Nonlinear coupling and squeezing in solid-state quantum circuits

We propose an attractive realization of nonlinear coupling of superconducting charge qubit coupled to a transmission-line resonator. Our scheme provides a new approach to produce the strong squeezing effect via a flexible design of the superconducting qubit and mature experimental setup of circuit QED. By properly tuning the external magnetic flux, considerable squeezing can be generated. Strong coupling strength, immunity to noises and suppression of spontaneous emission make our scheme more robust and may be realized with conservative experimental parameters.     

Entangling a single NV centre with a superconducting qubit via parametric couplings between photons and phonons in a hybrid system

We propose an efficient scheme for generating entangled states between a single nitrogen-vacancy (NV) centre in diamond and a superconducting qubit in a hybrid set-up. In this device, the NV centre and the superconducting qubit couple to a nanomechanical resonator and a superconducting coplanar waveguide cavity, respectively, while the microwave cavity and the mechanical resonator are parametrically coupled with a tunable coupling strength. We show that, highly entangled states between the NV centre and the superconducting qubit can be achieved, by means of the Jaynes–Cummings interactions in the NV-resonator and qubit-cavity subsystems which transfer the entanglement between the vibration phonons and the cavity photons to the NV centre and the superconducting qubit. This work may provide interesting applications in quantum computation and communication with single NV spins and superconducting qubits.     

Effects of Energy Dissipation on the Parametric Excitation of a Coupled Qubit–Cavity System

We consider a parametrically driven system of a qubit coupled to a cavity taking into account different channels of energy dissipation. We focus on the periodic modulation of a single parameter of this hybrid system, which is the coupling constant between the two subsystems. Such a modulation is possible within the superconducting realization of qubit–cavity coupled systems, characterized by an outstanding degree of tunability and flexibility. Our major result is that energy dissipation in the cavity can enhance population of the excited state of the qubit in the steady state, while energy dissipation in the qubit subsystem can enhance the number of photons generated from vacuum. We find optimal parameters for the realization of such dissipation-induced amplification of quantum effects. Our results might be of importance for the full control of quantum states of coupled systems as well as for the storage and engineering of quantum states.     

Scalable solid-state qubits: challenging decoherence and read-out

We review some basic facts about qubits and qubit processing. After a brief survey of solid-state qubits, we focus on quantized electrical circuits and superconducting qubits based on Josephson junctions. We review the general framework and indicate how the various qubits, such as the superconducting Cooper pair box charge qubit, the persistent current flux qubit, the hybrid charge-phase qubit, and the Andreev-level qubit, can be seen to appear due to different choices of design parameters. Finally, we consider multi-qubit systems and discuss some aspects of decoherence.     

Quantum Entanglement and Correlations in Superconducting Flux Qubits

We report on the quantum correlations dissipative dynamics followed by coupled superconducting flux qubits. The coupling between the superconducting quantum register and the reservoir is described by two different mechanisms: collective and independent decoherence. By means of the Bloch?CRedfield formalism, we solve the quantum master equation and show that coupling under collective quantum noise is more robust to decoherence. This result is demonstrated for different flux qubit initial preparations, taking into account the influence due to external fields and temperature. Furthermore, we compute the entanglement and the quantum discord dissipative dynamics as controlled by external parameters. We show that the discord is more robust against decoherence effects. This fact could be harnessed in the realization of quantum computing tasks that do not need to invoke entanglement in their implementation.     

Coherent Cooper-Pair Tunneling Through Capacitively-Coupled Superconducting Charge Qubits

Coherent Cooper-pair tunneling phenomena through two superconducting charge qubits are studied. The maximum current through the first qubit is calculated in the presence of the second qubit capacitively coupled to it. It is shown that the effective Josephson coupling of the second qubit may increase the maximum current of the first qubit by cooperative hopping of Cooper-pairs. The modulation of the maximum current by the external current through the second qubit is also discussed.     

Quantum computing based on a superconducting quantum interference device: exploiting the flux basis

Two classes of superconducting devices have been proposed as quantum bits (qubits) for realizing quantum logic operations. The flux qubits based on a superconducting quantum interference device (SQUID) appear to be particularly promising owing to the macroscopic nature of the qubit and potential integration with high-speed control circuitry in the form of rapid single-flux quantum electronics. Recent progress is discussed and near-term challenges mentioned. The radio frequency SQUID-based qubit offers a prospect for a reliably manufacturable scalable approach.     

Conservation of Angular Momentum in a Flux Qubit

Oscillations of superconducting current between clockwise and counterclockwise directions in a flux qubit do not conserve the angular momentum of the qubit. To compensate for this effect the solid containing the qubit must oscillate in unison with the current. This requires entanglement of quantum states of the qubit with quantum states of a macroscopic body. The question then arises whether slow decoherence of quantum oscillations of the current is consistent with fast decoherence of quantum states of a macroscopic solid. This problem is analyzed within an exactly solvable quantum model of a qubit embedded in an absolutely rigid solid and for the elastic model that conserves the total angular momentum. We show that while the quantum state of a flux qubit is, in general, a mixture of a large number of rotational states, slow decoherence is permitted if the system is macroscopically large. Practical implications of entanglement of qubit states with mechanical rotations are discussed.     

