Amplifiers based on Josephson junctions allow for a fast and noninvasive readout of superconducting qubits. Motivated by the ongoing progress toward the realization of fault-tolerant qubits based on Majorana bound states, we investigate the topological counterpart of the Josephson bifurcation amplifier. We predict that the bifurcation dynamics of a topological Josephson junction driven in the appropriate parameter regime may be used as an additional tool to detect the emergence of Majorana bound states.
We report single-shot readout of a superconducting flux qubit by using a flux-driven Josephson parametric amplifier (JPA). After optimizing the readout power, gain of the JPA and timing of the data acquisition, we observe the Rabi oscillations with a contrast of 74% which is mainly limited by the bandwidth of the JPA and the energy relaxation of the qubit. The observation of quantum jumps between the qubit eigenstates under continuous monitoring indicates the nondestructiveness of the readout scheme.
One of the central challenges in the development of parametric amplifiers is the control of the dynamic range relative to its gain and bandwidth, which typically limits quantum limited amplification to signals which contain only a few photons per inverse bandwidth. Here, we discuss the control of the dynamic range of Josephson parametric amplifiers by using Josephson junction arrays. We discuss gain, bandwidth, noise, and dynamic range properties of both a transmission line and a lumped element based parametric amplifier. Based on these investigations we derive useful design criteria, which ma…
Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmon qubit circuit using non-linear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bifurcation is a high-fidelity readout method, the scalability of which is not limited by the need of a large bandwidth nearly quantum-limited amplifier as is the case with linear readout resonators.
We have constructed a new type of amplifier whose primary purpose is the readout of superconducting quantum bits. It is based on the transition of an RF-driven Josephson junction between two distinct oscillation states near a dynamical bifurcation point. The main advantages of this new amplifier are speed, high-sensitivity, low back-action, and the absence of on-chip dissipation. Pulsed microwave reflection measurements on nanofabricated Al junctions show that actual devices attain the performance predicted by theory.
Josephson parametric amplifiers (JPA) have become key devices in quantum science and technology with superconducting circuits. In particular, they can be utilized as quantum-limited amplifiers or as a source of squeezed microwave fields. Here, we report on the detailed measurements of five flux-driven JPAs, three of them exhibiting a hysteretic dependence of the resonant frequency versus the applied magnetic flux. We model the measured characteristics by numerical simulations based on the two-dimensional potential landscape of the dc superconducting quantum interference devices (dc-SQUID), whi…
We present design and simulation of a Josephson parametric amplifier with bandwidth exceeding 1.6 GHz, and with high saturation power approaching -90 dBm at a gain of 22.8 dB. An improvement by a factor of roughly 50 in bandwidth over the state of the art is achieved by using well-established impedance matching techniques. An improvement by a factor of roughly 100 in saturation power over the state of the art is achieved by implementing the Josephson nonlinear element as an array of rf-SQUIDs with a total of 40 junctions. WRSpice simulations of the circuit are in excellent agreement with the c…
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…
We have developed a recently proposed Josephson traveling-wave parametric amplifier with three-wave mixing [A. B. Zorin, Phys. Rev. Applied 6, 034006, 2016]. The amplifier consists of a microwave transmission line formed by a serial array of nonhysteretic one-junction SQUIDs. These SQUIDs are flux-biased in a way that the phase drops across the Josephson junctions are equal to 90 degrees and the persistent currents in the SQUID loops are equal to the Josephson critical current values. Such a one-dimensional metamaterial possesses a maximal quadratic nonlinearity and zero cubic (Kerr) nonlinear…
