Starting from a quantum two-mode Bose-Hubbard Hamiltonian we determine the ground state properties, momentum distribution and dynamical evolution for a Bose Josephson junction realized by an ultracold Bose gas in a double-well trap. Varying the well asymmetry we identify Mott-like regions of parameters where number fluctuations are suppressed and the interference fringes in the momentum distribution are strongly reduced. We also show how Schroedinger cat states, realized from an initially phase coherent state by a sudden rise of the barrier among the two wells, will give rise to a destructive interference in the time-dependent momentum distribution.
We investigate ac Josephson effect in the resonant tunneling through mesoscopic superconducting junctions. In the presence of microwave irradiation, we show that the trajectory of multiple Andreev reflections can be closed by emitting or absorbing photons. Consequently, photon-assisted Andreev states are formed and play the role of carrying supercurrent. On the Shapiro steps, dc component appears when the resonant level is near a series of positions with spacing of half of the microwave frequency. Analytical result is derived in the limit of infinite superconducting gap, based on which new fea…
We study a circuit where a mesoscopic Josephson junction (JJ) is embedded in an environment consisting of a large bias resistor and a normal metal - superconductor tunnel junction (NIS). The effective Coulomb blockade of the JJ can be controlled by the tunneling current through the NIS junction leading to transistor-like characteristics. We show using phase correlation theory and numerical simulations that substantial current gain with low current noise ($i_{n}\lesssim 1$ fA/$\sqrt{\text{Hz}}$) and noise temperature ($\lesssim $ 0.1 K) can be achieved. Good agreement between our numerical simu…
We calculate the Josephson coupling energy $U_J(ϕ)$ (related to the supercurrent $I=(2e/\hbar) dU_J/dϕ$) for a disordered normal metal between two superconductors with a phase difference $ϕ$. We demonstrate that the symmetry of the scattering matrix of non-interacting quasiparticles in zero magnetic field implies that $U_J(ϕ)$ has a minimum at $ϕ=0$. A maximum (that would lead to a $π$-junction or negative superfluid density) is excluded for any realization of the disorder.
We model the 2-probe conductance of a quantum point contact (QPC), in linear response. If the QPC is highly non-adiabatic or near to scatterers in the open reservoir regions, then the usual distinction between leads and reservoirs breaks down and a technique based on scattering theory in the full two-dimensional half-plane is more appropriate. Therefore we relate conductance to the transmission cross section for incident plane waves. This is equivalent to the usual Landauer formula using a radial partial-wave basis. We derive the result that an arbitrarily small (tunneling) QPC can reach a p-w…
A theory is offered for the ballistic 4-terminal Josephson junction. The studied system consists of a mesoscopic two-dimensional normal rectangular layer which is attached in each side to the bulk superconducting banks (terminals). The relation between the currents through the different terminals, which is valid for arbitrary temperatures and junction sizes, is obtained. The nonlocal coupling of the supercurrents leads to a new effect, specific for the mesoscopic weak link between two superconducting rings; an applied magnetic flux through one of the rings produces a magnetic flux in the other…
We carry out an extensive experimental and theoretical study of the Josephson effect in S-N-S junctions made of a diffusive normal metal (N) embedded between two superconducting electrodes (S). Our experiments are performed on Nb-Cu-Nb junctions with highly-transparent interfaces. We give the predictions of the quasiclassical theory in various regimes on a precise and quantitative level. We describe the crossover between the short and the long junction regimes and provide the temperature dependence of the critical current using dimensionless units $eR_{N}I_{c}/ε_{c}$ and $k_{B}T/ε_{c}$ where $…
Josephson transport through a single molecule or carbon nanotube is considered in the presence of a local vibrational mode coupled to the electronic charge. The ground-state solution is obtained exactly in the limit of a large superconducting gap, and is extended to the general case by variational analysis. Coherent charge fluctuations are entangled with non-classical phonon states. The Josephson current induces squeezing of the phonon mode, which is controlled by the superconducting phase difference and by the junction asymmetry. Optical probes of non-classical phonon states are briefly discu…
Wide mesoscopic superconducting - normal-metal - superconducting (S-N-S) junctions exhibit Andreev bound states which carry substantial supercurrents, even at temperatures for which the equilibrium Josephson effect is exponentially small --- the currents carried by different states can cancel each other. This cancellation is incomplete whenever the junctions are driven out of equilibrium, e.g., by a dc voltage. This leads to phenomena similar to the usual dc and ac Josephson effects, but dominated by the second harmonic of the Josephson frequency, which may explain some striking recent experim…
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.
