Search Results (26 total)

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 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 superconducting quantum interference device in the inductive mode.

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.

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 ∼45 (antiferromagnetic) to ∼-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.

Experimental observation of the strong influence of an array of ferromagnetic nanodots on the critical current of a short overlap Josephson junction is reported. Pronounced commensurability effects are detected due to the presence of the additional peaks in the magnetic-field-induced diffraction pattern. The changes in the Fraunhofer pattern of the Josephson junctions are accounted for by the formation of Abrikosov vortices trapped in the electrodes which induce a phase inhomogeneity in the junction area.

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 investigated both theoretically and experimentally dynamic features of a phase-biased charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop. The effective inductance of the qubit was probed by a high-quality tank circuit. In the presence of a microwave power, with a frequency of the order of the qubit energy level separation, an alteration of the qubit inductance was observed. We demonstrate that this effect is caused by the redistribution of the qubit level population. The excitation of the qubit by one-, two-, and three-photon processes was detected. Quantitative agreement between theory and experimental data was found.

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.

We show that an LC parametric transducer can be effectively used to monitor an adiabatic evolution of the superconducting flux qubit. We propose a scheme to measure the qubit’s state, which is a quantum nondemolition measurement. The scheme can be easily extended to a three-qubit system and allows the reading out of the qubits’ states while the system remains in the ground state. An implementation of the adiabatic quantum algorithm MAXCUT for three superconducting flux qubits is discussed.

Superconductor∕normal conductor∕superconductor Josephson junctions with highly transparent interfaces are predicted to show significant deviations from sinusoidal supercurrent-phase relationships (CPR) at low temperatures. We investigate experimentally the CPR of a ballistic Nb∕InAs(2DES)∕Nb junction in the temperature range from 1.3 K to 9 K using a modified Rifkin-Deaver method. The CPR is obtained from the inductance of the phase-biased junction. Transport measurements complement the investigation. At low temperatures, substantial deviations of the CPR from conventional tunnel-junction behavior have been observed. The data are fitted with a model presented by Grajcar [Physica C 372–376, 27 (2002)], yielding good agreement.

We implemented experimentally an interferometer-type charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop that is in flip-chip configuration inductively coupled to a radio-frequency tank circuit. The tank permits us to readout the qubit state, acting as an inductance measuring apparatus. By applying continuous microwave power to the quantum device, we observed inductance alterations caused by redistributions of the energy-level populations. From the measured data we extracted the energy gap between ground and upper levels as a function of the transistor quasicharge as well as the Josephson phase across both junctions.

We have studied the low-frequency magnetic susceptibility of two inductively coupled flux qubits using the impedance measurement technique (IMT), through their influence on the resonant properties of a weakly coupled high-quality tank circuit. In a single qubit, an IMT dip in the tank's current-voltage phase angle at the level anticrossing yields the amplitude of coherent flux tunneling. For two qubits, the difference (IMT deficit) between the sum of single-qubit dips and the dip amplitude when both qubits are at degeneracy shows that the system is in a mixture of entangled states (a necessary condition for entanglement). The dependence on temperature and relative bias between the qubits allows one to determine all the parameters of the effective Hamiltonian and equilibrium density matrix, and confirms the formation of entangled eigenstates.

This review provides a theoretical basis for understanding the current-phase relation (CΦR) for the stationary (dc) Josephson effect in various types of superconducting junctions. The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CΦR from the standard sinusoidal form. A new experimental tool for measuring the CΦR is described and its practical applications are discussed. The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy. A number of examples illustrate the importance of the CΦR measurements for both fundamental physics and applications.

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.

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   μs, corresponding to an effective qubit quality factor ∼7000.

A detailed investigation of the magnetic response of YBa₂Cu₃O_x grain-boundary Josephson junctions has been carried out using both radio-frequency measurements and scanning superconducting quantum interference device microscopy. In a nominally zero-field-cooled regime we observed a paramagnetic response at low external fields for 45° asymmetric grain boundaries. We argue that the observed phenomenology results from the d-wave order-parameter symmetry and depends on Andreev bound states.

Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a 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 induce the voltage oscillations across the coil of a high quality resonant tank circuit, inductively coupled to the phase qubit. It is the presence of these voltage oscillations in the detected signal which reveals the existence of Rabi oscillations in the qubit. A detailed calculation for zero and nonzero temperatures are made for the case of persistent current qubit. According to the estimates for decoherence and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in the MHz range.

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 the IMT was successfully applied in the classical regime. It is shown that the 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.

We have measured the current-phase relationship I(ϕ) of symmetric 45° YBa₂Cu₃O_7-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≈T^*, the first harmonic of I(ϕ) changes sign. (iii) For T<T^*, the second harmonic of I(ϕ) 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 experimentally investigate the current-phase relation (CPR) of an Nb/AlO_x/Al/AlO_x/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.

The current-phase relation (CPR) for asymmetric 45° 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 YBa₂Cu₃O_7-x thin films. A remarkable amplitude of the π-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.

We present an experimental and theoretical study of the current-phase relation I_s(φ) for 45° grain boundaries in YBa₂Cu₃O_7-x films. A model of strongly inhomogeneous Josephson junctions, in which the presence of randomly alternating current leads to a deviation of I_s(φ) from the well-known sin(φ) dependence, has been used. This deviation decreases with the temperature T and is described by the formula I_s(φ)=I_c(T)(sinφ+γ(T)sin2φ). Using the developed model, the coefficient γ is calculated and its temperature dependence is found to be in good agreement with experiment.

For various configurations of Josephson junctions incorporating superconductors with unconventional order parameter symmetry, such as most high- T_c cuprates, deviations from the standard sinusoidal current-phase dependence have been predicted. To this point, these deviations have never been observed experimentally. We have measured the current-phase relation of high- T_c Josephson junctions, namely, YBa₂Cu₃O_7-x thin film bicrystals, comprising symmetric 45° [001] tilt grain boundaries. The current-phase relations of all junctions investigated were found to be extremely nonharmonic, in agreement with a d_x²-y²-wave dominated symmetry of the order parameter.

Aspects of magnetic-flux dynamics in different types of samples of the high-temperature superconductor YBa₂Cu₃O_x have been investigated in magnetic fields below 1 Oe and at 77 K. The experiments were carried out in an arrangement including a field coil, a flat sample perpendicular to the field, and a radio frequency-superconducting quantum interference device (RF-SQUID) along a common axis. For epitaxial thin films the Meissner effect was established. For a ceramic sample it was found that field changes of order 10^-2 Oe affect the flux distribution inside the sample. The observations can explain why RF-SQUID’s made from this ceramic operate in the nonhysteretic mode. The central object was an epitaxial film with a large density of defects. In this film the dynamics of the mixed state show features expected in ‘‘spin-glass’’ models.