Nature sets fundamental limits regarding how accurate the amplification of analog signals may be. For instance, a linear amplifier unavoidably adds some noise which amounts to half a photon at best. While for most applications much higher noise levels are acceptable, the readout of microwave quantum systems, such as spin or superconducting qubits, requires noise as close as possible to this ultimate limit. To date, it is approached only by parametric amplifiers exploiting non-linearities in superconducting circuits and driven by a strong microwave pump tone. However, this microwave drive makes them much more difficult to implement and operate than conventional DC powered amplifiers, which so far suffer from much higher noise. Here we present the first experimental proof that a simple DC-powered setup allows for amplification close to the quantum limit. Our amplification scheme is based on the stimulated microwave photon emission accompanying inelastic Cooper pair tunneling through a DC-biased Josephson junction, with the key to low noise lying in a well defined auxiliary idler mode, in analogy to parametric amplifiers.
Motivated by the recent experiments [Scientific reports 6, 23051 (2016), Phys. Rev. Lett. 114, 096602 (2015)], we theoretically investigate Cooper pair splitting current in a graphene based Cooper pair beam splitter geometry. By considering the graphene based superconductor as an entangler device, instead of normal (2D) BCS superconductor, we show that the Cooper pair splitting current mediated by Crossed Andreev process is amplified compared to its normal superconductor counterpart. This amplification is attributed to the strong suppression of local normal Andreev reflection process (arising …
Several aspects of intermolecular effects in molecular conduction have been studied in recent years. These experimental and theoretical studies, made on several setups of molecular conduction junctions, have focused on the current-voltage characteristic that is usually dominated by the elastic transmission properties of such junctions. In this paper we address cooperative intermolecular effects in the inelastic tunneling signal calculated for simple generic models of such systems. We find that peaks heights in the inelasticspectrum may be affected by such cooperative effects even when direct i…
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, …
We show that a properly dc-biased Josephson junction in series with two microwave resonators of different frequencies emits photon pairs in the resonators. By measuring auto- and inter-correlations of the power leaking out of the resonators, we demonstrate two-mode amplitude squeezing below the classical limit. This non-classical microwave light emission is found to be in quantitative agreement with our theoretical predictions, up to an emission rate of 2 billion photon pairs per second.
The interaction between propagating microwave fields and Cooper-pair tunneling across a DC voltage-biased Josephson junction can be highly nonlinear. We show theoretically that this nonlinearity can be used to convert an incoming single microwave photon into an outgoing $n$-photon Fock state in a different mode. In this process, the electrostatic energy released in a Cooper-pair tunneling event is transferred to the outgoing Fock state, providing energy gain. The created multi-photon Fock state is frequency entangled and highly bunched. The conversion can be made reflectionless (impedance-matc…
We demonstrate theoretically that charge transport across a Josephson junction, voltage-biased through a resistive environment, produces antibunched photons. We develop a continuous-mode description of the emitted radiation field in a semi-infinite transmission line terminated by the Josephson junction. Within a perturbative treatment in powers of the tunneling coupling across the Josephson junction, we capture effects originating in charging dynamics of consecutively tunneling Cooper pairs. We find that within a feasible experimental setup the Coulomb blockade provided by high zero-frequency …
Various applications of quantum devices call for an accurate calibration of cryogenic amplification chains. To this end, we present a convenient calibration scheme and use it to accurately measure the total gain and noise temperature of an amplification chain by employing normal-metal--insulator--superconductor (NIS) junctions. Our method is based on the radiation emitted by inelastic electron tunneling across voltage-biased NIS junctions. We derive an analytical equation that relates the generated power to the applied bias voltage which is the only control parameter of the device. After the s…
Including phonon-assisted inelastic process in thermoelectric devices is able to enhance the performance of nonequilibrium work extraction. In this work, we demonstrate that inelastic phonon-thermoelectric devices have a fertile functionality diagram, where particle current and phononic heat currents are coupled and fueled by chemical potential difference. Such devices can simultaneously perform multiple tasks, e.g., heat engines, refrigerators, and heat pumps. Guided by the entropy production, we mainly study the efficiencies and coefficients of performance of multitask quantum thermal machin…
