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.     

Quantum information transfer with Cooper-pair box qubits in circuit QED

We propose a feasible scheme to transfer quantum information with Cooper-pair box qubits arrayed in a circuit QED. Qubits interact with a quantum data bus generated by a one-dimensional transmission line resonator. Based on the Raman adiabatic passage, the cavity bus-assisted quantum population transfer between any selected pair of qubits can be controlled by addressing the applied gate pulses. Therefore, the scheme provides the possibility for effectively implementing scalable quantum information transfer with Josephson devices.     

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.     

Current to frequency conversion in a Josephson circuit

The voltage oscillations which occur in an ideally current-biased Josephson junction were proposed to make a current standard for metrology. We demonstrate similar oscillations in a more complex Josephson circuit derived from the Cooper pair box: the quantronium. When a constant current I is injected in the gate capacitor of this device, oscillations develop at the frequency f(B)=I/2e, with e the electron charge. We detect these oscillations through the sidebands induced at multiples of f(B) in the spectrum of a microwave signal reflected on the circuit, up to currents I exceeding 100 pA. We discuss the potential interest of this current-to-frequency conversion experiment for metrology.     

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.     

On Bosonic Magnetic Flux Operator and Bosonic Faraday Operator Formula

In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators＇ commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.     

Cooper-Pair Number-Phase Quantization for a Mesoscopic LC Circuit Including a Josephson Junction

By introducing the entangled state representation and Feynman assumption that ＇electron pairs are bosons, ..., a bound pair acts as a Bose particle ＇, we construct an operator Hamiltonian for a mesoscopic inductance-capacitance （LC） circuit including a Josephson junction, then we use the Heisenberg equation of motion to derive the current equation and the voltage equation across the inductance as well as across the Josephson junction. The result manifestly shows how the junction voltage is affected by the capacitance coupling. In this way the Cooper-pair number-phase quantization for this system is completed.     

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.     

ac Josephson effect and resonant Cooper pair tunneling emission of a single Cooper pair transistor

We measure the high-frequency emission of a single Cooper pair transistor (SCPT) in the regime where transport is only due to tunneling of Cooper pairs. This is achieved by coupling on chip the SCPT to a superconductor-insulator-superconductor junction and by measuring the photon assisted tunneling current of quasiparticles across the junction. This technique allows a direct detection of the ac Josephson effect of the SCPT and provides evidence of Landau-Zener transitions for proper gate voltage. The emission in the regime of resonant Cooper pair tunneling is also investigated. It is interpreted in terms of transitions between charge states coupled by the Josephson effect.     

Decoupling a Cooper-pair box to enhance the lifetime to 0.2 ms

We present results on a circuit QED experiment in which a separate transmission line is used to address a quasilumped element superconducting microwave resonator which is in turn coupled to an Al/AlO(x)/Al Cooper-pair box charge qubit. With our device, we find a strong correlation between the lifetime of the qubit and the inverse of the coupling between the qubit and the transmission line. At the smallest coupling we measured, the lifetime of the Cooper-pair box was T?=200 μs, which represents more than a twentyfold improvement in the lifetime of the Cooper-pair box compared with previous results. These results imply that the loss tangent in the AlO(x) junction barrier must be less than about 4×10?? at 4.5 GHz, about 4 orders of magnitude less than reported in larger area Al/AlO(x)/Al tunnel junctions.     

Shortcut-based quantum gates on superconducting qubits in circuit QED

Construction of optimal gate operations is significant for quantum computation. Here an efficient scheme is proposed for performing shortcut-based quantum gates on superconducting qubits in circuit quantum electrodynamics (QED). Two four-level artificial atoms of Cooper-pair box circuits, having sufficient level anharmonicity, are placed in a common quantized field of circuit QED and are driven by individual classical microwaves. Without the effect of cross resonance, one-qubit NOT gate and phase gate in a decoupled atom can be implemented using the invariant-based shortcuts to adiabaticity. With the assistance of cavity bus, a one-step SWAP gate can be obtained within a composite qubit-photon-qubit system by inversely engineering the classical drivings. We further consider the gate realizations by adjusting the microwave fields. With the accessible decoherence rates, the shortcut-based gates have high fidelities. The present strategy could offer a promising route towards fast and robust quantum computation with superconducting circuits experimentally.     