We report the successful fabrication of planar V/Cu/V mesoscopic Josephson weak-links of different size, and the analysis of their low-temperature behavior. The shorter junctions exhibit critical currents of several tens of microA at 350 mK, while Josephson coupling persists up to ~2.7 K. Good agreement is obtained by comparing the measured switching currents to a model which holds in the diffusive regime. Our results demonstrate that V is an excellent candidate for the implementation of superconducting nanodevices operating at a few kelvins.
We study the supercurrent in quasi-one-dimensional Josephson junctions with a weak link involving magnetism, either via magnetic impurities or via ferromagnetism. In the case of weak links longer than {\color{black}the magnetic pair-breaking} length, the Josephson effect is dominated by mesoscopic fluctuations. We establish the supercurrent-phase dependence $I(φ)$ along with statistics of its sample-dependent properties in junctions with transparent contacts between leads and link. High transparency gives rise to the inverse proximity effect, while the direct proximity effect is suppressed by …
Single-mode Josephson junction-based parametric amplifiers are often modeled as perfect amplifiers and squeezers. We show that, in practice, the gain, quantum efficiency, and output field squeezing of these devices are limited by usually neglected higher-order corrections to the idealized model. To arrive at this result, we derive the leading corrections to the lumped-element Josephson parametric amplifier of three common pumping schemes: monochromatic current pump, bichromatic current pump, and monochromatic flux pump. We show that the leading correction for the last two schemes is a single K…
We have experimentally studied the energy levels of a mesoscopic SQUID using inelastic Cooper-pair tunneling. The tunneling in a small Josephson junction depends strongly on its electromagnetic environment. We use this fact to do energy level spectroscopy of a SQUID-loop by coupling it to a small junction. Our samples with strong quasiparticle dissipation are well described by a model of a particle localized in one of the dips in a cosine-potential, while in the samples with weak dissipation we can see formation of energy bands.
We propose and analyze a mesoscopic Josephson junction consisting of two ferromagnetic insulator-superconductors (FI-Ss) coupled through a normal metal (N) layer. The Josephson current of the junction is non-trivially affected by the spin-splitting field induced by the FIs in the two superconductors. In particular, it shows sizeable enhancement by increasing the amplitude of the exchange field ($h_{ex}$) and displays a switchable current-phase relation which depends on the relative orientation of $h_{ex}$ in the FIs. In a realistic EuS/Al-based setup this junction can be exploited as a high-re…
We studied a mesoscopic cross-like normal metal structure connected to two superconducting (S) and two normal (N) reservoirs. We observed the Josephson effect under unusual conditions when there is no current through one of the two S/N interfaces. The potential difference between the S reservoirs was zero unless the voltage applied between S and N reservoirs exceeded a critical value although the electric potential in the N wire connecting the superconductors varied in a nonmonotonic way. The observed effects are discussed theoretically.
Magneto-fluctuations of the normal resistance R_N have been reproducibly observed in high critical temp erature superconductor (HTS) grain boundary junctions, at low temperatures. We attribute them to mesoscopic transport in narrow channels across the grain boundary line. The Thouless energy appears to be the relevant energy scale. Our findings have significant implications on quasiparticle relaxation and coherent transport in HTS grain boundaries.
We study the normal state conductance and the Josephson current in a superconductor-2DEG-superconductor structure where the size/shape of the 2DEG-region can be modified by an additional side-gate electrode. The considered transport properties follow from the retarded Green function which we compute by employing a tight-binding-like representation of the Hamiltonian in the 2DEG region. Our model studies offer a qualitative demonstration of the recently observed effects caused by side-gate modulation.
We report on the fabrication and characterization of a two-terminal mesoscopic interferometer based on three V/Cu/V Josephson junctions having nanoscale cross-section. The junctions have been arranged in a double-ring geometry realized by metallic thin film deposition through a suspended mask defined by electron beam lithography. Although a significant amount of asymmetry between the critical current of each junction is observed we show that the interferometer is able to suppress the supercurrent to a level lower than 6 parts per thousand, being here limited by measurement resolution. The pres…
Microwave irradiation of Nb-InAs-Nb junctions reveals frequency-doubled Josephson currents which persist to high temperatures, in the absence of a critical current. A nonequilibrium dynamical model, based on time-dependent Andreev bound states, successfully accounts for the resulting half-integer Shapiro step and an enhancement in the conductance near zero bias.
