Theory of microwave parametric down-conversion and squeezing using circuit QED

We study theoretically the parametric down-conversion and squeezing of microwaves using cavity quantum electrodynamics of a superconducting Cooper-pair box (CPB) qubit located inside a transmission line resonator. The nonlinear susceptibility chi2 describing three-wave mixing can be tuned by dc gate voltage applied to the CPB and vanishes by symmetry at the charge degeneracy point. We show that the coherent coupling of different cavity modes through the qubit can generate a squeezed state. Based on parameters realized in recent successful circuit QED experiments, squeezing of 95% approximately 13 dB below the vacuum noise level should be readily achievable.     

Generation of Entangled Coherent States in Circuit-QED

We study theoretically the generation of entangled states of microwaves in a circuit quantum electrodynamics (QED) system. Our system includes a transmission-line resonator and a Cooper-pair box which acts as an artificial atom. It is shown that in the dispersive regime of the circuit-QED system, a cross-Kerr interaction can be obtained by properly preparing the initial state of the qubit. Based on this cross-Kerr interaction, we show that the coherent coupling of the two lowest-lying cavity modes through the qubit can generate a macroscopic entangled state.     

Observation of quantum capacitance in the Cooper-pair transistor

We have fabricated a Cooper-pair transistor (CPT) with parameters such that for appropriate voltage biases, it behaves essentially like a single Cooper-pair box (SCB). The effective capacitance of a SCB can be defined as the derivative of the induced charge with respect to gate voltage and has two parts, the geometric capacitance, C(geom), and the quantum capacitance C(Q). The latter is due to the level anticrossing caused by the Josephson coupling and is dual to the Josephson inductance. It depends parametrically on the gate voltage and its magnitude may be substantially larger than C(geom). We have detected C(Q) in our CPT, by measuring the in phase and quadrature rf signal reflected from a resonant circuit in which the CPT is embedded. C(Q) can be used as the basis of a charge qubit readout by placing a Cooper-pair box in such a resonant circuit.     

Continuous measurement of the energy eigenstates of a nanomechanical resonator without a nondemolition probe

We show that it is possible to perform a continuous measurement that continually projects a nanoresonator into its energy eigenstates by employing a linear coupling with a two-state system. This technique makes it possible to perform a measurement that exposes the quantum nature of the resonator by coupling it to a Cooper-pair box and a superconducting transmission line resonator.     

Are "pinholes" the cause of excess current in superconducting tunnel junctions? A study of Andreev current in highly resistive junctions

In highly resistive superconducting tunnel junctions, excess subgap current is usually observed and is often attributed to microscopic pinholes in the tunnel barrier. We have studied the subgap current in superconductor-insulator-superconductor (SIS) and superconductor-insulator-normal-metal (SIN) junctions. In Al/AlO(x)/Al junctions, we observed a decrease of 2 orders of magnitude in the current upon the transition from the SIS to the SIN regime, where it then matched theory. In Al/AlO(x)/Cu junctions, we also observed generic features of coherent diffusive Andreev transport in a junction with a homogenous barrier. We use the quasiclassical Keldysh-Green function theory to quantify single- and two-particle tunneling and find good agreement with experiment over 2 orders of magnitude in transparency. We argue that our observations rule out pinholes as the origin of the excess current.     

Radio-frequency single-electron transistor as readout device for qubits: charge sensitivity and backaction

We study the radio-frequency single-electron transistor (rf-SET) as a readout device for charge qubits. We measure the charge sensitivity of an rf-SET to be 6.3microe/sqrt[Hz] and evaluate the backaction of the rf-SET on a single Cooper-pair box. This allows us to compare the needed measurement time with the mixing time of the qubit imposed by the measurement. We find that the mixing time can be substantially longer than the measurement time, which would allow readout of the state of the qubit in a single shot measurement.     

Coherence times of dressed states of a superconducting qubit under extreme driving

We measure longitudinal dressed states of a superconducting qubit, the single Cooper-pair box, and an intense microwave field. The dressed states represent the hybridization of the qubit and photon degrees of freedom and appear as avoided level crossings in the combined energy diagram. By embedding the circuit in an rf oscillator, we directly probe the dressed states. We measure their dressed gap as a function of photon number and microwave amplitude, finding good agreement with theory. In addition, we extract the relaxation and dephasing rates of these states.     