We develop a technique to overcome phase-mismatch in Josephson-junction traveling wave parametric amplifiers in order to achieve high gain over a broad bandwidth. Using "resonant phase matching," we design a compact superconducting device consisting of a transmission line with subwavelength resonant inclusions that simultaneously achieves a gain of 20 dB, an instantaneous bandwidth of 3 GHz, and a saturation power of -98 dBm. Such an amplifier is well-suited to cryogenic broadband microwave measurements such as the multiplexed readout of quantum coherent circuits based on superconducting, semi…
Detection of low-reflectivity objects can be improved by the so-called quantum illumination procedure. However, quantum detection probability exponentially decays with the source bandwidth. The Josephson Parametric Amplifiers (JPAs) technology utilized as a source, generating a pair of entangled signals called two-mode squeezed vacuum states, shows a very narrow bandwidth limiting the operation of the microwave quantum radar (MQR). In this paper, for the first time, a microwave quantum radar setup based on quantum illumination protocol and using a Josephson Traveling Wave Parametric Amplifier …
Detection of low-reflectivity objects can be enriched via the so-called quantum illumination procedure. In order that this quantum procedure outperforms classical detection protocols, entangled states of microwave radiation are initially required. In this paper, we discuss the role of Josephson Traveling Wave Parametric Amplifiers (JTWPAs), based on circuit-QED components, as suitable sources of a two-mode squeezed vacuum state, a special signal-idler entangled state. The obtained wide bandwidth makes the JTWPA an ideal candidate for generating quantum radiation in quantum metrology and inform…
We report on measurements of a Josephson amplifier (J-amp) suitable for quantum-state qubit readout in the microwave domain. It consists of two microstrip resonators which intersect at a Josephson ring modulator. A maximum gain of about 20 dB, a bandwidth of 9 MHz, and a center-frequency tunability of about 60 MHz with gain in excess of 10 dB have been attained for idler and signal of frequencies 6.4 GHz and 8.1 GHz, in accordance with theory. Maximum input power measurements of the J-amp show a relatively good agreement with theoretical prediction. We discuss how the amplifier characteristics…
We have realized a microwave quantum-limited amplifier that is directional and can therefore function without the front circulator needed in many quantum measurements. The amplification takes place in only one direction between the input and output ports. Directionality is achieved by multi-pump parametric amplification combined with wave interference. We have verified the device noise performances by using it to readout a superconducting qubit and observed quantum jumps. With an improved version of this device, qubit and preamplifer could be integrated on the same chip.
We study the dynamics of Josephson Parametric Amplifier (JPA) coupled to a mechanical oscillator, as realised with a dc Superconducting Quantum Interference Device (SQUID) with an embedded movable arm. We analyse this system in the regime when the frequency of the mechanical oscillator is comparable in magnitude with the plasma oscillation of the SQUID. When the nano-mechanical resonator is driven, it strongly affects the dynamics of the JPA. We show that this coupling can considerably modify the dynamics of JPA and induce its multistability rather than common bistability. This analysis is rel…
The ability to manipulate quantum information encoded in microwave fields has led to a renewed interest in Josephson parametric amplifiers (JPAs). For these applications the ability of JPAs to amplify signals with the least amount of added noise is critical. Unfortunately JPAs are typically narrow band amplifiers with small dynamic range. It is therefore important to understand the bandwidth and dynamic range of any particular JPA in order to determine if it is appropriate for these applications. We recently introduced a new kind of JPA. Although it is still narrow band, the amplified band can…
We present experimental results on a Josephson parametric amplifier tailored for readout of ultra-sensitive thermal microwave detectors. In particular, we discuss the impact of fabrication details on the performance. We show that the small volume of deposited dielectric materials enabled by the side-wall passivated spacer niobium junction technology leads to robust operation across a wide range of operating temperatures up to 1.5 K. The flux-pumped amplifier has gain in excess of 20 dB in three-wave mixing and its center frequency is tunable between 540 MHz and 640 MHz. At 600 MHz, the amplifi…
