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The key issue for the implementation of a metamaterial is to demonstrate the existence of collective modes corresponding to coherent oscillations of the meta-atoms. Atoms of natural materials interact with electromagnetic fields as quantum two-level systems. Artificial quantum two-level systems can be made, for example, using superconducting nonlinear resonators cooled down to their ground state. Here we perform an experiment in which 20 of these quantum meta-atoms, so-called flux qubits, are embedded into a microwave resonator. We observe the dispersive shift of the resonator frequency imposed by the qubit metamaterial and the collective resonant coupling of eight qubits. The realized prototype represents a mesoscopic limit of naturally occurring spin ensembles and as such we demonstrate the AC-Zeeman shift of a resonant qubit ensemble. The studied system constitutes the implementation of a basic quantum metamaterial in the sense that many artificial atoms are coupled collectively to the quantized mode of a photon field.

We study the microwave absorption of a driven three-level quantum system, which is realized by a superconducting flux quantum circuit (SFQC), with a magnetic driving field applied to the two upper levels. The interaction between the three-level system and its environment is studied within the Born-Markov approximation, and we take into account the effects of the driving field on the damping rates of the three-level system. We study the linear response of the driven three-level SFQC to a weak probe field. The linear magnetic susceptibility of the SFQC can be changed by both the driving field and the bias magnetic flux. When the bias magnetic flux is at the optimal point, the transition from the ground state to the second excited state is forbidden and the three-level SFQC has a ladder-type transition. Thus, the SFQC responds to the probe field like natural atoms with ladder-type transitions. However, when the bias magnetic flux deviates from the optimal point, the three-level SFQC has a cyclic transition, thus it responds to the probe field like a combination of natural atoms with ladder-type transitions and natural atoms with $\Lambda$-type transitions. In particular, we provide detailed discussions on the conditions for realizing electromagnetically induced transparency and Autler-Townes splitting in three-level SFQCs., Comment: 20 pages, 8 figures

The requirements of quantum computations impose high demands on the level of qubit protection from perturbations; in particular, from those produced by the environment. Here we propose a superconducting flux qubit design that is naturally protected from ambient noise. This decoupling is due to the qubit interacting with the electromagnetic field only through its toroidal moment, which provides an unusual qubit-field interaction, which is suppressed at low frequencies.

We investigate the complex conductivity of a highly disordered MoC superconducting film with $k_Fl\approx 1$, where $k_F$ is the Fermi wavenumber and $l$ is the mean free path, derived from experimental transmission characteristics of coplanar waveguide resonators in a wide temperature range below the superconducting transition temperature $T_c$. We find that the original Mattis-Bardeen model with a finite quasiparticle lifetime, $\tau$, offers a perfect description of the experimentally observed complex conductivity. We show that $\tau$ is appreciably reduced by scattering effects. Characteristics of the scattering centers are independently found by the scanning tunneling spectroscopy and agree with those determined from the complex conductivity., Comment: 8 pages, 10 figures

We have measured the current-phase relationship $I(\ensuremath{\phi})$ of symmetric 45\ifmmode^\circ\else\textdegree\fi{} ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ grain boundary Josephson junctions. Substantial deviations of the Josephson current from conventional tunnel-junction behavior have been observed: (i) The critical current exhibits, as a function of temperature $T$, a local minimum at a temperature ${T}^{*}$. (ii) At $T\ensuremath{\approx}{T}^{*}$, the first harmonic of $I(\ensuremath{\phi})$ changes sign. (iii) For $Tl{T}^{*}$, the second harmonic of $I(\ensuremath{\phi})$ is comparable to the first harmonic, and (iv) the ground state of the junction becomes degenerate. The results are in good agreement with a microscopic model of Josephson junctions between $d$-wave superconductors.

We report an experimental and theoretical study of various metastable states of a superconducting loop including a Josephson junction (a single-junction superconducting quantum interferometer). In the experiment, the metastable states manifest themselves by sharp drops in the magnetic-field dependence of the interferometer's response to an externally applied weak alternating bias current. At low temperatures we also observe satellite drops that appear at small values of ac bias. By making use of a mapping to the theory of nonlinear oscillator, we argue that this feature is due to the presence of nonequilibrium ac-induced libration states of the interferometer.

The second harmonic in the dependence of a superconducting current on the phase difference of superconducting wave functions of the electrodes was observed experimentally in Nb/Au/(001)YBa2Cu3Ox heterojunctions. Possible reasons for its appearance were discussed within the framework of a mixed (d±s) symmetry order parameter of YBa2Cu3Ox.