We study a new effect of Cooper-pair-based two-photon gain in semiconductor-superconductor structures, showing broadband enhancement of ultrafast two-photon amplification. We further show that with the superconducting enhancement, at moderately high seed intensities the two-photon gain contribution approaches that of the one-photon gain. A full quantum-optical model of singly- and fully-stimulated two-photon emission is developed. Our results provide new insights on nonlinear light-matter interaction in the superconducting state, including the possibility of coherent control in two-photon semi…
We predict a new mechanism of surface plasmon amplification in graphene-insulator-graphene van der Waals heterostructures. The amplification occurs upon the stimulated interlayer electron tunneling accompanied by the emission of a coherent plasmon. The quantum-mechanical calculations of the non-local high-frequency tunnel conductivity show that a relative smallness of the tunneling exponent can be compensated by a strong resonance due to the enhanced tunneling between electron states with collinear momenta in the neighboring graphene layers. With the optimal selection of the barrier layer, the…
We propose a scheme involving a Cooper pair transistor (CPT) embedded in a superconducting microwave cavity, where the CPT serves as a charge tunable quantum inductor to facilitate ultra-strong coupling between photons in the cavity and a nano- to meso-scale mechanical resonator. The mechanical resonator is capacitively coupled to the CPT, such that mechanical displacements of the resonator cause a shift in the CPT inductance and hence the cavity's resonant frequency. The amplification provided by the CPT is sufficient for the zero point motion of the mechanical resonator alone to cause a sign…
We analyze how functionality could be obtained within single-molecule devices by using a combination of non-equilibrium Green's functions and ab-initio calculations to study the inelastic transport properties of single-molecule junctions. First we apply a full non-equilibrium Green's function technique to a model system with electron-vibration coupling. We show that the features in the inelastic electron tunneling spectra (IETS) of the molecular junctions are virtually independent of the nature of the molecule-lead contacts. Since the contacts are not easily reproducible from one device to ano…
We analyze tunneling of Cooper pairs across voltage biased asymmetric single-Cooper-pair transistors. Also tunneling of Cooper pairs across two capacitively coupled Cooper-pair boxes is considered, when the capacitive coupling and Cooper pair tunneling are provided by a small Josephson junction between the islands. The theoretical analysis is done at subgap voltages, where the current-voltage characteristics depend strongly on the macroscopic eigenstates of the island(s) and their coupling to the dissipative environment. As the environment we use an impedance which satisfies Re[Z]<<R_Q and a f…
We explore the photonic (bright) side of 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 to 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 rad…
We demonstrate low-power amplification process in cavity optomechanics (COM). This operation is based on the nonlinear position-modulated self-Kerr interaction. Owing to this nonlinear term, the effective coupling highly scales with the photon number, resulting in a giant enhancement of the cooperativity. Even for small nonlinearity, the system reaches the amplification threshold for weak driving strength, leading to low-power phonon lasing. This amplifier can be phase-preserving and provides a practical advantage related to the power consumption issues. This work opens up new avenues to reali…
We study theoretically electromagnetic radiation emitted by inelastic Cooper-pair tunneling. We consider a dc-voltage-biased superconducting transmission line terminated by a Josephson junction. We show that the generated continuous-mode electromagnetic field can be expressed as a function of the time-dependent current across the Josephson junction. The leading-order expansion in the tunneling coupling, similar to the "$P(E)$-theory", has previously been used to investigate the photon emission statistics in the limit of sequential (independent) Cooper-pair tunneling. By explicitly evaluating t…
We propose a scheme of multilayer thermoelectric engine where {\em one} electric current is coupled to {\em two} temperature gradients in three-terminal geometry. This is realized by resonant tunneling through quantum dots embedded in two thermal and electrical resisting polymer matrix layers between highly conducting semiconductor layers. There are two thermoelectric effects, one of which is pertaining to inelastic transport processes (if energies of quantum dots in the two layers are different) while the other exists also for elastic transport processes. {These two correspond to the transver…