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.     

One-shot quantum measurement using a hysteretic dc SQUID

We propose a single shot quantum measurement to determine the state of a Josephson charge quantum bit (qubit). The qubit is a Cooper pair box and the measuring device is a two junction superconducting quantum interference device (dc SQUID). This coupled system exhibits a close analogy with a Rydberg atom in a high Q cavity, except that in the present device we benefit from the additional feature of escape from the supercurrent state by macroscopic quantum tunneling, which provides the final readout. We test the feasibility of our idea against realistic experimental circuit parameters and by analyzing the phase fluctuations of the qubit.     

Scalable quantum computing in decoherence-free subspaces with Cooper-pair box qubits

We theoretically propose a feasible scheme to perform quantum computing in decoherence-free subspaces (DFSs) with Cooper-pair box (CPB) qubits arrayed in a circuit QED architecture. Based on the cavity-bus assisted interaction, the selective and controllable interqubit couplings occur only by adjusting the individual gate pulses, by which we obtain the scalable DFS-encoded universal quantum gates to resist certain collective noises. Further analysis shows the protocol may implement the scalable fault-tolerant quantum computing with current experimental means.     

Cooper-pair number-phase quantization analysis in double-Josephson-junction mesoscopic circuit coupled by a capacitor

This paper examines the quantization of mesoscopic circuit including Josephson junctions. Following Feynman＇s assumption, via the Hamilton dynamic approach and by virtue of the entangled state representation, it constructs Hamiltonian operator for the double-Josephson-junction mesoscopic circuit coupled by a capacitor. Then it uses the Heisenberg equation of motion to derive the induction voltage across each Josephson junction. The result manifestly shows how the voltage is affected by the capacitance coupling.     

Out-of-equilibrium admittance of single electron box under strong Coulomb blockade

We study admittance and energy dissipation in an out-of-equilibrium single electron box. The system consists of a small metallic island coupled to a massive reservoir via single tunneling junction. The potential of electrons in the island is controlled by an additional gate electrode. The energy dissipation is caused by an AC gate voltage. The case of a strong Coulomb blockade is considered. We focus on the regime when electron coherence can be neglected but quantum fluctuations of charge are strong due to Coulomb interaction. We obtain the admittance under the specified conditions. It turns out that the energy dissipation rate can be expressed via charge relaxation resistance and renormalized gate capacitance even out of equilibrium. We suggest the admittance as a tool for a measurement of the bosonic distribution corresponding collective excitations in the system.     

Nanoscale superconducting quantum bits

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits. In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses. The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a d.c.-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.     

Variable electrostatic transformer: controllable coupling of two charge qubits

We propose and investigate a novel method for the controlled coupling of two Josephson charge qubits by means of a variable electrostatic transformer. The value of the coupling capacitance is given by the discretized curvature of the lowest energy band of a Josephson junction, which can be positive, negative, or zero. We calculate the charging diagram of the two-qubit system that reflects the transition from positive to negative through vanishing coupling. We also discuss how to implement a phase gate making use of the controllable coupling.     

Quantum antidot as an electrometer:Observation of fractional charge

In experiments on resonant tunneling through a quantum antidot in the quantum Hall (QH) regime, we observe periodic conductance peaks both versus magnetic field and a global gate voltage, i.e., electric field. Each conductance peak can be attributed to tunneling through a quantized antidot-bound state. The fact that the variation of the uniform electric field produces conductance peaks implies that the deficiency of the electrical charge on the antidot is quantized in units of charge of quasiparticles of surrounding QH condensate. The period in magnetic field gives the effective area of the antidot state through which tunneling occurs, the period in electric field (obtained from the global gate voltage) then constitutes a direct measurement of the charge of the tunneling particles. We obtain electron charge C in the integer QH regime, and quasiparticle charge C for the QH state.