Bloch oscillations were predicted and observed long ago in Josephson junctions, which are thin insulating or conducting layers bridging two superconductors. Here we forward a scheme for utilizing these oscillations to amplify nano-metric mechanical vibrations. Highly coherent non-classical mechanical states can be produced and controlled by simply applying a DC bias current and an in-plane magnetic field. The vibrations induce peaks in the I-V characteristic of the junction and can be detected by simple DC voltage measurements.
Half a century ago Brian Josephson made a series of striking predictions related to a tunnelling barrier sandwiched between two superconductors. One particular prediction, later became known as the a.c.-Josephson effect, said that under a finite d.c. bias the tunnelling current contains an a.c. supercurrent component, oscillating at microwave frequency. This prediction was experimentally verified through observation of the junction current-voltage characteristics modified by the interaction with the electromagnetic radiation, and direct detection of the microwave radiation emitted from the jun…
We have measured the current-voltage characteristics of a Josephson junction with tunable Josephson energy $E_J$ embedded in an inductive environment provided by a chain of SQUIDs. Such an environment induces localization of the charge on the junction, which results in an enhancement of the zero-bias resistance of the circuit. We understand this result quantitatively in terms of the Bloch band dynamics of the localized charge. This dynamics is governed by diffusion in the lowest Bloch band of the Josephson junction as well as by Landau-Zener transitions out of the lowest band into the higher b…
We discuss the properties of devices of small Josephson junctions in the light of the phase fluctuation theory and the energy band structure, which arises from the delocalization of the phase variable. The theory is applied in the realization of a mesoscopic amplifier, the Bloch oscillating transistor. The device characteristics and comparison with theory and simulations are discussed. The current gain of the device in a stable operating mode has been measured to be as high as 30. Measurements on input impedance and the power gain show that the BOT is an amplifier designed for middle-range imp…
We consider a combined nanomechanical-supercondcuting device that allows the Cooper pair tunneling to interfere with the mechanical motion of the middle superconducting island. Coupling of mechanical oscillations of a superconducting island between two superconducting leads to the electronic tunneling generate a supercurrent which is modulated by the oscillatory motion of the island. This coupling produces alternating finite and vanishing supercurrent as function of the superconducting phases. Current peaks are sensitive to the superconducting phase shifts relative to each other. The proposed …
We show that the electrical impedance of a small-capacitance Josephson junction includes besides the capacitive term $-i/ωC_B$ also an inductive term $iωL_B$. Similar to the known Bloch capacitance $C_B(q)$, the Bloch inductance $L_B(q)$ also depends periodically on the quasicharge $q$, and its maximum value achieved at $q=e (\textrm{mod} 2e)$ always exceeds the value of the Josephson inductance of this junction $L_J(ϕ)$ at fixed $ϕ=0$. The effect of the Bloch inductance on the dynamics of a single junction and a one-dimensional array is described.
We consider a nanoelectromechanical Josephson junction, where a suspended nanowire serves as a superconducting weak link, and show that an applied DC bias voltage an result in suppression of the flexural vibrations of the wire. This cooling effect is achieved through the transfer of vibronic energy quanta first to voltage driven Andreev states and then to extended quasiparticle electronic states. Our analysis, which is performed for a nanowire in the form of a metallic carbon nanotube and in the framework of the density matrix formalism, shows that such self-cooling is possible down to a level…
Bloch oscillations predicted to occur in current-biased single Josephson junctions have eluded direct observation up to now. Here, we demonstrate similar Bloch oscillations in a slightly richer Josephson circuit, the quantronium. The quantronium is a Bloch transistor with two small junctions in series, defining an island, in parallel with a larger junction. In the ground state, the microwave impedance of the device is modulated periodically with the charge on the gate capacitor coupled to the transistor island. When a current flows across this capacitor, the impedance modulation occurs at the …
Recent advances have attracted attention to non-standard Josephson junctions in which a supercurrent can flow despite zero phase difference between the constituent superconducting leads. Here, we propose a zero-phase-difference nanoelectromechanical junction which, in contrast to other considered systems, exhibits symmetry between leftward and rightward tunneling through the junction. We show that a supercurrent is nevertheless possible as a result of spontaneous symmetry breaking. In the suggested junction, the supercurrent is mediated by tunneling via a superconducting Cooper-pair box on a b…
Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging energy comparable to the Josephson coupling energy are explored within the context of a model previously considered by Geigenmüller and Schön that includes Zener tunneling and treats quasiparticle tunneling as an explicit shot-noise process. The dynamics of the junction quasicharge are investigated numerically using both Monte Carlo and ensemble approaches to calculate voltage--current characteristics in the presence of microwaves. We examine in detail the origin of harmonic and subharmonic Bloch steps at dc biases $I=…
