Ac Josephson Effect Research Articles

Quantum theory of Bloch oscillations in a resistively shunted transmon

A transmon qubit embedded in a high-impedance environment acts in a way dual to a conventional Josephson junction. In analogy to the AC Josephson effect, biasing of the transmon by a direct current leads to the oscillations of voltage across it. These oscillations are known as the Bloch oscillations. We find the Bloch oscillations spectrum, and show that the zero-point fluctuations of charge make it broadband. Despite having a broad-band spectrum, Bloch oscillations can be brought in resonance with an external microwave radiation. The resonances lead to steps in the voltage-current relation, which are dual to the conventional Shapiro steps. We find how the shape of the steps depends on the environment impedance R, parameters of the transmon, and the microwave amplitude. The Bloch oscillations rely on the insulating state of the transmon which is realized at impedances exceeding the Schmid transition point, R > RQ = h/(2e)2.

Creation of two-dimensional circular motion of charge qubit

We suggest a nanoelectromechanical setup which generates a particular type of motion—the circular motion of mesoscopic superconducting grain, where motion is described by entangled nanomechanical coherent states. The setup is based on mesoscopic terminal utilizing the ac Josephson effect between the superconducting electrodes and the grain, operating in the regime of the Cooper pair box controlled by the gate voltage. The grain is placed on the free end of the suspended cantilever, performing controlled two-dimensional mechanical vibrations. Required functionality is achieved by operating two external parameters, bias voltage between the superconducting electrodes and voltage between gate electrodes, by which the nanomechanical coherent states are formed and organized in a pair of entangled cat-states in two perpendicular spatial directions, which evolve in time in the way to provide a circular motion.

Dynamical Exciton Condensates in Biased Electron-Hole Bilayers.

Bilayer materials may support interlayer excitons comprised of electrons in one layer and holes in the other. In experiments, a nonzero exciton density is typically sustained by a bias chemical potential, implemented either by optical pumping or by electrical contacts connected to the two layers. We show that if charge can tunnel between the layers, the chemical potential bias means that an exciton condensate is in the dynamical regime of ac Josephson effect. It has physical consequences such as tunneling currents and the ability to tune a condensate from bright (emitting coherent photons) to dark by experimental controlling knobs. If the system is placed in an optical cavity, coupling with cavity photons favors different dynamical states depending on the bias, realizing superradiant phases.

Feynman paradox about the Josephson effect and a sawtooth current in the double junction

We revisit the Feynman approach to the Josephson effect, which employs a pair of linear coupling equations for its modeling. It is found that while the exact solutions can account for the AC Josephson effect when the coupling strength is significantly less than the voltage, they fail to produce the DC Josephson effect in any practical scenario. To address this fundamental discrepancy, we derive the coupled Ginzburg-Landau (GL) equations for two interconnected superconductors based on BCS theory. These equations reveal that the nonlinear coupling, which is overlooked in the Feynman approach, is crucial in describing the spontaneous symmetry breaking in superconductors, a critical factor for achieving the DC Josephson effect. When the coupled GL equations are applied to a double junction, a sawtooth current pattern emerges, a result unattainable via the Feynman approach.

Absence of fractional ac Josephson effect in superconducting junctions

Absence of fractional ac Josephson effect in superconducting junctions

Fractional AC Josephson effect in a topological insulator proximitized by a self-formed superconductor

Fractional AC Josephson effect in a topological insulator proximitized by a self-formed superconductor

Autonomous dynamics of two-dimensional insulating domain with superclimbing edges

Superclimbing dynamics is the signature feature of transverse quantum fluids describing wide superfluid one-dimensional interfaces and/or edges with negligible Peierls barrier. Using Lagrangian formalism, we show how the essence of the superclimb phenomenon—dynamic conjugation of the fields of the superfluid phase and geometric shape—clearly manifests itself via characteristic modes of autonomous motion of the insulating domain (“droplet”) with superclimbing edges. In the translation invariant case and in the absence of supercurrent along the edge, the droplet demonstrates ballistic motion with the velocity-dependent shape and zero bulk currents. In an isotropic trapping potential, the droplet features a doubly degenerate sloshing mode. The period of the ground-state evolution of the superfluid phase (dictating the frequency of the AC Josephson effect) is sensitive to the geometry of the droplet. The supercurrent along the edge dramatically changes the droplet dynamics: The motion acquires features resembling that of a two-dimensional charged particle interacting with a perpendicular magnetic field. In a linear external potential (uniform force field), the state with a supercurrent demonstrates a spectacular gyroscopic effect—uniform motion in the perpendicular to the force direction. Published by the American Physical Society 2024

Observation of Momentum Space Josephson Effects in Weakly Coupled Bose-Einstein Condensates.