The signal properties of radio frequency (rf) SQUIDs with a finite amplitude of the second harmonic in the current-phase relationship have been theoretically and experimentally investigated. Both amplitude as well as phase detection has been considered in order to readout the SQUID's output signal. We observed peculiarities of the rf SQUID response of a SQUID with YBCO 45 degree grain boundary Josephson junction. We found that the current-phase relationship contains a finite amplitude of the second harmonic. Comparison of the theoretical and experimental results is given. It is shown that the sign of the amplitude of the second harmonic can be determined from the shape of experimental curves, and the value of this amplitude is defined by the positions of extrema of these curves.

The supercurrent-phase relation (CPR) of NbAl based Josephson elements of superconductor/insulator/normal conductor/insulator/superconductor-type is deduced from impedance measurements of the phase-biased junction. The chosen temperature range from 1.9 to 8.0 K covers the superconducting transition of the aluminum interlayer below which a pronounced non-harmonic CPR is found. At temperatures higher than the corresponding critical temperature, the CPR did not deviate significantly from purely harmonic shape. Both results are in agreement with theoretical predictions.

We report the parametric amplification of a microwave signal in a Kerr medium formed from superconducting qubits. Two mutually coupled flux qubits, embedded in the current antinode of a superconducting coplanar waveguide resonator, are used as a nonlinear element. Shared Josephson junctions provide the qubit-resonator coupling, resulting in a device with a measured gain of about 20 dB. We argue, that this arrangement represents a unit cell which can be straightforwardly extended to a quasi one-dimensional quantum metamaterial with a large tunable Kerr nonlinearity., 4 pages, 4 figures

We experimentally investigate the current-phase relation (CPR) of an ${\mathrm{N}\mathrm{b}/\mathrm{A}\mathrm{l}\mathrm{O}}_{x}/{\mathrm{A}\mathrm{l}/\mathrm{A}\mathrm{l}\mathrm{O}}_{x}/\mathrm{Nb}$ Josephson junction when it is cooled down to the superconducting transition of the aluminum interlayer at about 1.9 K. While the critical current rises by more than one order of magnitude, the CPR changes from sinusoidal to nonsinusoidal behavior. The experimental results are compared with the predictions of a recently developed microscopic model for double-barrier junctions in the dirty limit. We have found quantitative agreement between experiment and theory regarding both, the rise of critical current and the shape of the CPR.

Single-layer washer-type high- T c YBa 2 Cu 3 O 7− x rf SQUIDs with grain-boundary Josephson junctions, as well as low- T c Nb rf SQUIDs with Nb–Al 2 O 3 –Nb tunnel junctions, have been investigated in finite magnetic fields. It was shown experimentally that the suppression of the critical current of the Josephson junction due to the magnetic field leads to a modulation of the amplitude of the SQUID output signal. The role of the “unwanted” junction in high- T c rf SQUIDs, which is formed by the grain boundary running through the washer of the SQUIDs on bicrystal substrates, has also been clarified. The drop of the SQUID signal at a finite magnetic field is originated by the penetration of the magnetic field into the unwanted junction. Based on these results, a direct radio-frequency method for the determination of the first critical field H c1 for long Josephson junctions has been developed.

We report on preliminary results on the measurement of variations of the Casimir energy in rigid cavities through its influence on the superconducting transition of in-cavity aluminium (Al) thin films. After a description of the experimental apparatus we report on a measurement made with thermal photons, discussing its implications for the zero-point photons case. Finally we show the preliminary results for the zero-point case., Comment: 9 pages, 7 figures, Talk given at QFEXT07 Conference in Liepzig: Quantum Field Theory Under the Influence of External Conditions

The current-phase relation (CPR) for asymmetric 45\ifmmode^\circ\else\textdegree\fi{} 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 these kinds of junctions in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ thin films. A remarkable amplitude of the $\ensuremath{\pi}$-periodical component of the CPR has been experimentally found, providing an additional source of evidence for the d-wave symmetry of the pairing state of the cuprates.

Planar dc SQUID gradiometers with integrated antenna were designed and investigated. With low-T/sub c/ superconductors they were realized as washer type and as transformer type SQUID gradiometers. With high-T/sub c/ superconductors we tested galvanometer SQUIDs. Field gradient sensitivities of 32 fT/(cm/spl radic/(Hz)) could be achieved with low-T/sub c/ SQUIDs and of 520 fT/(cm/spl radic/(Hz)) with high-T/sub c/ SQUIDs, respectively. All types of gradiometers could work stable in disturbed environments. The influence of the SQUID gradiometer layout and the construction of the sample holder on the degree of disturbance suppression is shown.