Flux Dynamics in NdO1−x F x FeAs Bulk Sample

We present data of multiharmonic magneto-dynamic experiments. In particular, we performed ac magnetic susceptibility experiments on layered pnictide-oxide quaternary compound NdOFeAs doped with fluorine. The experiments allow one to measure the critical temperature and probe the flux dynamic behavior using the third harmonic component of the ac susceptibility of an NdF_0.16FeAsO_0.84 bulk sample as a function of temperature and frequency of the applied ac magnetic fields. Measured signals are connected with the nonlinear superconducting flux dynamic behavior and are characterized by a “flux critical states” sustaining a superconducting critical current. In this framework the irreversibility line that describes the stable superconducting state has been extracted from the onset of the third harmonic signal vs. frequency. Finally we present also the analysis of the flux dynamic dimensionality in the investigated sample.     

Dispersive Charge and Flux Qubit Readout as a Quantum Measurement Process

We analyze the dispersive readout of superconducting charge and flux qubits as a quantum measurement process. The measurement oscillator frequency is considered much lower than the qubit frequency. This regime is interesting because large detuning allows for strong coupling between the measurement oscillator and the signal transmission line, thus allowing for fast readout. Due to the large detuning we may not use the rotating wave approximation in the oscillator-qubit coupling. Instead we start from an approximation where the qubit follows the oscillator adiabatically, and show that non-adiabatic corrections are small. We find analytic expressions for the measurement time, as well as for the back-action, both while measuring and in the off-state. The quantum efficiency is found to be unity within our approximation, both for charge and flux qubit readout.      

Observation of X-band SQUID signals in a High-T c superconducting film device

A microwave superconducting magnetometer is described in which a microstrip resonator is coupled to a two-hole high-T _c thin-film SQUID device. Both the microstrip circuit and the thin-film SQUID were fabricated by photolithography techniques. The YBCO thin film was deposited on single-crystal substrate of yttria-stabilized zirconia [YSZ(100)] by an ion beam sputtering technique producing a superconducting transition measured at a critical temperature ofT _c =92 K to within ΔT ～ 3 K. Non linear oscillatory behavior was observed in the microstrip resonator when inductively coupled to the SQUID. This nonlinear behavior yielded a microwave device in which the reflected microwave power varied with applied DC magnetic flux.     

Study and Application of Controlled Vortex Dynamics in?Patterned YBCO Films

Quantitative imaging of the local magnetic field and of current density distribution in superconductors (with microscopic resolution over macroscopic length scales) is achieved by means of the Magneto-Optical Imaging technique with an indicator film. We exploit this technique to study the vortex arrangement and the corresponding supercurrent distribution in high temperature superconducting YBa₂Cu₃O_7?x films. Several patterned superconducting films were studied, either non-simply connected structures, which imply macroscopic flux quantization, and superconductors whose local properties were tailored by means of confined heavy-ion irradiation. Moreover, by means of electrical transport measurements coupled with the real-time imaging of the magnetic pattern, it is directly shown how the local current distribution in patterned superconductors is affected by the electrical transport both in the Meissner and in the vortex regimes. The relevance of a controlled and localized dissipation induced by the confined vortex motion in tailored superconducting films is demonstrated for direct applications of this phenomenology to superconducting devices, such as magnetic field and photon detectors.     

Reduction of fault current peak in an inductive high-Tc superconducting fault current limiter

This paper dealt with current-limiting performances of an inductive high-T_c superconducting fault current limiter with an auxiliary coil. The fault current limiter mainly consists of the primary copper coil, secondary high-T_c superconducting rings, and auxiliary high-T_c superconducting coils, which are magnetically coupled through three-legged core. The superconducting fault current limiter as a series element in the power system is inserted to limit the fault current. The device presents fast variable-impedance features in the event of a fault condition. The fault current peak can become relatively large for certain ranges of the flux and the fault instant due to the core saturation. The auxiliary coil proposed in this paper was proven to increase the impedance of the SFCL up to more than 31% while preventing the core saturation.     

Dynamics of a Phase Qubit-Resonator System: Requirements for Fast Nondemolition Readout of a Phase Qubit

We examine the time-dependent evolution of a coupled qubit-transmission line-resonator system coupled to an external drive and a resonator environment. By solving the equation for a non-stationary resonator field, we determine the requirements for a single-shot nondestructive dispersive measurement of the phase qubit state. Reliable isolation of the qubit from the “electromagnetic environment” is necessary for a dispersive readout and can be achieved if the whole system interacts with the external fields only through a resonator that is weakly coupled to the qubit. A set of inequalities involving the resonator-qubit detuning and a coupling parameter, the resonator leakage and the measurement time, together with the requirement of multi-photon outgoing flux is derived. In particular, it is shown that to decrease the measurement time one must increase the resonator leakage. This leakage increase reduces the quality factor and decreases the resolution of the resonator eigenfrequencies corresponding to different qubit states. The consistency of our inequalities for two sets of experimental parameters is discussed. Our results can be used for optimizing experimental setups, parameters, and measurement protocols.     