We demonstrate that a supercurrent can pump energy from a battery that provides a voltage bias into nanomechanical vibrations. Using a device containing a nanowire Josephson weak link as an example we show that a nonlinear coupling between the supercurrent and a static external magnetic field leads to a Lorentz force that excites bending vibrations of the wire at resonance conditions. We also demonstrate the possibility to achieve more than one regime of stationary nonlinear vibrations and how to detect them via the associated dc Josephson currents and we discuss possible applications of such …
We show that an Ideal Bose gas that is contained within a very thin ring exhibits phenomena analogous to the Bloch and Josephson oscillations of a charged Ideal Fermi gas in a thin ring. If the walls of the ring are constrained to have an angular velocity $ω$, the angular momentum has an anomalous component that is periodic in $ω$, with a period equal to the quantum of angular velocity $ω_{0}\equiv \hbar /mR^{2}$. If a constant applied torque is applied to the walls, there will be component of the angular momentum of the gas that is periodic in time, with a 'Josephson frequency' given by $f_{J…
Josephson-Phase Reversal of Non-Bloch Andreev Propagation
College of Physics and Materials Science, Tianjin Normal University（天津师范大学物理与材料科学学院）；Interdisciplinary Center, Tianjin Normal University（天津师范大学交叉研究中心）；Center for Joint Quantum Studies & Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系量子联合研究中心及天津市低维材料物理与制备技术重点实验室）
The Bloch-oscillating transistor (BOT) is an amplifier that utilizes semiclassical dynamics of states in energy bands under traveling quasimomentum. In a BOT, a single quasiparticle tunneling across a base tunnel junction switches the state of a superconducting tunnel junction to a lower Bloch band, triggering a series of resonant Cooper-pair tunnelings through an emitter Josephson junction (Bloch oscillations). Here, we investigate experimentally and theoretically an alternative realization of this device, based only on superconducting tunnel junctions. We discover new amplification schemes, …
Low-noise amplification atmicrowave frequencies has become increasingly important for the research related to superconducting qubits and nanoelectromechanical systems. The fundamental limit of added noise by a phase-preserving amplifier is the standard quantum limit, often expressed as noise temperature $T_{q} = \hbar ω/2k_{B}$. Towards the goal of the quantum limit, we have developed an amplifier based on intrinsic negative resistance of a selectively damped Josephson junction. Here we present measurement results on previously proposed wide-band microwave amplification and discuss the challen…
We have measured the current-voltage characteristics of a single Josephson junction placed in a high impedance environment. The transfer of Cooper pairs through the junction is governed by overdamped quasicharge dynamics, leading to Coulomb blockade and Bloch oscillations. Exact duality exists to the standard overdamped phase dynamics of a Josephson junction, resulting in a dual shape of the current-voltage characteristic, with current and voltage changing roles. We demonstrate this duality with experiments which allow for a quantitative comparison with a theory that includes the effect of flu…
Multi-terminal Josephson junctions were recently proposed as a versatile and tunable platform to emulate topological Bloch-like Hamiltonians in arbitrary dimensions. In this perspective article, we will give a brief overview of the subject and recognize these mesoscopic devices as realizations of topological flux networks as the ones envisioned by J. E. Avron and coworkers in their seminal works on the early days of the quantum Hall effect. We summarize the current state-of-the-art theoretical and experimental research regarding these Josephson devices, highlighting recent developments and giv…
We have fabricated the Bloch transistor shunted on-chip by a small-sized Cr resistor with Rs about 1 kOhm. The Bloch transistor normally consists of two small Josephson junctions connected in series, which in our case have been replaced by two superconducting interferometer loops, each with two junctions in parallel. A capacitively coupled gate is supplied to control the induced charge of the small intermediate electrode (island) of the transistor. The measured I-V curves show no hysteresis and correspond to the operation of a effective Josephson junction at the high-damping and strong-noise l…
We considered a nanoelectromechanical system consisting of a movable Cooper-pair box qubit which is subject to an electrostatic field, and coupled to the two bulk superconductors via tunneling processes. We suggest that qubit dynamics is related to the one of a quantum oscillator and demonstrate that a bias voltage applied between superconductors generates states represented by the entanglement of qubit states and coherent states of the oscillator if certain resonant conditions are fulfilled. It is shown that a structure of this entanglement may be controlled by the bias voltage in a way that …
