Session F39: Superconducting Circuits: Amplifiers I

Photon statistics of shot noise measured using a Josephson parametric amplifier

Quantum measurements are very sensitive to external noise sources. Such measurements require careful amplification chain design so as not to overwhelm the signal with extraneous noise. A quantum-limited amplifier, like the Josephson parametric amplifier (paramp), is thus an ideal candidate for this purpose. We used a paramp to investigate the quantum noise of a tunnel junction. This measurement scheme allowed us to improve upon previous observations of shot noise by an order of magnitude in terms of noise temperature. With this setup, we have measured the second and fourth cumulants of current fluctuations generated by the tunnel junction within a 40 MHz bandwidth around 6 GHz. From theses measurements, we deduce the variance of the photon number fluctuations for various bias schemes of the junction. In particular, we investigate the regime where the junction emits pairs of photons.   

Imaging non-Gaussian output fields produced by Josephson parametric amplifiers: theory

Josephson parametric amplifiers (JPA) have facilitated significant improvements in the~readout~fidelity of superconducting qubits [1]. Understanding and detailed characterization of current designs is necessary in order to improve the current generation of quantum-limited amplifiers with the goal of obtaining larger gain, bandwidth and dynamic range. In this talk, we theoretically explore the impact of terms going beyond the standard ``stiff-pump'' approximation in the description of JPAs. In particular we consider the impact of usually neglected nonlinear corrections on the properties of the JPA. ~Using the maximum entropy principle [2], we show how to reconstruct the filtered output state of a JPA. This reconstruction allows us to quantify the non-gaussianity of the output field and the noise properties of the JPA. \\[4pt] [1] Jeffrey, E. et al., PRL~\textbf{112}, 190504~(2014)\\[0pt] [2] Buzek, V. et al., PRA~\textbf{54}, 804 (1996)   

Imaging non-Gaussian output fields produced by Josephson parametric amplifiers: experiments

In recent years, squeezed microwave states have become the focus of intense research motivated by applications in continuous-variables quantum computation and precision qubit measurement. Despite numerous demonstrations of vacuum squeezing with superconducting parametric amplifiers such as the Josephson parametric amplifier (JPA), most experiments have also suggested that the squeezed output field becomes non-ideal at the large ($>$ 10dB) signal gains required for low-noise qubit measurement. Here we describe a systematic experimental study of JPA squeezing performance in this regime for varying lumped-element device designs and pumping methods. We reconstruct the JPA output fields through homodyne detection of the field moments and quantify the deviations from an ideal squeezed state using maximal entropy techniques. These methods provide a powerful diagnostic tool to understand how effects such as gain compression impact JPA squeezing. Our results highlight the importance of weak device nonlinearity for generating highly squeezed states.   

Theory of Dispersion Engineering in Traveling-Wave Kinetic Inductance Amplifiers

Coplanar-waveguide parametric amplifiers of length extending to the order of a meter have been patterned from superconducting materials using long meandering geometries fabricated on $cm^2$ chips [B. H. Eom, et al., Nat. Phys. 8, 623 (2012)]. These waveguides have highly reactive impedance and operate below the critical current by leveraging the low-temperature nonlinear kinetic inductance $L(x,t)$ of the underlying superconductor, where $L(x,t) = L_o(x) \left\{ 1 + {\left[ I(x,t) \left/ I_* \right. \right] }^2 \right\} $ at point $x$ along the waveguide and time $t$. Here, $L_o(x)$ is the linear kinetic inductance at $x$, $I_*$ is a scaling constant, and $I(x,t)$ is the total microwave current within the waveguide. As a consequence of the nonlinear kinetic inductance, degenerate four-wave mixing between a pump and signal can result in an idler product as well as significant signal gain as the pump transfers energy to these two side features. Frequency stops and other periodic loadings may be engineered to mitigate effects of higher pump harmonics as well as enhance signal gain, via alteration of phase mismatch. We describe here a simple band theory applicable to the waveguide frequency spectrum that allows us to optimize stop gaps and nonlinear signal gain.   

Frequency Comb Generation in Superconducting Resonators

We have generated frequency combs spanning 0.5 to 20 GHz in superconducting $\lambda =$2 resonators at T $=$3 K. Thin films of niobium-titanium nitride enabled this development due to their low loss, high nonlinearity, low frequency dispersion, and high critical temperature. The combs nucleate as sidebands around multiples of the pump frequency. Selection rules for the allowed frequency emission are calculated using perturbation theory, and the measured spectrum is shown to agree with the theory. Sideband spacing is measured to be accurate to 1 part in 10$^{8}$ The sidebands coalesce into a continuous comb structure observed to cover at least several frequency octaves. Generation of combs in this frequency range allows for unprecedented analysis of this non-linear phenomena in the time domain.   