Approaching unit visibility for control of a superconducting qubit with dispersive readout

In a Rabi oscillation experiment with a superconducting qubit we show that a visibility in the qubit excited state population of more than 95% can be attained. We perform a dispersive measurement of the qubit state by coupling the qubit non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. In a measurement of Ramsey fringes, the qubit coherence time is larger than 500 ns.     

The transition from quantum Zeno to anti-Zeno effects for a qubit in a cavity by varying the cavity frequency

We propose a strategy to demonstrate the transition from the quantum Zeno effect (QZE) to the anti-Zeno effect (AZE) using a superconducting qubit coupled to a transmission line cavity, by varying the central frequency of the cavity mode. Our results are obtained without the rotating wave approximation (RWA), and the initial state (a dressed state) is easy to prepare. Moreover, we find that in the presence of both qubit?s intrinsic bath and the cavity bath, the emergence of the QZE and the AZE behaviors relies not only on the match between the qubit energy-level-spacing and the central frequency of the cavity mode, but also on the coupling strength between the qubit and the cavity mode.     

Fabrication and characterization of ultra-low noise narrow and wide band Josephson parametric amplifiers

We have fabricated two types of lumped-element Josephson parameter amplifiers (JPAs) by using a multilayer micro-fabrication process involving wet etching of Al films. The first type is a narrow band JPA which shows typical gain above 14 dB in a bandwidth around 35 MHz. The second type is a wideband JPA which is coupled to an input 50 Ω transmission line via an impedance transformer that changes the impedance from about 15 Ω on the non-linear resonator side to 50 Ω on the input transmission line side. The wideband JPA could operate in a 200 MHz range with a gain higher than 14 dB. The amplifiers were used for superconducting qubit readout. The results showed that the signal to noise ratio and hence the readout fidelity were improved significantly.     

Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED

We investigate theoretically the dynamical behavior of a qubit obtained with the two ground eigenstates of an ultrastrong coupling circuit-QED system consisting of a finite number of Josephson fluxonium atoms inductively coupled to a transmission line resonator. We show a universal set of quantum gates by using multiple transmission line resonators (each resonator represents a single qubit). We discuss the intrinsic "anisotropic" nature of noise sources for fluxonium artificial atoms. Through a master equation treatment with colored noise and many-level dynamics, we prove that, for a general class of anisotropic noise sources, the coherence time of the qubit and the fidelity of the quantum operations can be dramatically improved in an optimal regime of ultrastrong coupling, where the ground state is an entangled photonic "cat" state.     

Continuous-time monitoring of Landau-Zener interference in a cooper-pair box

Landau-Zener (LZ) tunneling can occur with a certain probability when crossing energy levels of a quantum two-level system are swept across the minimum energy separation. Here we present experimental evidence of quantum interference effects in solid-state LZ tunneling. We used a Cooper-pair box qubit where the LZ tunneling occurs at the charge degeneracy. By employing a weak nondemolition monitoring, we observe interference between consecutive LZ-tunneling events; we find that the average level occupancies depend on the dynamical phase. The system's unusually strong linear response is explained by interband relaxation. Our interferometer can be used as a high-resolution Mach-Zehnder-type detector for phase and charge.     

Site connectivities in sodium aluminoborate glasses: multinuclear and multiple quantum NMR results

In a series of sodium aluminoborate glasses, we have applied triple-quantum magic-angle spinning (3QMAS) 17O NMR to obtain high-resolution information about the connections among various network structural units, to explore the mixing of aluminum and boron species. Oxygen-17 3QMAS spectra reveal changes in connectivities between AlO4 ([4]Al), AlO5 and AlO6 ([5,6]Al), BO3 ([3]B) and BO4 ([4]B) units, by quantifying populations of bridging oxygens such as Al-O-Al, Al-O-B and B-O-B and of non-bridging oxygens. Several linkages such as [4]Al-O-[4]Al and three-coordinated oxygen associated with [5,6]Al in Al-O-Al, [4]Al-O-[4]B, [4]Al-O-[3]B and [5,6]Al-O-[3]B in Al-O-B as well as [4]B-O-[3]B and [3]B-O-[3]B in B-O-B can be distinguished for the first time. The fractions of these linkages were calculated from models of random mixing and of mixing with maximum avoidance of tetrahedral-tetrahedral linkages. The results suggest that the structure of all of glasses in this study is well approximated by the latter model. However, the energetic "penalty" for formation of [4]Al-O-[4]B may be somewhat less than for [4]Al-O-[4]Al and [4]B-O-[4]B. In general, the new results presented here are similar to those obtained on glasses in this system by 27Al{11B} REDOR NMR (J. Phys. Chem. B 104 (2000) 6541), but provide considerably more detail on network connectivity and ordering schemes.     