We study mesoscopic fluctuations in the supercurrent of a Josephson junction consisting of a topological insulator microbridge between two conventional superconductors. In the model, we account for the strong proximity effect when superconductors induce a gap in the spectrum of surface states as well as a magnetic field piercing the junction area that causes depairing and gap filling. The overall magnitude and functional form of the Josephson current fluctuations are determined analytically, and found to sensitively depend on the coupling strength to surface states, Thouless energy, and pair-b…
Josephson parametric amplifiers (JPA) are promising devices for applications in circuit quantum electrodynamics (QED) and for studies on propagating quantum microwaves because of their good noise performance. In this work, we present a systematic characterization of a flux-driven JPA at millikelvin temperatures. In particular, we study in detail its squeezing properties by two different detection techniques. With the homodyne setup, we observe squeezing of vacuum fluctuations by superposing signal and idler bands. For a quantitative analysis we apply dual-path cross-correlation techniques to r…
Two mesoscopic SQUID rings which are far from each other, are considered. A source of two-mode nonclassical microwaves irradiates the two rings with correlated photons. The Josephson currents are in this case quantum mechanical operators, and their expectation values with respect to the density matrix of the microwaves, yield the experimentally observed currents. Classically correlated (separable) and quantum mechanically correlated (entangled) microwaves are considered, and their effect on the Josephson currents is quantified. Results for two different examples that involve microwaves in numb…
We study the influence of superconducting correlations on the electronic specific heat in a diffusive superconductor-normal metal-superconductor Josephson junction. We present a description of this system in the framework of the diffusive-limit Green's function theory, taking into account finite temperatures, phase difference as well as junction parameters. We find that proximity effect may lead to a substantial deviation of the specific heat as compared to that in the normal state, and that it can be largely tuned in magnitude by changing the phase difference between the superconductors. A me…
We study mesoscopic fluctuations and weak localization correction to the supercurrent in Josephson junctions with coherent diffusive electron dynamics in the normal part. Two kinds of junctions are considered: a chaotic dot coupled to superconductors by tunnel barriers and a diffusive junction with transparent normal--superconducting interfaces. The amplitude of current fluctuations and the weak localization correction to the average current are calculated as functions of the ratio between the superconducting gap and the electron dwell energy, temperature, and superconducting phase difference …
We investigate nonlocal coherent transport in ballistic four-terminal Josephson structures (where bulk superconductors (terminals) are connected through a clean normal layer, e.g., a two-dimensional electron gas). Coherent anisotropic superposition of macroscopic wave functions of the superconductors in the normal region produces phase slip lines (2D analogs to phase slip centres) and time-reversal symmetry breaking 2D vortex states in it, as well as such effects as phase dragging and magnetic flux transfer. The tunneling density of local Andreev states in the normal layer was shown to contain…
Quantum fluctuations of the phases of the order parameter in 2D arrays of mesoscopic Josephson junctions and their effect on the destruction of superconductivity in the system are investigated by means of a quantum-cosine model that is free of the incorrect application of the phase operator. The proposed model employs trigonometric phase operators and makes it possible to study arrays of small superconducting granules, pores filled with superfluid helium, or Josephson junctions in which the average number of particles $n_0$ (effective bosons, He atoms, and so on) is small, and the standard app…
A theory is offered for a novel device, mesoscopic four-terminal SQUID. The studied system consists of a mesoscopic four-terminal junction, one pair of terminals of which is incorporated in a superconducting ring and the other one is connected with a transport circuit. The nonlocal weak coupling between the terminals leads to effects of phase dragging and magnetic flux transfer. The behaviour of a four-terminal SQUID, controlled by the external parameters, the applied magnetic flux and the transport current is investigated. The critical current and the current voltage characteristics as functi…