We investigate transport in weakly-coupled metal nanoparticle arrays, focusing on the regime where tunneling is competing with strong single electron charging effects. This competition gives rise to an interplay between two types of charge transport. In sequential tunneling, transport is dominated by independent electron hops from a particle to its nearest neighbor along the current path. In inelastic cotunneling, transport is dominated by cooperative, multi-electron hops that each go to the nearest neighbor but are synchronized to move charge over distances of several particles. In order to t…
We address the tunneling conductance and spin inelastic tunneling spectroscopy of localized paramagnetic moments in a superconducting environment, pertaining to recent measurements on Fe-octaethylporphyrin-chloride using superconducting scanning tunneling microscopy. We demonstrate that the Cooper pair correlations in the tip and substrate generate a finite uniaxial anisotropy field acting on the local spin moment, and we argue that this field may be a source for the observed changes in the conductance spectrum for decreasing distance between the scanning tunneling tip and the local magnetic m…
Inelastic Cooper pair tunneling across a voltage-biased Josephson junction in series with one or more microwave cavities can generate photons via resonant processes in which the energy lost by the Cooper pair matches that of the photon(s) produced. We generalise previous theoretical treatments of such systems to analyse cases where two or more different photon generation processes are resonant simultaneously. We also explore in detail a specific case where generation of a single photon in one cavity mode is simultaneously resonant with the generation of two photons in a second mode. We find th…
Phonon-assisted electronic tunnelings through a vibrating quantum dot embedded between normal and superconducting leads are studied in the Kondo regime. In such a hybrid device, with the bias applied to the normal lead, we find a series of Kondo sidebands separated by half a phonon energy in the differential conductance, which are distinct from the phonon-assisted sidebands previously observed in the conventional Andreev tunnelings and in systems with only normal leads. These Kondo sidebands originate from the Kondo-Andreev cooperative cotunneling mediated by phonons, which exhibit a novel Kon…
We investigate Bardeen-Cooper-Schrieffer (BCS)- Bose-Einstein condensation (BEC) crossover in a two-band superfluid Fermi gas with an energy shift between the bands. When the intraband coupling in the cold (first) band is fixed as weak, we find that in the case of vanishing interband interaction and in the strong-coupling limit of the hot (second) band the system undergoes a transition to a single-component configuration with the full suppression of the first energy gap and with the full redistribution of particles between bands. For non-vanishing interband interaction we reveal the non-monoto…
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 present a microscopic theory for the current through a tunnel Josephson junction coupled to a non-linear environment, which consists of an Andreev two-level system coupled to a harmonic oscillator. It models a recent experiment [Bretheau, Girit, Pothier, Esteve, and Urbina, Nature (London) 499, 312 (2013)] on photon spectroscopy of Andreev bound states in a superconducting atomic-size contact. We find the eigenenergies and eigenstates of the environment and derive the current through the junction due to inelastic Cooper pair tunneling. The current-voltage characteristic reveals the transiti…
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…
The combination of low mass density, high frequency, and high quality-factor of mechanical resonators made of two-dimensional crystals such as graphene make them attractive for applications in force sensing/mass sensing, and exploring the quantum regime of mechanical motion. Microwave optomechanics with superconducting cavities offers exquisite position sensitivity and enables the preparation and detection of mechanical systems in the quantum ground state. Here, we demonstrate coupling between a multilayer graphene resonator with quality factors up to 220,000 and a high-$\textit{Q}$ supercondu…
We measured the Josephson radiation emitted by an InSb semiconductor nanowire junction utilizing photon assisted quasiparticle tunneling in an AC-coupled superconducting tunnel junction. We quantify the action of the local microwave environment by evaluating the frequency dependence of the inelastic Cooper-pair tunneling of the nanowire junction and find the zero frequency impedance $Z(0)=492\,Ω$ with a cutoff frequency of $f_0=33.1\,$GHz. We extract a circuit coupling efficiency of $η\approx 0.1$ and a detector quantum efficiency approaching unity in the high frequency limit. In addition to t…