We develop a concept of the traveling-wave Josephson parametric amplifier exploiting quadratic nonlinearity of a serial array of one-junction SQUIDs embedded in a superconducting transmission line. The external magnetic flux applied to the SQUIDs makes it possible to efficiently control the shape of their current-phase relation and, hence, the balance between quadratic and cubic (Kerr-like) nonlinearities. This property allows us to operate in the favorable three-wave-mixing mode with minimal phase mismatch, an exponential dependence of the power gain on number of sections $N$, a large bandwid…
We realize and characterize a quantum-limited, directional Josephson amplifier suitable for qubit readout. The device consists of two nondegenerate, three-wave-mixing amplifiers that are coupled together in an interferometric scheme, embedded in a printed circuit board. Nonreciprocity is generated by applying a phase gradient between the same-frequency pumps feeding the device, which plays the role of the magnetic field in a Faraday medium. Directional amplification and reflection-gain elimination are induced via wave interference between multiple paths in the system. We measure and discuss th…
We analyzed the Josephson bifurcation amplifier (JBA) readout process of a superconducting qubit quantum mechanically. This was achieved by employing numerical analyses of the dynamics of the density operator of a driven nonlinear oscillator and a qubit coupled system during the measurement process. In purely quantum cases, the wavefunction of the JBA is trapped in a quasienergy-state, and bifurcation is impossible. Introducing decoherence enables us to reproduce the bifurcation with a finite hysteresis. Moreover, we discuss in detail the dynamics involved when a qubit is initially in a superp…
We have developed a Josephson parametric amplifier, comprising a superconducting coplanar waveguide resonator terminated by a dc SQUID (superconducting quantum interference device). An external field (the pump, $\sim 20$ GHz) modulates the flux threading the dc SQUID, and, thereby, the resonant frequency of the cavity field (the signal, $\sim 10$ GHz), which leads to parametric signal amplification. We operated the amplifier at different band centers, and observed amplification (17 dB at maximum) and deamplification depending on the relative phase between the pump and the signal. The noise tem…
A directional superconducting parametric amplifier in the GHz frequency range is designed and analyzed, suitable for low-power read-out of microwave kinetic inductance detectors employed in astrophysics and when combined with a nonreciprocal device at its input also for circuit quantum electrodynamics (cQED). It consists of an one wavelength long nondegenerate Josephson parametric reflection amplifier circuit. The device has two Josephson junction oscillators, connected via a tailored impedance to an on-chip passive circuit which directs the in- to the output port. The amplifier provides a gai…
We present an analysis of wave-mixing in recently developed Josephson Travelling Wave Parametric Amplifiers (JTWPAs). Circuit simulations performed using WRspice show the full behaviour of the JTWPA allowing propagation of all tones. The Coupled Mode Equations (CMEs) containing only pump, signal, and idler propagation are shown to be insufficient to completely capture complex mixing behaviour in the JTWPA. Extension of the CMEs through additional state vectors in the analytic solutions allows closer agreement with WRspice. We consider an ordered framework for the systematic inclusion of extend…
We have developed and measured a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of 8 superconducting quantum interference devices (SQUIDs). This amplifier is parametrically pumped by modulating the flux threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum gain of 31 dB, a product amplitude-gain x bandwidth above 60 MHz, and a 1 dB compression point of -123 dBm at 20 dB gain are obtained in the non-degenerate mode of operation. Phase sensitive amplification-deamplification i…
We have constructed a new type of amplifier whose primary purpose is the readout of superconducting quantum bits. It is based on the transition of an RF-driven Josephson junction between two distinct oscillation states near a dynamical bifurcation point. The main advantages of this new amplifier are speed, high-sensitivity, low back-action, and the absence of on-chip dissipation. Using pulsed microwave techniques, we demonstrate bifurcation amplification in nanofabricated Al junctions and verify that the performance predicted by theory is attained.