We report the results of several nonequilibrium experiments performed on superconducting/normal/superconducting (S/N/S) Josephson junctions containing either one or two extra terminals that connect to normal reservoirs. Currents injected into the junctions from the normal reservoirs induce changes in the electron energy distribution function, which can change the properties of the junction. A simple experiment performed on a 3-terminal sample demonstrates that quasiparticle current and supercurrent can coexist in the normal region of the S/N/S junction. When larger voltages are applied to the …
Mesoscopic superconducting-normal-metal-superconducting (S-N-S) junctions with a large separation between the superconducting electrodes (i.e. wide junctions) exhibit nonequilibrium supercurrents, even at temperatures for which the equilibrium Josephson effect is exponentially small. The second harmonic of the Josephson frequency dominates these currents, as observed in recent experiments. A simple description of these effects, in the spirit of the Resistively-Shunted-Junction model, is suggested here. It is used to calculate dc I-V characteristics, and to examine the effects of various types …
We investigate mesoscopic Josephson junction arrays created by patterning superconducting disks on monolayer graphene, concentrating on the high-$T/T_c$ regime of these devices and the phenomena which contribute to the superconducting glass state in diffusive arrays. We observe features in the magnetoconductance at rational fractions of flux quanta per array unit cell, which we attribute to the formation of flux-quantized vortices. The applied fields at which the features occur are well described by Ginzburg-Landau simulations that take into account the number of unit cells in the array. We fi…
Superconductor/semiconductor-nanowire hybrid structures can serve as versatile building blocks to realize Majorana circuits or superconducting qubits based on quantized levels such as Andreev qubits. For all these applications it is essential that the superconductor-semiconductor interface is as clean as possible. Furthermore, the shape and dimensions of the superconducting electrodes needs to be precisely controlled. We fabricated self-defined InAs/Al core/shell nanowire junctions by a fully in-situ approach, which meet all these criteria. Transmission electron microscopy measurements confirm…
We show that the three-junction SQUID device designed for the Josephson flux qubit can be used to study the dynamics of quantum chaos when operated at high energies. We determine the parameter region where the system is classically chaotic. We calculate numerically the fidelity or Loschmidt echo (LE) in the quantum dynamics under perturbations in the magnetic field and in the critical currents, and study different regimes of the LE. We discuss how the LE could be observed experimentally considering both the preparation of the initial state and the measurement procedure.
We consider the charge and spin effects in low dimensional superconducting weak links. The first part of the review deals with the effects of electron-electron interaction in Superconductor/Luttinger liquid/Superconductor junctions. The experimental realization of this mesoscopic hybrid system can be the individual single wall carbon nanotube that bridges the gap between two bulk superconductors. The dc Josephson current through a Luttinger liquid in the limits of perfectly and poorly transmitting junctions is evaluated. The relationship between the Josephson effect in a long SNS junction and …
We show that the three-junction SQUID device designed for the Josephson flux qubit can be used to study quantum chaos when operated at high energies. In the parameter region where the system is classically chaotic we analyze the spectral statistics. The nearest neighbor distributions $P(s)$ are well fitted by the Berry Robnik theory employing as free parameters the pure classical measures of the chaotic and regular regions of phase space in the different energy regions. The phase space representation of the wave functions is obtained via the Husimi distributions and the localization of the sta…
We discuss the dependence of the Josephson current correlations in mesoscopic superconductor/normal-conductor/superconductor (SNS) devices on the transparency of the superconductor/normal-conductor (SN) interfaces. Focusing on short junctions we apply the supersymmetry method to construct an effective field theory for mesoscopic SNS devices which is evaluated in the limit of highly and weakly transparent interfaces. We show that the two-point Josephson-current correlator differs by an universal factor 2 in these two cases.
