Non-degenerate parametric amplifiers based on dispersion engineered Josephson junction arrays
Patrick Winkel, Ivan Takmakov, Dennis Rieger, Luca Planat, Wiebke Hasch-Guichard, Lukas Grünhaupt, Nataliya Maleeva, Farshad Foroughi, Fabio Henriques, Kiril Bo… 展开作者
Patrick Winkel, Ivan Takmakov, Dennis Rieger, Luca Planat, Wiebke Hasch-Guichard, Lukas Grünhaupt, Nataliya Maleeva, Farshad Foroughi, Fabio Henriques, Kiril Borisov, Julian Ferrero, Alexey V. Ustinov, Wolfgang Wernsdorfer, Nicolas Roch, Ioan M. Pop
备注：
P.W. and I.T. contributed equally. 9 pages, 5 figures and appendices
Determining the state of a qubit on a timescale much shorter than its relaxation time is an essential requirement for quantum information processing. With the aid of a new type of non-degenerate parametric amplifier, we demonstrate the continuous detection of quantum jumps of a transmon qubit with 90% fidelity in state discrimination. Entirely fabricated with standard two-step optical lithography techniques, this type of parametric amplifier consists of a dispersion engineered Josephson junction (JJ) array. By using long arrays, containing $10^3$ JJs, we can obtain amplification at multiple eigenmodes with frequencies below $10~\mathrm{GHz}$, which is the typical range for qubit readout. Moreover, by introducing a moderate flux tunability of each mode, employing superconducting quantum interference device (SQUID) junctions, a single amplifier device could potentially cover the entire frequency band between 1 and $10~\mathrm{GHz}$.
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 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…
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 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 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 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 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 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.
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…
A Josephson parametric amplifier (JPA) can create squeezed states of microwave light, lowering the noise associated with certain quantum measurements. We experimentally study how the JPA's pump influences the phase-sensitive amplification and deamplification of a coherent tone's amplitude when that amplitude is commensurate with vacuum fluctuations. We predict and demonstrate that by operating the JPA with a pump power greater than the value that maximizes gain, the amplifier distortion is reduced and consequently squeezing is improved. Optimizing the JPA's operation in this fashion, we direct…
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…
We describe a wide-band Josephson Parametric Amplifier (JPA) that is impedance-matched using an integrated compact superconducting transmission line transformer. The impedance transformer consists of two broadside coupled transmission lines configured in a Ruthroff topology which enables a wide matching bandwidth from 2 to 18 GHz, reducing the input line impedance and the device resonance quality factor by a factor of 4. This enables gain flatness and flexibility in the choice of the amplifier's tuning range. The amplifier has up to 20dB gain, with less than 1 dB of ripple, 2-3 GHz gain-bandwi…
Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by Josephson ring modulator which acts as a three-wave mixing non-degenerate parametric amplifier. Here, we solve the master equation of three bosonic modes describing the Josephson ring modulator with a novel numerical method to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity…
Non-linearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA), the only device in which the quantum limit has so far been achieved at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) non-linearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type non-linearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction non-linearity in the linear response regim…
Josephson junction parametric amplifiers are playing a crucial role in the readout chain in superconducting quantum information experiments. However, their integration with current 3D cavity implementations poses the problem of transitioning between waveguide, coax cables and planar circuits. Moreover, Josephson amplifiers require auxiliary microwave components, like directional couplers and/or hybrids, that are sources of spurious losses and impedance mismatches that limit measurement efficiency and amplifier tunability. We have developed a new wireless architecture for these parametric ampli…
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…
A Josephson parametric amplifier (JPA) is executed in a three-dimensional (3D) microwave cavity by coupling it to a superconducting quantum interference device (SQUID) that is embedded in a two-dimensional resonator. The JPA is activated in a three-wave mixing configuration by injecting ac magnetic flux, at twice the 3D cavity frequency, into the SQUID. An 8.3 GHz cavity is measured in a non-degenerate phase-insensitive configuration which yields gains in excess of 40 dB, where a 20 dB gain results in an operational bandwidth of 0.4 MHz, a 1 dB compression point of -115 dBm with half a quantum…