The real and imaginary part of the rf impedance of a phase-biased weak link based on YBa/sub 2/Cu/sub 3/O/sub 7-x/ thin films were investigated experimentally at 77 K. The investigated weak links were step-edge or bicrystal Josephson junctions incorporated into a washer type superconducting ring with a small inductance L=80...300 pH. The ring was inductively coupled to a tank circuit with a resonant frequency of about 23 MHz. The phase shift /spl alpha/ between the rf voltage and rf current through the tank circuit was found to be a convenient measure of the change of inductance of a weak link. From the dependence of /spl alpha/ on the magnetic flux in the ring one can deduce the current-phase relation I(/spl phi/)=I/sub c/ f(/spl phi/) of the weak link. The influence of thermal noise on f(/spl phi/) was estimated numerically using a Gaussian distribution of the noise amplitude. The experimentally observed dependence /spl alpha/(/spl phi/) for the bicrystal weak link can be sufficiently good described with f(/spl phi/)=sin (/spl phi/) and with a reasonable value of the noise amplitude. The step-edge junction shows remarkable deviation from the sinusoidal current-phase relation.

Inductive reply of the high Tc rf SQUIDs were investigated at 77 K. It is shown experimentally that the SQUIDs operate in adiabatic nonhysteretic (dispersive) mode. The SQUIDs were operable even if (i) the Josephson coupling energy is considerably smaller than the thermal energy, and (ii) the SQUID inductance is larger than the so called “fluctuation-threshold inductance”. The influence of thermal noise on the response of nonhysteretic SQUIDs is estimated theoretically. The validity limits of the estimation are discussed.

We analyse a system composed of a qubit coupled to electromagnetic fields of two high quality quantum oscillators. Particular realization of such a system is the superconducting qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonator's harmonics. One strong signal is used for exciting the system to a high energetic state while the second weak signal is applied for probing effective eigenstates of the system. We demonstrate that a description of the system dynamics as doubly dressed qubit is applicable. Experiments show that in the case of high quality resonators the energy levels and the resonance conditions can be probed even for high driving amplitudes. The interaction of the qubit with photons of two harmonics has prospects to be used as a quantum amplifier or an attenuator., 10 pages, 3 figures

The effect of complex dynamics of solitons on the output noise of the system (thermal jitter) is studied in the frame of the driven underdamped Frenkel-Kontorova model. In contrast to the continuous case, we have observed a dramatic splash of the jitter. It is demonstrated that this jitter increase is related to the joining of an initial soliton with the one generated by large amplitude oscillations of the Cherenkov radiation tail, which results in the establishment of a unified soliton structure.

We propose a method of resolving a spatially coherent signal, which contains on average just a single photon, against the background of local noise at the same frequency. The method is based on detecting the signal simultaneously in several points more than a wavelength apart through the entangling interaction of the incoming photon with the quantum metamaterial sensor array. The interaction produces the spatially correlated quantum state of the sensor array, characterised by a collective observable (e.g., total magnetic moment), which is read out using a quantum nondemolition measurement. We show that the effects of local noise (e.g., fluctuations affecting the elements of the array) are suppressed relative to the signal from the spatially coherent field of the incoming photon as ~1√N, where N is the number of array elements. The realisation of this approach in the microwave range would be especially useful and is within the reach of current experimental techniques.

We demonstrate the narrow switching distribution of an underdamped Josephson junction from the zero to the finite voltage state at millikelvin temperatures. We argue that such junctions can be used as ultrasensitive detectors of the single photons in the GHz range, operating close to the quantum limit: a given initial (zero voltage) state can be driven by an incoming signal to the finite voltage state. The width of the switching distribution at a nominal temperature of about T = 10 mK was 4.5 nA, which corresponds to an effective noise temperature of the device below 60 mK.