The momentum space Josephson effect describes the supercurrent flow between weakly coupled Bose-Einstein condensates (BECs) at two discrete momentum states. Here, we experimentally observe this exotic phenomenon using a BEC with Raman-induced spin-orbit coupling, where the tunneling between two local band minima is implemented by the momentum kick of an additional optical lattice. A sudden quench of the Raman detuning induces coherent spin-momentum oscillations of the BEC, which is analogous to the ac Josephson effect. We observe both plasma and regular Josephson oscillations in different parameter regimes. The experimental results agree well with the theoretical model and numerical simulation and showcase the important role of nonlinear interactions. We also show that the measurement of the Josephson plasma frequency gives the Bogoliubov zero quasimomentum gap, which determines the mass of the corresponding pseudo-Goldstone mode, a long-sought phenomenon in particle physics. The observation of momentum space Josephson physics offers an exciting platform for quantum simulation and sensing utilizing momentum states as a synthetic degree.

Nanomechanical manipulation of superconducting charge-qubit quantum networks

We suggest a nanoelectromechanical setup and corresponding time-protocol for controlling parameters in order to demonstrate nanomechanical manipulation of superconducting charge-qubit quantum network. We illustrate it on an example reflecting important task for quantum information processing — transmission of quantum information between two charge-qubits facilitated by nanomechanics. The setup is based on terminals utilizing the AC Josephson effect between bias voltage-controlled bulk superconductors and mechanically vibrating mesoscopic superconducting grain in the regime of the Cooper pair box, controlled by the gate voltage. The described manipulation of quantum network is achieved by transduction of quantum information between charge-qubits and intentionally built nanomechanical coherent states, which facilitate its transmission between qubits. This performance is achieved using quantum entanglement between electrical and mechanical states.

Superconducting D/A Converters Generating Quantum Voltage Defined by the Reference Microwave Frequency and the AC Josephson Effect

Superconducting D/A Converters Generating Quantum Voltage Defined by the Reference Microwave Frequency and the AC Josephson Effect

Nonequilibrium Transport in a Superfluid Josephson Junction Chain: Is There Negative Differential Conductivity?

We consider the far-from-equilibrium quantum transport dynamics in a 1D Josephson junction chain of multimode Bose-Einstein condensates. We develop a theoretical model to examine the experiment of Labouvie etal. [Phys. Rev. Lett. 115, 050601 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.050601], wherein the phenomenon of negative differential conductivity (NDC) was reported in the refilling dynamics of an initially depleted site within the chain. We demonstrate that a unitary c-field description can quantitatively reproduce the experimental results over the full range of tunnel couplings, and requires no fitted parameters. With a view toward atomtronic implementations, we further demonstrate that the filling is strongly dependent on spatial phase variations stemming from quantum fluctuations. Our findings suggest that the interpretation of the device in terms of NDC is invalid outside of the weak coupling regime. Within this restricted regime, the device exhibits a hybrid behavior of NDC and the ac Josephson effect. A simplified circuit model of the device will require an approach tailored to atomtronics that incorporates quantum fluctuations.

Charge-4e supercurrent in a two-dimensional InAs-Al superconductor-semiconductor heterostructure

AbstractSuperconducting qubits with intrinsic noise protection offer a promising approach to improve the coherence of quantum information. Crucial to such protected qubits is the encoding of the logical quantum states into wavefunctions with disjoint support. Such encoding can be achieved by a Josephson element with an unusual charge-4e supercurrent emerging from the coherent transfer of pairs of Cooper-pairs. In this work, we demonstrate the controlled conversion of a conventional charge-2e dominated to a charge-4e dominated supercurrent in a superconducting quantum interference device (SQUID) consisting of gate-tunable planar Josephson junctions. We investigate the ac Josephson effect of the SQUID and measure a dominant photon emission at twice the fundamental Josephson frequency together with a doubling of the number of Shapiro steps, both consistent with the appearance of charge-4e supercurrent. Our results present a step towards protected superconducting qubits based on superconductor-semiconductor hybrid materials.

Recent advancements and perspectives of INRiM’s time-dependent Josephson voltage standards

Quantum voltage standards based on ac Josephson effect have been used in metrology since a few years after the discovery of the physical phenomenon. The role of quantum standards is now crucial following the SI redefinition in 2019: electrical units are today defined in terms of the fundamental constants e (elementary charge) and h (Planck’s constant). The extremely low uncertainty in dc measurements, that can be lower than 1 nV/V at 10 V, is stimulating research to extend application to ac and signals arbitrarily changing with time. Approaching the dc accuracy is challenging, however. The two main technologies used for the generation of non-steady voltage signals are programmable and pulsed Josephson junction arrays. In this work we discuss the main advancements obtained at the Italian Istituto Nazionale di Ricerca Metrologica (INRiM) with both technologies, and the most recent developments taking advantage of He-free device cooling techniques.