Josephson Parametric Amplifiers (JPA) are nonlinear devices that are used for quantum sensing and qubit readout in the microwave regime. While JPAs regularly operate in the quantum limit, their gain saturates for very small (few photons) input power. In a previous work, we showed that the saturation power of JPAs is not limited by pump depletion, but instead by the high-order nonlinearity of Josephson junctions, the nonlinear circuit elements that enable amplification in JPAs. Here, we present a systematic study of the nonlinearities in JPAs, we show which nonlinearities limit the saturation p…
We introduce a novel near-quantum-limited amplifier with a large tunable bandwidth and high dynamic range - the Josephson Array Mode Parametric Amplifier (JAMPA). The signal and idler modes involved in the amplification process are realized by the array modes of a chain of 1000 flux tunable, Josephson-junction-based, nonlinear elements. The frequency spacing between array modes is comparable to the flux tunability of the modes, ensuring that any desired frequency can be occupied by a resonant mode, which can further be pumped to produce high gain. We experimentally demonstrate that the device …
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…
Squeezing of the electromagnetic vacuum is an essential metrological technique used to reduce quantum noise in applications spanning gravitational wave detection, biological microscopy, and quantum information science. In superconducting circuits, the resonator-based Josephson-junction parametric amplifiers conventionally used to generate squeezed microwaves are constrained by a narrow bandwidth and low dynamic range. In this work, we develop a dual-pump, broadband Josephson traveling-wave parametric amplifier that combines a phase-sensitive extinction ratio of 56 dB with single-mode squeezing…
The recently proposed Josephson traveling-wave parametric amplifier (JTWPA) based on a ladder transmission line consisting of radio-frequency SQUIDs and exploiting three-wave mixing (3WM), has great potential in achieving both a gain of 20 dB and a flat bandwidth of at least 4 GHz. To realize this concept in practical amplifiers we model the advanced JTWPA circuit with periodic modulation of the circuit parameters (engineered dispersion loadings), which allow the basic mixing process, i.e., $ω_s=ω_p-ω_i$, where $ω_s$, $ω_p$, and $ω_i$ are the signal, the pump, and the idler frequencies, respec…
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…
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 develop a quantum theory describing the input-output properties of Josephson traveling wave parametric amplifiers. This allows us to show how such a device can be used as a source of nonclassical radiation, and how dispersion engineering can be used to tailor gain profiles and squeezing spectra with attractive properties, ranging from genuinely broadband spectra to "squeezing combs" consisting of a number of discrete entangled quasimodes. The device's output field can be used to generate a multi-mode squeezed bath--a powerful resource for dissipative quantum state preparation. In particular…
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…
Josephson-junction based parametric amplifiers have become a ubiquitous component in superconducting quantum machines. Although parametric amplifiers regularly achieve near-quantum limited performance, they have many limitations, including low saturation powers, lack of directionality, and narrow bandwidth. The first is believed to stem from the higher order Hamiltonian terms endemic to Josephson junction circuits, and the latter two are direct consequences of the nature of the parametric interactions which power them. In this work, we attack both of these issues. First, we have designed a new…
Josephson parametric amplifier (JPA) engineering is a significant component in the quantum two-mode squeezed radar (QTMS), to enhance, for instance, radar performance and the detection range or bandwidth. In this study, we apply quantum theory to a research domain focusing the design of QTMS radar. We apply engineered JPA (EJPA) to enhance the performance of a quantum radar (QR). We investigate the correlation between the signal and idler using and we propose strategies for maintaining entanglement at room temperature. We define the quantum signal-to-noise ratio (SNR) and detection range equat…
With a large portfolio of elemental quantum components, superconducting quantum circuits have contributed to dramatic advances in microwave quantum optics. Of these elements, quantum-limited parametric amplifiers have proven to be essential for low noise readout of quantum systems whose energy range is intrinsically low (tens of $μ$eV ). They are also used to generate non classical states of light that can be a resource for quantum enhanced detection. Superconducting parametric amplifiers, like quantum bits, typically utilize a Josephson junction as a source of magnetically tunable and dissipa…
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 report on the design and implementation of a Field Programmable Josephson Amplifier (FPJA) - a compact and lossless superconducting circuit that can be programmed \textit{in situ} by a set of microwave drives to perform reciprocal and nonreciprocal frequency conversion and amplification. In this work we demonstrate four modes of operation: frequency conversion ($-0.5~\mathrm{dB}$ transmission, $-30~\mathrm{dB}$ reflection), circulation ($-0.5~\mathrm{dB}$ transmission, $-30~\mathrm{dB}$ reflection, $30~\mathrm{dB}$ isolation), phase-preserving amplification (gain $>20~\mathrm{dB}$, $1~\math…