We have studied nonlinear superconducting resonators: lambda/2 coplanar-waveguide (CPW) resonators with Josephson junctions (JJs) placed in the middle and lambda/4 CPW resonators terminated by JJs, which can be used for the qubit readout as "bifurcation amplifiers." The nonlinearity of the resonators arises from the Josephson junctions, and because of the nonlinearity, the resonators with appropriate parameters are expected to show a hysteretic response to the frequency sweep, or "bifurcation," when they are driven with a sufficiently large power. We designed and fabricated resonators whose re…
We have developed a concept for a traveling-wave parametric amplifier driven by a magnetic flux wave. The circuit consists of a serial array of symmetric dc SQUIDs coupled inductively to a separate superconducting LC transmission line carrying the pump microwave; thereby the signal and pump are applied to different ports. The proposed three-wave-mixing amplifier includes, firstly, an adjustable phase velocity of the signal (idler) wave and hence good phase matching yielding large gain in a wide frequency range and, secondly, overcoming of the pump depletion problem. The experimental parameters…
We present measurements of an amplifier based on a dc superconducting quantum interference device (SQUID) with submicron Al-AlOx-Al Josephson junctions. The small junction size reduces their self-capacitance and allows for the use of relatively large resistive shunts while maintaining nonhysteretic operation. This leads to an enhancement of the SQUID transfer function compared to SQUIDs with micron-scale junctions. The device layout is modified from that of a conventional SQUID to allow for coupling signals into the amplifier with a substantial mutual inductance for a relatively short microstr…
We performed magnetic field and frequency tunable electron paramagnetic resonance spectroscopy of an Er$^{3+}$ doped Y$_2$SiO$_5$ crystal by observing the change in flux induced on a direct current-superconducting quantum interference device (dc-SQUID) loop of a tunable Josephson bifurcation amplifer. The observed spectra show multiple transitions which agree well with the simulated energy levels, taking into account the hyperfine and quadrupole interactions of $^{167}$Er. The sensing volume is about 0.15 pl, and our inferred measurement sensitivity (limited by external flux noise) is approxim…
Josephson parametric amplifiers have become a critical tool in superconducting device physics due to their high gain and quantum-limited noise. Traveling wave parametric amplifiers (TWPAs) promise similar noise performance while allowing for significant increases in both bandwidth and dynamic range. We present a TWPA device based on an LC-ladder transmission line of Josephson junctions and parallel plate capacitors using low-loss amorphous silicon dielectric. Crucially, we have inserted $λ/4$ resonators at regular intervals along the transmission line in order to maintain the phase matching co…
We present a lumped-element Josephson parametric amplifier designed to operate with strong coupling to the environment. In this regime, we observe broadband frequency dependent amplification with multi-peaked gain profiles. We account for this behaviour using the "pumpistor" model which allows for frequency dependent variation of the external impedance. Using this understanding, we demonstrate control over gain profiles through changes in the environment impedance at a given frequency. With strong coupling to a suitable external impedance we observe a significant increase in dynamic range, and…
The advent of ultra-low noise microwave amplifiers revolutionized several research fields demanding quantum-limited technologies. Exploiting a theoretical bimodal description of a linear phase-preserving amplifier, in this contribution we analyze some of the intrinsic properties of a model architecture (i.e., an rf-SQUID based Josephson Traveling Wave Parametric Amplifier) in terms of amplification and noise generation for key case study input states (Fock and coherents). Furthermore, we present an analysis of the output signals generated by the parametric amplification mechanism when thermal …
We develop the concept of quasi-phasematching (QPM) by implementing it in the recently proposed Josephson traveling-wave parametric amplifier (JTWPA) with three-wave mixing (3WM). The amplifier is based on a ladder transmission line consisting of flux-biased radio-frequency SQUIDs whose nonlinearity is of $χ^{(2)}$-type. QPM is achieved in the 3WM process, $ω_p=ω_s+ω_i$ (where $ω_p$, $ω_s$, and $ω_i$ are the pump, signal, and idler frequencies, respectively) due to designing the JTWPA to include periodically inverted groups of these SQUIDs that reverse the sign of the nonlinearity. Modeling sh…
We have simulated the performance of the Josephson Travelling Wave Parametric Amplifier (JTWPA) based on the one-dimensional array of RF SQUIDs. Unlike the ideal model in which all SQUIDs are assumed to be identical, we allowed variation of the device parameters such as the geometric inductance of the SQUID loop, capacitance to ground, Josephson junction capacitance and critical current. Our simulations confirm the negative effects of variation of the device parameters leading to microwave reflections between individual cells and the shift of the flux bias from the optimal point. The strongest…