Supercurrent, Multiple Andreev Reflections and Shapiro Steps in InAs Nanosheet Josephson Junctions.

We report an experimental study of proximity induced superconductivity in planar Josephson junction devices made from free-standing InAs nanosheets. The nanosheets are grown by molecular beam epitaxy, and the Josephson junction devices are fabricated by directly contacting the nanosheets with superconductor Al electrodes. The fabricated devices are explored by low-temperature carrier transport measurements. The measurements show that the devices exhibit a gate-tunable supercurrent, multiple Andreev reflections, and a good quality superconductor-semiconductor interface. The superconducting characteristics of the Josephson junctions are investigated at different magnetic fields and temperatures and are analyzed based on the Bardeen-Cooper-Schrieffer (BCS) theory. The measurements of the ac Josephson effect are also conducted under microwave radiations with different radiation powers and frequencies, and integer Shapiro steps are observed. Our work demonstrates that InAs nanosheet based hybrid devices are desired systems for investigating the forefront of physics, such as two-dimensional topological superconductivity.

Observation of half-integer Shapiro steps in graphene Josephson junctions

We study quantum transport and AC Josephson effect of hexagonal boron nitride encapsulated graphene (BGB) Josephson junctions (JJs). Our experiments reveal the emergence of the half-integer Shapiro steps in the n-type regime with high electron carrier densities. We attribute this observation to the gate-tunable transmission probability of the graphene junction. Our numerical simulations are consistent with the appearance of half-integer Shapiro steps at high transparency, which suggests a skewed current phase relationship in the graphene JJ.

Transduction of quantum information from charge qubit to nanomechanical cat-state

We suggest a nanoelectromechanical setup and corresponding time-protocol of its manipulation by which we transduce quantum information from charge qubit to nanomechanical cat-state. The setup is based on the AC Josephson effect between bulk superconductors and mechanically vibrating mesoscopic superconducting island in the regime of the Cooper pair box. Starting with a pure state with quantum information initially encoded into superposition of the Cooper pair box states, applying a specially tailored time-protocol upon bias voltage and gate electrodes, we obtain a new pure state with information finally encoded into superposition of nanomechanical coherent states constituting the cat-state. This performance is achieved using quantum entanglement between electrical and mechanical states. Nanomechanical cat-states serve as a “storage” of quantum information, motivated by significantly longer decoherence time with respect to the charge qubit states, from which the information can be transdued back to the charge qubit applying the reverse time-protocol.

Oscillating Solitons and ac Josephson Effect in Ferromagnetic Bose-Bose Mixtures.

Close to the demixing transition, the degree of freedom associated with relative density fluctuations of a two-component Bose-Einstein condensate is described by a nondissipative Landau-Lifshitz equation. In the quasi-one-dimensional weakly immiscible case, this mapping surprisingly predicts that a dark-bright soliton should oscillate when subject to a constant force favoring separation of the two components. We propose a realistic experimental implementation of this phenomenon which we interpret as a spin-Josephson effect in the presence of a movable barrier.

Discrete time translation symmetry breaking in a Josephson junction laser

A Josephson junction laser is realized when a microwave cavity is driven by a voltage-biased Josephson junction. Through the ac Josephson effect, a dc voltage generates a periodic drive that acts on the cavity and generates interactions between its modes. A sufficiently strong drive enables processes that downconvert a drive resonant with a high harmonic into photons at the cavity fundamental frequency, breaking the discrete time translation symmetry set by the Josephson frequency. Using a classical model, we determine when and how this transition occurs as a function of the bias voltage and the number of cavity modes. We find that certain combinations of mode number and voltage tend to facilitate the transition which emerges via an instability within a subset of the modes. Despite the complexity of the system, there are cases in which the critical drive strength can be obtained analytically.

Particle conserving approach to ac-dc driven interacting quantum dots with superconducting leads

The combined action of a dc bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent nonequilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U(1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak-coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the ac Josephson effect and an ac voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net dc current, the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport, we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net dc current flowing against the applied dc bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied dc bias.

A distributed active patch antenna model of a Josephson oscillator.

Optimization of Josephson oscillators requires a quantitative understanding of their microwave properties. A Josephson junction has a geometry similar to a microstrip patch antenna. However, it is biased by a dc current distributed over the whole area of the junction. The oscillating electric field is generated internally via the ac-Josephson effect. In this work, I present a distributed, active patch antenna model of a Josephson oscillator. It takes into account the internal Josephson electrodynamics and allows for the determination of the effective input resistance, which couples the Josephson current to cavity modes in the transmission line formed by the junction. The model provides full characterization of Josephson oscillators and explains the origin of the low radiative power efficiency. Finally, I discuss the design of an optimized Josephson patch oscillator capable of reaching high efficiency and radiation power for emission into free space.