We investigate theoretically and experimentally the transport properties of a plain Al superconducting strip in the presence of a single straight current-carrying wire, oriented perpendicular to the superconducting strip. It is well known that the critical current of the superconducting strip, Ic, in such cryotron--like system can be tuned by changing the current in the control wire, Iw. We demonstrated that the discrete change in the number of the pinned vortices/antivortices inside the narrow and long strip nearby the current-carrying wire results in a peculiar oscillatory dependence of Ic o…
We study Josephson effect in a ballistic graphene strip of length $L$ smaller than the superconducting coherence length and arbitrary width $W$. We find that the dependence of the critical supercurrent $I_{c}$ on $W$ is drastically different for different types of the edges. For \textit{smooth} and \textit{armchair} edges at low concentration of the carriers $I_{c}$ decreases monotonically with decreasing $W/L$ and tends to a constant minimum for a narrow strip $W/L\lesssim1$. The minimum supercurrent is zero for smooth edges but has a finite value $eΔ_{0}/\hbar$ for the armchair edges. At hig…
We consider a $SBS$ Josephson junction the superconducting electrodes $S$ of which are in contact with normal metal reservoirs ($B$ means a barrier). For temperatures near $T_{c}$ we calculate an effective critical current $% I_{c}^{\ast}$ and the resistance of the system at the currents $I<$ $% I_{c}^{\ast}$ and $I>>I_{c}^{\ast}$. It is found that the charge imbalance, which arises due to injection of quasiparticles from the $N$ reservoirs into the $S$ wire, affects essentially the characteristics of the structure. The effective critical current $I_{c}^{\ast}$ is always larger than the critic…
The measurement of higher order cumulants of the current noise generated by a nonlinear mesoscopic conductor using a Josephson junction as on-chip detector is investigated theoretically. The paper addresses the regime where the noise of the mesoscopic conductor initiates activated escape of the Josephson detector out of the zero-voltage state, which can be observed as a voltage rise. It is shown that the deviations from Johnson-Nyquist noise can mostly be accounted for by an effective temperature which depends on the second noise cumulant of the conductor. The deviations from Gaussian statisti…
A superconductor-normal metal-superconductor mesoscopic Josephson junction has been realized in which the critical current is tuned through normal current injection using a symmetric electron cooler directly connected to the weak link. Both enhancement of the critical current by more than a factor of two, and supercurrent suppression have been achieved by varying the cooler bias. Furthermore, this transistor-like device demonstrates large current gain $\sim$20) and low power dissipation.
Recent experiments have demonstrated the nonequilibrium control of the supercurrent through diffusive phase-coherent normal-metal weak links. The experimental results have been accurately described by the quasiclassical Green's function technique in the Keldysh formalism. Taking into account the geometry of the structure, different energy scales and the nonidealities at the interfaces allows us to obtain a quantitative agreement between the theory and the experimental results in both the amplitude and the phase dependence of the supercurrent, with no or very few fitting parameters. Here we dis…
The macroscopic quantum interference effects in ballistic Josephson microstructures are investigated. The studied system consists of four bulk superconductors (terminals) which are weakly coupled through the mesoscopic rectangular normal metal (two dimensional electron gas). We show that nonlocal electrodynamics of ballistic systems leads to specific current-phase relations for the mesoscopic multiterminal Josephson junction. The nonlocal coupling of supercurrents produces the "dragging" effect for phases of the superconducting order parameter in different terminals. The composite Josephson ju…
We analyze the quantum dynamics of a superconducting cavity coupled to a voltage biased Josephson junction. The cavity is strongly excited at resonances where the voltage energy lost by a Cooper pair traversing the circuit is a multiple of the cavity photon energy. We find that the resonances are accompanied by substantial squeezing of the quantum fluctuations of the cavity over a broad range of parameters and are able to identify regimes where the fluctuations in the system take on universal values.
The transport through a metal-superconductor interface is governed by a special charge conversion process, the Andreev reflection, where each incident electron drags another electron with itself to form a Cooper pair. At the normal side a hole is left behind dressed by superconducting correlations. For a low transparency interface the simultaneous transfer of two charges is strongly suppressed leading to a reduced conductance. Here we demonstrate that this reduced conductance can be turned to an infinite one by tuning the nanoscale geometry. Creating variable size nanojunctions between a thin …
It has recently become possible to encode the quantum state of superconducting qubits and the position of nanomechanical oscillators into the states of microwave fields. However, to make an ideal measurement of the state of a qubit, or to detect the position of a mechanical oscillator with quantum-limited sensitivity requires an amplifier that adds no noise. If an amplifier adds less than half a quantum of noise, it can also squeeze the quantum noise of the electromagnetic vacuum. Highly squeezed states of the vacuum serve as an important quantum information resource. They can be used to gener…
We have investigated the influence of shot noise on the IV-curves of a single mesoscopic Josephson junction. We observe a linear enhancement of zero-bias conductance of the Josephson junction with increasing shot noise power. Moreover, the IV-curves become increasingly asymmetric. Our analysis on the asymmetry shows that the Coulomb blockade of Cooper pairs is strongly influenced by the non-Gaussian character of the shot noise.
We investigate Josephson currents in mesoscopic rings with a weak link which are in or near a topological superconducting phase. As a paradigmatic example, we consider the Kitaev model of a spinless p-wave superconductor in one dimension, emphasizing how this model emerges from more realistic settings based on semiconductor nanowires. We show that the flux periodicity of the Josephson current provides signatures of the topological phase transition and the emergence of Majorana fermions situated on both sides of the weak link even when fermion parity is not a good quantum number. In large rings…
We couple a proximity Josephson junction to a Joule-heated normal metal film and measure its electron temperature under steady state and nonequilibrium conditions. With a timed sequence of heating and temperature probing pulses, we are able to monitor its electron temperature in nonequilibrium with effectively zero back-action from the temperature measurement in the form of additional dissipation or thermal conductance. The experiments demonstrate the possibility of using a fast proximity Josephson junction thermometer for studying thermal transport in mesoscopic systems and for calorimetry.