Recent progress in solid state quantum information processing has stimulated the search for ultra-low-noise amplifiers and frequency converters in the microwave frequency range, which could attain the ultimate limit imposed by quantum mechanics. In this article, we report the first realization of an intrinsically phase-preserving, non-degenerate superconducting parametric amplifier, a so far missing component. It is based on the Josephson ring modulator, which consists of four junctions in a Wheatstone bridge configuration. The device symmetry greatly enhances the purity of the amplification p…
The axion, a hypothetical elementary pseudoscalar, is expected to solve the strong CP problem of QCD and is also a promising candidate for dark matter. The most sensitive axion search experiments operate at millikelvin temperatures and hence rely on instrumentation that carries signals from a system at cryogenic temperatures to room temperature instrumentation. One of the biggest limiting factors affecting the parameter scanning speed of these detectors is the noise added by the components in the signal detection chain. Since the first amplifier in the chain limits the minimum noise, low-noise…
Photon-pressure coupling between two superconducting circuits is a promising platform for investigating radiation-pressure coupling in novel parameter regimes and for the development of radio-frequency (RF) quantum photonics and quantum-limited RF sensing. So far, the intrinsic Josephson nonlinearity of photon-pressure coupled circuits has not been considered a potential resource for enhanced devices or novel experimental schemes. Here, we implement photon-pressure coupling between a RF circuit and a microwave cavity containing a superconducting quantum interference device (SQUID) which can be…
A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semi-classic limit. The spectrum of Andreev bound states is obtained from the single-valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the compo…
We analyze the effect of circuit parameter variation on the performance of Josephson traveling-wave parametric amplifiers (JTWPAs). Specifically, the JTWPA concept we investigate is using flux-biased nonhysteretic rf-SQUIDs in a transmission line configuration, which harnesses the three-wave mixing (3WM) regime. Dispersion engineering enables phasematching to achieve power gain of $\sim$20 dB, while suppressing the generation of unwanted mixing processes. Two dispersion engineering concepts using a 3WM-JTWPA circuit model, i.e., resonant phase-matching (RPM) and periodic capacitance modulation…
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 construct a semiclassical theory for the transport of topological junctions starting from a microscopic Hamiltonian that comprehensively includes the interplay among the Majorana qubit, the Josephson phase, and the dissipation process. With the path integral approach, we derive a set of semiclassical equations of motion that can be used to calculate the time evolution of the Josephson phase and the Majorana qubit. In the equations we reveal rich dynamical phenomena such as the qubit induced charge pumping, the effective spin-orbit torque, and the Gilbert damping. We demonstrate the influenc…
We demonstrate a high dynamic range Josephson parametric amplifier (JPA) in which the active nonlinear element is implemented using an array of rf-SQUIDs. The device is matched to the 50 $Ω$ environment with a Klopfenstein-taper impedance transformer and achieves a bandwidth of 250-300 MHz, with input saturation powers up to -95 dBm at 20 dB gain. A 54-qubit Sycamore processor was used to benchmark these devices, providing a calibration for readout power, an estimate of amplifier added noise, and a platform for comparison against standard impedance matched parametric amplifiers with a single d…
We present a new theoretical framework to analyze microwave amplifiers based on the dc SQUID. Our analysis applies input-output theory generalized for Josephson junction devices biased in the running state. Using this approach we express the high frequency dynamics of the SQUID as a scattering between the participating modes. This enables us to elucidate the inherently nonreciprocal nature of gain as a function of bias current and input frequency. This method can, in principle, accommodate an arbitrary number of Josephson harmonics generated in the running state of the junction. We report deta…
We present the Josephson junction intersected superconducting transmission line resonator. In contrast to the Josephson parametric amplifier, Josephson bifurcation amplifier and Josephson parametric converter we consider the regime of few microwave photons. We review the derivation of eigenmode frequencies and zero point fluctuations of the nonlinear transmission line resonator and the derivation of the eigenmode Kerr nonlinearities. Remarkably these nonlinearities can reach values comparable to Transmon qubits rendering the device ideal for accessing the strongly correlated regime. This is pa…
