Effect of the Coulomb blockade of Cooper pairs on the dynamic properties of small-size Josephson junctions

The dynamics of Cooper pair tunneling under Coulomb blockade in small-size Josephson junctions is studied in terms of the resistive model. A relationship between the delay time and temperature fluctuations of the Coulomb blockade edge and the rate of rise of the voltage across the junction is derived.     

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.     

Mesoscopic Josephson effect

In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current–voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.     

Coherent Cooper pair tunneling in systems of Josephson junctions: Effects of quasiparticle tunneling and of the electromagnetic environment

Small capacitance tunnel junctions show single electron effects and, in the superconducting state, the coherent tunneling of Cooper pairs. We study these effects in a system of two Josephson junctions, driven by a voltage source with a finite impedance. Novel features show up in theI?V characteristics, in particular pronounced structures at subgap voltages. These are due to Cooper pair tunneling, combined with tunneling of quasiparticles or with excitation of the electromagnetic environment.     

Single Cooper pair pump

We have operated a Cooper pair pump, a linear array of superconducting tunnel junctions in which single Cooper pairs are moved under the influence of ac signals applied to two gate electrodes. The pump is based on the Coulomb blockade of charge tunneling. Because of the small junction capacitance precisely one Cooper pair is transferred per ac cycle. The current-voltage characteristics of this device show current plateaus close to 2ef, wheref is the frequency of the ac voltages. Deviations are explained in terms of Zener tunneling, Cooper pair co-tunneling, and sporadic quasiparticle tunneling.     

Bright side of the Coulomb blockade

We explore the photonic (bright) side of the dynamical Coulomb blockade (DCB) by measuring the radiation emitted by a dc voltage-biased Josephson junction embedded in a microwave resonator. In this regime Cooper pair tunneling is inelastic and associated with the transfer of an energy 2eV into the resonator modes. We have measured simultaneously the Cooper pair current and the photon emission rate at the resonance frequency of the resonator. Our results show two regimes, in which each tunneling Cooper pair emits either one or two photons into the resonator. The spectral properties of the emitted radiation are accounted for by an extension to DCB theory.     

A quasiparticle SIN mixer for the 230 GHz frequency range

We report on quasiparticle mixing in the frequency range 220 to 230 GHz using SIN junctions. The lowest double sideband receiver noise temperature measured was about 230 K. This result shows that the SIN junction provides an interesting alternative for high frequency heterodyne receivers where pair tunneling in SIS junctions could give rise to interference from Josephson effects.     

Quantum dynamics of superconducting point contacts: chiral anomaly,Landau–Zener transitions,and all that

Quantum effects in the dynamics of the Josephson phase difference in Josephson junctions with large electron transparency D are studied in the adiabatic regime, when the characteristic charging energyE_C of the junction is much smaller than the superconducting energy gap Δ. In isolated junctions, quantum phase fluctuations are large and manifest themselves as Coulomb blockade of Cooper pair tunneling. The amplitude of the Coulomb blockade oscillations is calculated for single-mode junctions with arbitrary D. In particular, it is shown that the chiral anomaly completely suppresses Coulomb blockade in ballistic junctions with D =  1, and the suppression process at D →  1 can be described as the Landau–Zener transition in imaginary time. In the regime when quantum phase fluctuations are small, they lead to quantum decay of supercurrent states due to macroscopic quantum tunneling of phase through the Josephson potential barrier. The decay rate is found in the nearly-ballistic junctions.     

Josephson effect due to odd-frequency pairs in diffusive half metals

Motivated by a recent experiment [Keizer et al., Nature (London) 439, 825 (2006)], we study the Josephson effect in superconductor/diffusive half metal/superconductor junctions using the recursive Green function method. The spin-flip scattering at the junction interfaces opens the Josephson channel of the odd-frequency spin-triplet Cooper pairs. As a consequence, the local density of states in a half metal has a large peak at the Fermi energy. Therefore the odd-frequency pairs can be detected experimentally by using the scanning tunneling spectroscopy.     

Spin-asymmetric Josephson effect

We propose that with ultracold Fermi gases one can realize a spin-asymmetric Josephson effect in which the two spin components of a Cooper pair are driven asymmetrically--corresponding to driving a Josephson junction of two superconductors with different voltages V(↑) and V(↓) for spin up and down electrons, respectively. We predict that the spin up and down components oscillate at the same frequency but with different amplitudes. Furthermore our results reveal that the standard interpretation of the Josephson supercurrent in terms of coherent bosonic pair tunneling is insufficient. We provide an intuitive interpretation of the Josephson supercurrent as interference in Rabi oscillations of pairs and single particles, the latter causing the asymmetry.     

Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction

We report on the first realization of a single bosonic Josephson junction, implemented by two weakly linked Bose-Einstein condensates in a double-well potential. In order to fully investigate the nonlinear tunneling dynamics we measure the density distribution in situ and deduce the evolution of the relative phase between the two condensates from interference fringes. Our results verify the predicted nonlinear generalization of tunneling oscillations in superconducting and superfluid Josephson junctions. Additionally, we confirm a novel nonlinear effect known as macroscopic quantum self-trapping, which leads to the inhibition of large amplitude tunneling oscillations.     

Quasiparticle and Cooper pair tenneling in small capacitance Josephson junctions

The tunneling of single electrons in small capacitance tunnel junctions is influenced by charging effects and by the fluctuations of the elecromagnetic environment. We study the effect of an external circuit with arbitrary impedance on the tunneling of quasiparticles and Cooper pairs in voltage driven Josephson junctions. We present results at finite temperatures and also consider an acdriven system.     

Dissipative dynamics of planar d-wave Josephson junctions

We study quantum dynamics of and phase transitions in a Josephson junction between two planar d-wave superconductors where the processes of both quasiparticle and Cooper pair tunneling give rise to nonlocal dissipative terms in the effective action. By combining a perturbative weak coupling analysis in the charge representation with a variational approach in the phase representation at strong coupling, we ascertain a layout of the junction's phase diagram and discuss the corresponding behaviors.     

Superconducting single-charge transistor in a tunable dissipative environment

We study a superconducting single-charge transistor, where the coherence of Cooper pair tunneling is destroyed by the coupling to a tunable dissipative environment. Sequential tunneling and cotunneling processes are analyzed to construct the shape of the conductance peaks and their dependence on the dissipation and temperature. Unexpected features are found due to a crossover between two distinct regimes, one "environment assisted" the other "environment dominated." Several of the predictions have been confirmed by recent experiments. The model and results apply also to the dynamics of Josephson junction quantum bits on a conducting ground plane, thus explaining the influence of dissipation on the coherence.     

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.     

Dynamics of Information Coded in a Single Cooper Pair Box

In this paper, we investigate the dynamics of coded information in a single Cooper pair interacting with a single Cavity mode. The effect of the relative ratio of Josephson junction capacity and the gate capacities on the purity, coherent vectors and the entropy of the travelling Cooper pair are investigated. The exchange information between the environment and the Cooper pair is quantified for different values of the Cooper qubit and environment parameters.     

Aharonov-Casher-effect suppression of macroscopic tunneling of magnetic flux

We suggest a system in which the amplitude of macroscopic flux tunneling can be modulated via the Aharonov-Casher effect. The system is an rf SQUID with the Josephson junction replaced by a Bloch transistor--two junctions separated by a small superconducting island on which the charge can be induced by an external gate voltage. When the Josephson coupling energies of the junctions are equal and the induced charge is q = e, destructive interference between tunneling paths brings the flux tunneling rate to zero. The device may also be useful as a qubit for quantum computation.     

Resonance tunneling of cooper pairs in a superconductor-polymer-superconductor josephson junction

It is shown that the superconducting current flowing though a polymer in a superconductor-polymer-superconductor Josephson structure is due to resonant tunneling of Cooper pairs. The critical current and the thickness of the polymer in which the superconducting current is observed depend on the coherence length of a Cooper pair in the superconductor contacting the polymer.     

Quantum fluctuations in a distributed Josephson junction and the spectral properties of Josephson oscillators

Within the framework of a tunneling Hamiltonian, we obtain an equation for the reduced density matrix to describe quasiclassical dynamics and fluctuation effects in distributed Josephson junctions for voltages comparable with the superconducting gap. For quasiclassical dynamics, we derive the Langevin equation describing in a self-consistent way the resistive state and fluctuations due to both the tunneling current and the electromagnetic field. Current-voltage characteristics of a Josephson oscillator are calculated in the high magnetic field approximation. The intensity and shape of the spectral line of radiation due to vortices moving in a distributed Josephson junction are found.     

Josephson effect between conventional and non-centrosymmetric superconductors

We analyze the Josephson effect between a conventional and a non-centrosymmetric superconductor to examine characteristic features of such junctions and the symmetry of the superconducting phases. As a concrete example, we consider the non-centrosymmetric superconductor CePt₃Si where Rashba spin-orbit coupling plays a crucial role and affects the Josephson pair tunneling. In this case, the Josephson coupling is composed of two parts, spin-singlet-like and spin-triplet-like components. The triplet-like component can lead to a Josephson coupling shifted by π relative to the singlet-like coupling. This has important implications on the interference effects and may explain some recent experimental results for the Al/CePt₃Si junction.