudospin Hamiltonian found using both methods. We argue that by making use of the ground state measurements the Hamiltonian of N coupled flux qubits can be reconstructed as well at temperatures smaller than the energy level separation. Such a reconstruction of a many-qubit Hamiltonian can be useful for future quantum information processing devices.

We study the loss rate for a set of lambda/2 coplanar waveguide resonators at millikelvin temperatures (20 mK - 900mK) and different applied powers (3E-19 W - 1E-12 W). The loss rate becomes power independent below a critical power. For a fixed power, the loss rate increases significantly with decreasing temperature. We show that this behavior can be caused by two-level systems in the surrounding dielectric materials. Interestingly, the influence of the two-level systems is of the same order of magnitude for the different material combinations. That leads to the assumption that the nature of these two-level systems is material independent.Comment: 3 pages, 5 figures, Submitted to Applied Physics Letter

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.

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 back action on the qubit. The detailed theoretical analysis and simulations give good agreement with the experimental data and allow us to make the qubit characterization.

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 inductance and resistance 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 the multiphoton fringes. PACS numbers: 74.25.Nf, 85.25.Am, 85.25.Hv, 03.67.Mn.

The current-phase relationship has been measured as a function of temperature for niobium nanobridges with different widths. A deformation from Josephson-like sinusoidal characteristics at high temperatures to sawtooth shaped curves at intermediate and multivalued relationships at low temperatures was observed. Based on this, possible hysteresis in the current-voltage characteristics of niobium nanobridge superconducting quantum interference devices can be attributed to phase slippage.