The dc transport properties of long arrays of small Al Josephson junctions, biased through on-chip Cr resistors, are studied. The IV-characteristics show a large Coulomb threshold for current as well as negative-slope regions indicating the regime of autonomous Bloch oscillations up to rather high frequencies of f = I/2e ~1 GHz, comparable to those reported by other groups for single junctions. On the other hand, a small depth of the back-bending implies a low duty cycle and a broad spectrum of the oscillations, which we attribute to the insufficiently high impedance of the bias resistors. A s…
We introduce Weyl Josephson circuits: small Josephson junction circuits that simulate Weyl band structures. We first formulate a general approach to design circuits that are analogous to Bloch Hamiltonians of a desired dimensionality and symmetry class. We then construct and analyze a six-junction device that produces a 3D Weyl Hamiltonian with broken inversion symmetry and in which topological phase transitions can be triggered \emph{in situ}. We argue that currently available superconducting circuit technology allows experiments that probe topological properties inaccessible in condensed mat…
The Bloch oscillating transistor (BOT) is a device, where single electron current through a normal tunnel junction can be used to enhance Cooper pair current in a mesoscopic Josephson junction leading to signal amplification. In this paper we develop a theory, where the BOT dynamics is described as a two-level system. The theory is used to predict current-voltage characteristics and small-signal response. Transition from stable operation into hysteretic regime is studied. By identifying the two-level switching noise as the main source of fluctuations, the expressions for equivalent noise sourc…
Université Grenoble-Alpes, CNRS, Grenoble INP, Institut NEEL（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔理工学院、NEEL研究所）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Department of Electrical Engineering, The Pennsylvania State University（宾夕法尼亚州立大学电气工程系）
We present a detailed study of photonic heat transport across a Josephson junction coupled to two arbitrary linear circuits having different temperatures. First, we consider the linear approximation, in which a nonlinear Josephson potential is replaced by a quadratic one and the junction acts as an inductor. Afterwards, we discuss the effects of junction anharmonicity. We separately consider the weak-coupling limit, in which the Bloch band structure of the junction energy spectrum plays an important role, and the opposite strong-coupling regime. We apply our general results to two specific mod…
We study the effect of external driving on the two level systems (TLSs) assumed to be a major obstacle in increasing the coherence time of solid state Josephson-junction qubits. We find, by use of a Bloch-Redfield approach, that external driving has two major effects on the TLS. The first is increased fluctuations between the two states of the TLS, the significance of this effect compared to thermal fluctuations depend on the energy splitting of the TLS compared to temperature. The second effect is a reduction in the intensity of the noise spectrum at low frequencies, and at the same time an i…
Bloch oscillations in a single Josephson junction in the phase-slip regime relate current to frequency. They can be measured by applying a periodic drive to a DC-biased, small Josephson junction. Phase-locking between the periodic drive and the Bloch oscillations then gives rise to steps at constant current in the I-V curves, also known as dual Shapiro steps. Unlike conventional Shapiro steps, a measurement of these dual Shapiro steps is impeded by the presence of a parasitic capacitance. This capacitance shunts the junction resulting in a suppression of the amplitude of the Bloch oscillations…
Quantum fluctuations in quasi-one-dimensional superconducting channels leading to spontaneous changes of the phase of the order parameter by $2π$, alternatively called quantum phase slips (QPS), manifest themselves as the finite resistance well below the critical temperature of thin superconducting nanowires and the suppression of persistent currents in tiny superconducting nanorings. Here we report the experimental evidence that in a current-biased superconducting nanowire the same QPS process is responsible for the insulating state -- the Coulomb blockade. When exposed to RF radiation, the i…
We show theoretically the possibility of quantum synchronization of Josephson and Bloch oscillations in a superconducting device. One needs an $LC$ oscillator to achieve exponentially small rate of synchronization errors. The synchronization leads to quantization of transresistance similar to that in (Fractional) Quantum Hall Effect.
We present a simple model for multiphoton transitions between the quasi-bound states of a current-driven Josephson junction. The transitions are induced by applying an ac voltage with controllable frequency and amplitude across the junction. The voltage induces transitions when the ac frequency equals n times the splitting between the ground and first excited quasi-bound state of the junction. We calculate the transition matrix elements as functions of the dc bias current I, and the frequency and amplitude of the ac voltage, for representative junction parameters. We also calculate the frequen…
High-field Josephson effect enabled by a moiré Hofstadter spectrum
Ludwig-Maximilians-Universität（路德维希-马克西米利安大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Nanomaterials and Nanotechnology Research Center (CINN-CSIC), Universidad de Oviedo (UO)（阿斯图里亚斯大学纳米材料与纳米技术研究中心（CINN-CSIC））；Yale University（耶鲁大学）；Aalto University（阿尔托大学）；National Institute for Materials Science（国立材料研究所）
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.