A Lagrangian formalism is used to derive the Hamiltonian for a $\lambda$/4 resonator shunted by a current-biased Josephson junction. The eigenstates and the quantum dynamics of the system are analyzed numerically, and we show that the system can function as an efficient detector of weak incident microwave fields., Comment: 8 pages, 6 figures

We demonstrate amplification of a microwave signal by a strongly driven two-level system in a coplanar waveguide resonator. The effect, similar to the dressed-state lasing known from quantum optics, is observed with a single quantum system formed by a persistent current (flux) qubit. The transmission through the resonator is enhanced when the Rabi frequency of the driven qubit is tuned into resonance with one of the resonator modes. Amplification as well as linewidth narrowing of a weak probe signal has been observed. The stimulated emission in the resonator has been studied by measuring the emission spectrum. We analyzed our system and found an excellent agreement between the experimental results and the theoretical predictions obtained in the dressed-state model.

An important desired ingredient of superconducting quantum circuits is a readout scheme whose complexity does not increase with the number of qubits involved in the measurement. Here, we present a readout scheme employing a single microwave line, which enables simultaneous readout of multiple qubits. Consequently, scaling up superconducting qubit circuits is no longer limited by the readout apparatus. Parallel readout of 6 flux qubits using a frequency division multiplexing technique is demonstrated, as well as simultaneous manipulation and time resolved measurement of 3 qubits. We discuss how this technique can be scaled up to read out hundreds of qubits on a chip., 4 pages, 4 figures

In parametric systems, squeezed states of radiation can be generated via extra work done by external sources. This eventually increases the entropy of the system despite the fact that squeezing is reversible. We investigate the entropy increase due to squeezing and show that it is quadratic in the squeezing rate and may become important in the repeated operation of tunable oscillators (quantum buses) used to connect qubits in various proposed schemes for quantum computing., 11 pages, 1 figure

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 figures

We implement the impedance measurement technique in order to characterize superconducting structures designed for applications in quantum computing. We report an experimental study of the circuit consisting of three small Josephson junctions incorporated in a low-inductance superconducting loop. Measurements of the circuit response to an applied weak ac bias as a function of the external magnetic flux φe yield complete information on the properties of the circuit. We found that the system displays two metastable states. From experimental data, we have determined the magnetic field dependent Josephson energy U(φe) of these states, the potential barrier ΔU between these states, as well as the difference of the critical currents of the junction in the loop.

An ultra-low-noise one-stage SiGe heterojunction bipolar transistor amplifier was designed for cryogenic temperatures and a frequency range of 10 kHz-100 MHz. A noise temperature T(N) ≈ 1.4 K was measured at an ambient temperature of 4.2 K at frequencies between 100 kHz and 100 MHz for a source resistance of ~50 Ω. The voltage gain of the amplifier was 25 dB at a power consumption of 720 μW. The input voltage noise spectral density of the amplifier is about 35 pV/√Hz. The low noise resistance and power consumption makes the amplifier suitable for readout of resistively shunted DC SQUID magnetometers and amplifiers.

We present a detailed study of the microstructure of submicron Al/Al-O/Al Josephson junctions fabricated by the conventional shadow evaporation technique. The morphology of the dielectric Al-O layer, which plays the key role for junction transport properties, has been investigated by making use of high resolution electron microscopy. We demonstrate, that the flatness and thickness of the aluminum oxide layer strongly depends on its grain structure. The most pronounced thickness deviations are observed in the vicinity of so-called "triple points," where the grain boundary crosses the interlayer, forming a two-grain contact. Additionally we show that even for the single-grain contact, the Al/Al-O interface is not atomically flat, which can cause additional flicker noise at subkelvin temperatures. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3670003]

Applying a radio-frequency (rf) interference method, we were able to investigate the supercurrent across Josephson junctions down to some tens of nA, where the Josephson coupling energy is considerably smaller than the thermal energy at 4.2 K, the temperature of operation. We report about the measurement of small supercurrents by a rf interference method. The critical current Ic as well as the supercurrent-phase relation were derived from the measurement of the impedance of the phase-biased Josephson element at 10–30 MHz. Several single and double Nb/AlOx/Nb tunnel junctions with critical currents ranging from 50 nA to 3 μA have been studied. As expected, highly asymmetrical double junction structures exhibited a harmonic current-phase relation, while the latter indeed distinctly deviated from sin ϕ in the case of more balanced double junctions.

We study the multiphoton spectroscopy of artificial solid-s tate four-level quantum system. This system is formed by two coupled superconducting flux qubits. When mult iple 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. Our calculations sh ow, that for the latter transitions, in particular, the inverse population of the excited state with respect to the gro und one is realized. These processes can be useful for the control of the level population for the multilevel sc alable quantum systems.