Measurement of the excited-state lifetime of a microelectronic circuit

We demonstrate that a continuously measured microelectronic circuit, the Cooper-pair box measured by a radio-frequency single-electron transistor, approximates a quantum two-level system. We extract the Hamiltonian of the circuit through resonant spectroscopy and measure the excited-state lifetime. The lifetime is more than 10(5) times longer than the inverse transition frequency of the two-level system, even though the measurement is active. This lifetime is also comparable to an estimate of the known upper limit, set by spontaneous emission, for this circuit.     

Mesoscopic entangled coherent states implemented with a circuit quantum electrodynamics system

We show a scheme to generate entangled coherent states in a circuit quantum electrodynamics system, which consists of a nanomechanical resonator, a superconducting Cooper-pair box (CPB), and a superconducting transmission line resonator. In the system, the CPB plays the role of a nonlinear medium and can be conveniently controlled by a gate voltage including direct-current and alternating-current components. The scheme provides a powerful tool for preparing the multipartite mesoscopic entangled coherent states.     

Scalable geometric quantum computing with Cooper-pair box qubits in circuit QED

We theoretically present a scheme to realize the scalable geometric quantum computing with Cooper-pair box (CPB) qubits in circuit QED. A one-dimensional transmission line resonator in circuit QED acting as quantum data bus generates a common cavity mode and interacts with each CPB. It is found that the interqubit couplings between any pair of qubits are switchable by individually adjusting the gate pulses applied to the selected CPBs. In this proposed scheme, we can both controllably and selectively address logic gates in geometric scenarios, which opens the possibility to implement the scalable fault-tolerant quantum computing with Josephson qubits.     

Perspectives for a superconducting charge qubit system interacting with bimodal cavity fields

We report on the observation of new features in a superconducting charge qubit system. The system we analyze comprises of a single Cooper-pair box sequentially coupled to two microwave cavity fields. Simulations of the full qubit–field dynamics show significant total correlation and coherence loss. By suitably choosing the system’s parameters and precisely controlling the dynamics, we demonstrate the generation of two-mode field states. We explore the nonclassical behavior of the system by studding the quasi-probability distribution function. Our scheme can be realized within the current experimental technology and may well be of use in quantum information processing applications.     

27Al and 23Na double-rotation NMR of sodalites.

The 27Al NMR spectra of calcium tungstate aluminate sodalite (CAW), Ca8[Al12O24](WO4)2, and the 23Na NMR spectra of sodium aluminosilicate sodalites of general composition Na9[Si6Al6O24]A2 with A = B(OH)4- (SBS), SCN- (SRS) and A2 = SO4(2-) (SSS), MoO4(2-) (SMS) have been measured using magic-angle spinning (MAS) and double-rotation (DOR) techniques. Rotor synchronized pulse excitation is applied in the DOR experiments. Dramatic line narrowing is observed in the DOR spectra of all samples. The 27Al DOR NMR spectra of CAW measured at 9.4 and 11.7 T and spinning rates of 800-1150 Hz of the outer and 5 kHz of the inner rotor show seven sharp central lines accompanied by a manifold of spinning sidebands. These lines correspond to the seven crystallographically inequivalent Al sites of the CAW framework derived from X-ray structure analysis. From the difference of the line positions in the 9.4 and 11.7 T spectra the quadrupole coupling constant, QCC, quadrupole induced shift, sigma qs, and isotropic chemical shift, delta cs, of each Al site have been calculated. QCC values in the range of 5 to 9 MHz are obtained which reflect the strong tetragonal distortion of the AlO4 tetrahedra in CAW. delta cs shows only small changes in the range between 74.4 and 77.2 ppm. A tentative assignment of all lines to the distinct Al sites is derived from the correlation between QCC and a "shear strain parameter" describing quantitatively the distortion of the AlO4 tetrahedra.(ABSTRACT TRUNCATED AT 250 WORDS)     

Effective gauge potentials induced by superconducting quantum circuits

We theoretically propose a scheme to induce non-Abelian and Abelian gauge potentials by the same superconducting circuit device. The level spacings of Cooper-pair box can be designed to resonantly match or largely detune from the mode frequencies of the one-dimensional transmission line resonators. We show the appearances of the effective gauge potentials via field quadrature operators. This scheme could help investigating the fundamental characteristics of the gauge theories with Josephson circuits.