Mesoscopic modelling of high TC superconductors

Advances in experimental techniques, such as magneto-optical imaging, have influenced the way modelling studies are to be approached. In particular, these studies should be coupled with the fundamental understanding of flux lattices, vortex motion, melting and pinning, obtained from phenomenological theories and via various measurement techniques, such as Hall probe arrays, scanning superconducting quantum interference devices and by Lorentz microscopy. There are a range of models and questions to be addressed such as those concerning critical current density in relation to thin films. The ultimate goal is to obtain a cohesive picture of the properties of high T_C superconductors that will be useful from the standpoint of superconducting technology.     

Observation of X-band SQUID signals in a High-Tc superconducting film device

A microwave superconducting magnetometer is described in which a microstrip resonator is coupled to a two-hole high-T _c thin-film SQUID device. Both the microstrip circuit and the thin-film SQUID were fabricated by photolithography techniques. The YBCO thin film was deposited on single-crystal substrate of yttria-stabilized zirconia [YSZ(100)] by an ion beam sputtering technique producing a superconducting transition measured at a critical temperature ofT _c =92 K to within T 3 K. Non linear oscillatory behavior was observed in the microstrip resonator when inductively coupled to the SQUID. This nonlinear behavior yielded a microwave device in which the reflected microwave power varied with applied DC magnetic flux.     

Flux Phase and Its Competition with Superconductivity in the t–J Model

The phase diagram of the t–J model is investigated within the X-operator formalism using the Baym–Kadanoff theory and a 1/N expansion. In this way, no auxiliary fields are introduced. For finite Coulomb repulsion, the system shows a strong competition between d-wave superconductivity and d-wave flux phase, leading to a strong suppression of superconductivity in the flux state. The underdoped region is characterized by flux order in the normal state, with a d-wave gap in the excitation spectrum, and by coexistence of both superconductivity and flux phases below the superconducting transition temperature T _c. The balance between the two phases is determined by the short-range Coulomb repulsion, while the long-range part of Coulomb interaction prevents phase separation and leads to incommensurate charge-density-wave state far away from the superconducting region.     

High resolution magneto-optical studies of the intermediate state in thin film superconductors

The structure of the intermediate state in superconducting lead films has been investigated as a function of magnetic field and film thickness. The detection system utilized the high specific Faraday rotation in thin films of a mixture of EuS and EuF₂ in combination with a polarizing microscope, yielding a resolution of about 1 μm. The thickness of the Pb films ranged between 0.7 and 9 μm, thus including the critical film thickness at which the transition from the intermediate state to the vortex state occurs. At low fields a liquid-like mixed state of multi-quanta flux tubes was observed which appeared to be stable up to increasing magnetic fields with decreasing film thickness. The diameter of these flux tubes varied approximately with the square root of the film thickness. At intermediate fields the intermediate state pattern was found to persist down to a film thickness of 0.7 μm, the smallest thickness investigated. The periodicity length of the intermediate state structure was in reasonable agreement with the non-branching model of Landau. Just below H_c, small superconducting domains were observed in increasing field, whereas long threads of superconducting material were formed abruptly in decreasing field. These superconducting threads were absent in the specimentsthinner than 1–2μ, being replaced by a liquid-like mixed state of superconducting tubes. After the passage of a sufficiently high electrical current through the specimen, the flux structure was found to be rearranged into long domains oriented predominantly perpendicular to the current, leading to current hysteresis effects. Finally, some dynamic observations were made during current induced flux flow.     

Experiments on a Superconducting Qubit Manipulated by Fast Flux Pulses: The Issue of Non-adiabaticity

The double SQUID qubit is a superconducting interferometer (SQUID) made of two Josephson junctions and two superconducting loops. Its energy potential can be greatly modified in shape and symmetry by using two magnetic control fluxes that can change the potential from a double well to an almost harmonic single well: This feature is exploited for manipulating the qubit without resorting to the usual NMR-like techniques with microwave irradiation. The qubit machinery relies on these operations being performed non-adiabatically, realizing a transition between the two lowest-lying energy levels, at the same time avoiding excitation of upper levels, a condition that can be satisfied by using control pulses with proper risetime. We show experimental results referring to manipulation of the qubit at different rates and make a qualitative comparison with theoretical expectations.     

Hall probe Cdx Hg1-x Te for use in magnetic investigations of Nb3Sn superconducting layers

The critical temperature of a superconducting Nb₃Sn layer has been measured by repulsion of magnetic flux as a function of temperature, using a Hall probe. Hall probes of an active semiconductor film, Cd_xHg_1-xTe (x = 0.175), have been made by thermal evaporation in a vacuum. The chemical composition of the Cd_xHg_1-xTe thin films have been determined by spectrophotometric analysis. The Hall probes have been characterized by electric measurements over a temperature range of 4.2–18.5 K in a magnetic field. The probes are particulary suitable for magnetic measurements of superconducting Nb₃Sn layers at low temperatures.