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 figures

For four decades semiconductor electronics has followed Moore's law: with each generation of integration the circuit features became smaller, more complex and faster. This development is now reaching a wall so that smaller is no longer any faster. The clock rate has saturated at about 3-5 GHz and the parallel processor approach will soon reach its limit. The prime reason for the limitation the semiconductor electronics experiences is not the switching speed of the individual transistor, but its power dissipation and thus heat. Digital superconductive electronics is a circuit- and device-technology that is inherently faster at much less power dissipation than semiconductor electronics. It makes use of superconductors and Josephson junctions as circuit elements, which can provide extremely fast digital devices in a frequency range - dependent on the material - of hundreds of GHz: for example a flip-flop has been demonstrated that operated at 750 GHz. This digital technique is scalable and follows similar design rules as semiconductor devices. Its very low power dissipation of only 0.1 mu W per gate at 100 GHz opens the possibility of three-dimensional integration. Circuits like microprocessors and analogue-to-digital converters for commercial and military applications have been demonstrated. In contrast to semiconductor circuits, the operation of superconducting circuits is based on naturally standardized digital pulses the area of which is exactly the flux quantum Phi(0). The flux quantum is also the natural quantization unit for digital-to-analogue and analogue-to-digital converters. The latter application is so precise, that it is being used as voltage standard and that the physical unit 'Volt' is defined by means of this standard. Apart from its outstanding features for digital electronics, superconductive electronics provides also the most sensitive sensor for magnetic fields: the Superconducting Quantum Interference Device (SQUID). Amongst many other applications SQUIDs are used as sensors for magnetic heart and brain signals in medical applications, as sensor for geological surveying and food-processing and for non-destructive testing. As amplifiers of electrical signals. SQUIDs can nearly reach the theoretical limit given by Quantum Mechanics. A further important field of application is the detection of very weak signals by 'transition-edge' bolo-meters, superconducting nanowire single-photon detectors, and superconductive tunnel junctions. Their application as radiation detectors in a wide frequency range, from microwaves to X-rays is now standard. The very low losses of superconductors have led to commercial microwave filter designs that are now widely used in the USA in base stations for cellular phones and in military communication applications. The number of demonstrated applications is continuously increasing and there is no area in professional electronics, in which superconductive electronics cannot be applied and surpasses the performance of classical devices. Superconductive electronics has to be cooled to very low temperatures. Whereas this was a bottleneck in the past, cooling techniques have made a huge step forward in recent years: very compact systems with high reliability and a wide range of cooling power are available commercially, from microcoolers of match-box size with milli-Watt cooling power to high-reliability coolers of many Watts of cooling power for satellite applications. Superconductive electronics will not replace semiconductor electronics and similar room-temperature techniques in standard applications, but for those applications which require very high speed, low-power consumption, extreme sensitivity or extremely high precision, superconductive electronics is superior to all other available techniques. To strengthen the European competitiveness in superconductor electronics research projects have to be set-up in the following field: - Ultra-sensitive sensing and imaging. - Quantum measurement instrumentation. - Advanced analogue-to-digital converters. - Superconductive electronics technology.

For a study of the supercurrent–phase relationship, we have fabricated Nb/Al/AlOx/Al/AlOx/Al/Nb-based Josephson junctions of low critical current density. At 4.2 K, junctions of a nominal area of 10×10 μm2 showed a nonhysteretic dc current–voltage characteristic with a critical current of about 10 μA. Similar junctions were part of washer-type rf superconductor quantum interference devices. These samples were inductively coupled to high-quality tank circuits for measurements at 4.2 K or at higher temperatures up to values close to the critical temperature of niobium. In this range, the current–phase relation, as deduced from impedance measurements of the phase-biased junction, did not deviate significantly from the sinusoidal shape.

The current-phase relation (CPR) of high-Tc ramp-edge Josephson junctions (YBa2Cu3O7−x/PrBa2Cu3O7/YBa2Cu3O7−x) was investigated experimentally in the temperature range 65

We demonstrate theoretically the noise-stimulated enhancement of quantum coherence in a superconducting flux qubit. First, an external classical noise can increase the off-diagonal components of the qubit density matrix. Second, in the presence of noise, the Rabi oscillations survive for times significantly longer than the Rabi decay time in a noiseless system. These Rabi oscillations appear as a modulation of the forced response of the qubit to the ac driving field. These effects can be considered as a manifestation of quantum stochastic resonance and are relevant to experimental techniques, such as Rabi spectroscopy., Figures replaced. References added. Text improved