The controlled growth of nanowires (NWs) with dimensions comparable to the Fermi wavelengths of the charge carriers allows fundamental investigations of quantum confinement phenomena. Here, we present studies of proximity-induced superconductivity in undoped Ge/Si core/shell NW heterostructures contacted by superconducting leads. By using a top gate electrode to modulate the carrier density in the NW, the critical supercurrent can be tuned from zero to greater than 100 nA. Furthermore, discrete sub-bands form in the NW due to confinement in the radial direction, which results in stepwise incre…
Squeezing of the quadratures of the electromagnetic field has been extensively studied in optics and microwaves. However, previous works focused on the generation of squeezed states in a low impedance ($Z_0 \approx 50 Ω$) environment. We report here on the demonstration of the squeezing of bosonic edge magnetoplasmon modes in a quantum Hall conductor whose characteristic impedance is set by the quantum of resistance ($R_K \approx 25 k Ω$), offering the possibility of an enhanced coupling to low-dimensional quantum conductors. By applying a combination of dc and ac drives to a quantum point con…
We study exact self duality in the model of a Brownian particle in a washboard (WB) potential which describes a Josephson Junction (JJ) coupled to an environment, for arbitrary temperature and arbitrary form of the spectral density of the environment. To this end we introduce the Quantum Dissipative Villain Model (QDVM), which models tunneling of a degree of freedom coupled to a linear quantum environment through an infinite set of states. We derive general exact mappings on various dual discrete representations (one-dimensional Coulomb gases or surface roughening models) which are exactly sel…
We discuss how threshold detectors can be used for a direct measurement of the full counting statistics (FCS) of current fluctuations and how to implement Jose phson junctions in this respect. We propose a scheme to characterize the full co unting statistics from the current dependence of the escape rate measured. We il lustrate the scheme with explicit results for tunnel, diffusive and quasi-ballis tic mesoscopic conductors.
The phase diagram of a two-dimensional Josephson array of mesoscopic objects is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number $n_0$ of the sites in the system leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemic…
A superconducting single-electron transistor (SSET) coupled to an anharmonic oscillator, e.g., a Josephson junction-L-C circuit, can drive the latter to a nonequilibrium photon number state. By biasing the SSET in a regime where the current is carried by a combination of inelastic quasiparticle tunneling and coherent Cooper-pair tunneling (Josephson quasiparticle cycle), cooling of the oscillator as well as a laser like enhancement of the photon number can be achieved. Here we show, that the cut-off in the quasiparticle tunneling rate due to the superconducting gap, in combination with the anh…
A mesoscopic device in the simple tunnel junction or quantum point contact geometry emits microwaves with remarkable quantum properties, when subjected to a sinusoidal drive in the GHz range. In particular, single and two-photon squeezing as well as entanglement in the frequency domain have been reported. By revising the photo-assisted noise analysis developed in the framework of electron quantum optics, we present a detailed comparison between the cosine drive case and other experimentally relavent periodic voltages such as rectangular and Lorentzian pulses. We show that the latter drive is t…
We consider the conductivity quantization in two-dimensional arrays of mesoscopic Josephson junctions, and examine the associated degeneracy in various regimes of the system. The filling factor of the system may be controlled by the gate voltage as well as the magnetic field, and its appropriate values for quantization is obtained by employing the Jain hierarchy scheme both in the charge description and in the vortex description. The duality between the two descriptions then suggests the possibility that the system undergoes a change in degeneracy while the quantized conductivity remains fixed…
In this paper, we consider a system consisting of two capacitively coupled superconducting islands via Josephson junctions. We show that it can be reduced to two coupling harmonic oscillators under certain conditions, and solved exactly in terms of a displacing transformation, a beam-splitter-like transformation, and a squeezing transformation. It is found that the system evolves by a rotated-squeezed-coherent state when the system is initially in a coherent state. Quantum dynamics of the Cooper pairs in the two superconducting islands is investigated. It is shown that the number of the Cooper…