We analyze the back-action influence of nuclear spins on the motion of the cantilever of a magnetic force resonance microscope. We calculate the contribution of nuclear spins to the damping and frequency shift of the cantilever. We show that, at the Rabi frequency, the energy exchange between the cantilever and the spin system cools or heats the cantilever depending on the sign of the high-frequency detuning. We also show that the spin noise leads to a significant damping of the cantilever motion., 15 pqges, 11 figures. The last part of Section IV.A and Section IV B were rewritten. We added three new graphs: Figs. 5, 7, 9 and all graphs in this subsection were recalculated for T=600 mK as in the experiment. Several new references were added

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. B

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 Letters

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., 11 pages, 11 figures; v.2: minor changes

Superconducting oscillators have been successfully used for quantum control and readout devices in conjunction with superconducting qubits. Also, squeezed states can improve the accuracy of measurements to subquantum, or at least subthermal, levels. Here, we show theoretically how to produce squeezed states of microwave radiation in a superconducting oscillator with tunable parameters. Its resonance frequency can be changed by controlling an rf SQUID inductively coupled to the oscillator. By repeatedly shifting the resonance frequency between any two values, it is possible to produce squeezed and subthermal states of the electromagnetic field in the (0.1--10) GHz range, even when the relative frequency change is small. We propose experimental protocols for the verification of squeezed state generation, and for their use to improve the readout fidelity when such oscillators serve as quantum transducers.

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., Comment: 4 pages, 4 figures

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.

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. Coupling such qubits to resonators 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. Furthering these analogies between quantum optical and superconducting systems we demonstrate here Sisyphus cooling 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. 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., Comment: 7 pages, 4 figures

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 sections

Nonlinear effects in mesoscopic devices can have both quantum and classical origins. We show that a three-Josephson-junction (3JJ) flux qubit in the classical regime can produce low-frequency oscillations in the presence of an external field in resonance with the (high-frequency) harmonic mode $\ensuremath{\omega}$ of the system. Like in the case of quantum Rabi oscillations, the frequency of these pseudo-Rabi oscillations is much smaller than $\ensuremath{\omega}$ and scales approximately linearly with the amplitude of the external field. This classical effect can be reliably distinguished from its quantum counterpart because it can be produced by the external drive not only at the resonance frequency $\ensuremath{\omega}$ and its subharmonics $(\ensuremath{\omega}/n)$, but also at its overtones, $n\ensuremath{\omega}$.

The current-phase relation (CPR) of YBa2Cu3O7−x step-edge Josephson junctions was investigated experimentally at various temperatures. The investigated junctions were incorporated into a washer-shaped superconducting ring with inductance L∼300 pH. The ring was inductively coupled to a tank circuit with a resonance frequency between 9 MHz and 40 MHz. The CPR was obtained from the measurement of the impedance of the phase-biased junction. At high temperatures and low critical current the experimentally observed CPR is sinusoidal. The same results were obtained at low temperatures when the rms flux noise in the ring is negligible. In the case of larger critical current and finite noise, deviations of the apparent CPR from sinusoidal dependence were found. The deviations can be described by thermal fluctuations of the magnetic flux in the ring.

Aladin2 is an experiment devoted to the first measurement of variations of Casimir energy in a rigid body. The main short-term scientific motivation relies on the possibility of the first demonstration of a phase transition influenced by vacuum fluctuations while, in the long term and in the mainframe of the cosmological constant problem, it can be regarded as the first step towards a measurement of the weight of vacuum energy. In this paper, after a presentation of the guiding principle of the measurement, the experimental apparatus and sensitivity studies on final cavities will be presented., 4 pages, Latex macros, 10th Conference on Frontier Detectors for Frontier Physics, Isola D'Elba, 21-27 May 2006

The ground state susceptibility of a system consisting of three flux-qubits was measured in the complete three dimensional flux space around the common degeneracy point of the qubits. The system's Hamiltonian could be completely reconstructed from measurements made far away from the common degeneracy point. The subsequent measurements made around this point show complete agreement with the theoretical predictions which follow from this Hamiltonian. The ground state anti-crossings of the system could be read-out directly from these measurements. This allows one to determine the ground-state flux diagram, which provides the solution for the non-polynomial optimization problem MAXCUT encoded in the Hamiltonian of the three-flux-qubit system. Our results show that adiabatic quantum computation can be demonstrated with this system provided that the energy gap and/or the speed of the read-out is increased., accepted for publication by Europhysics Letters