Phase-matched Josephson traveling-wave parametric amplifier for superconducting qubit readout - theory

Josephson parametric amplifiers approach quantum-noise-limited performance and are used in experiments requiring high-fidelity detection of single-photon-level microwave signals. Current Josephson parametric amplifiers couple the Josephson junction (a nonlinear inductor) to a resonant cavity, achieving high gain at the expense of limited instantaneous bandwidth. In contrast, Josephson traveling wave parametric amplifiers (JTWPAs) avoid this gain-bandwidth trade-off by employing long propagation lengths rather than a resonant cavity. A major challenge in JTWPA design is that optimum parametric gain is only achieved when the four-wave mixing process is phase matched. We show that by adding a series of resonant elements to the transmission line, phase matching and exponential gain can be achieved. Generation of higher harmonics is automatically suppressed due to the junction plasma resonance. We present the theory and selected results, including the gain, bandwidth, and dynamic range of the amplifier. The simultaneous achievement of high gain (greater than 20 dB), large instantaneous bandwidth (greater than 2 GHz), and high dynamic range make the JTWPA a promising device for the simultaneous readout of frequency-multiplexed superconducting qubits.   

Phase-matched Josephson traveling-wave parametric amplifier for superconducting qubit readout - experiment

We have developed a new generation of Josephson traveling wave parametric amplifiers (JTWPAs) utilizing the technique of resonant phase matching. Due to its transmission line geometry, the JTWPA is not limited by the gain-bandwidth tradeoffs inherent in resonator-based parametric amplifiers. We present experimental results on the amplifier performance of the JTWPA, demonstrating gain in excess of 20 dB over an instantaneous bandwidth of more than 2 GHz with a 1 dB compression power of -100 dBm. The system noise temperature with the JTWPA is less than a factor of 3 above the quantum limit as measured using a 3D transmon in the weak measurement regime to provide a precise power calibration at the relevant experimental reference plane. We also utilize quantum weak measurement to provide an independent measure of the quantum measurement efficiency, in good agreement with the noise power measurement. We demonstrate projective qubit readout with a raw measurement fidelity exceeding 98\% in an 80 ns integration window, and extrapolate this performance to a multi-qubit system.   

High-Fidelity Measurements of Long-Lived Flux Qubits

We report on high-fidelity dispersive measurements of a long-lived flux qubit using a Josephson superconducting traveling wave parametric amplifier (JTWPA). A capacitively shunted flux qubit that incorporates high-Q MBE aluminum will have longer relaxation and dephasing times when compared to a conventional flux qubit, while also maintaining the large anharmonicity necessary for complex gate operations. The JTWPA relies on a Josephson junction embedded transmission line to deliver broadband, nonreciprocal gain with large dynamic range. This research was funded in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA); and by the Assistant Secretary of Defense for Research {\&} Engineering under Air Force Contract number FA8721-05-C-0002. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of   

Quantum-limited Amplification via Dissipation in Superconducting Circuits

The development of parametric amplifiers based on superconducting circuits has led to an impressive improvement in the precision and sensitivity of measurements in the quantum regime. However, standard cavity-based parametric amplifiers suffer from a fixed gain-bandwidth product. Moreover they are reciprocal devices, i.e., they amplify in both directions, leading to the requirement of additional noisy elements as circulators in the measurement chain. In our recent work we discussed a phase-insensitive quantum amplifier which utilizes dissipative interactions in a parametrically-coupled three-mode bosonic system [PRL 112, 133904 (2014)]. The use of dissipative interactions provides a fundamental advantage over standard cavity-based parametric amplifiers: large photon number gains are possible with quantum-limited added noise, with no limitation on the gain-bandwidth product. In this talk we present how this can be extended to phase-sensitive amplifiers and discuss the possibilities of making the amplifier directional.   

Dispersive qubit measurement using an on-chip parametric amplifier: theory

Superconducting circuits directly integrating qubits and parametric amplifiers are a promising avenue for scalable measurement in circuit QED architectures. In such devices, the qubit is not protected against the amplified fluctuations of the paramp; understanding the backaction characteristics is thus crucial. We dicuss recent theory work examining measurement-induced dephasing in a system where a flux-pumped paramp is directly coupled to a qubit, both in the limit of weak and strong dispersive coupling. We show that by careful design choices, the measurement-induced dephasing can be near quantum-limited despite the lack of circulators or explicitly directional amplifiers to protect the qubit. This work is supported by ARO.   

Dispersive qubit measurement using an integrated on-chip parametric amplifier

Superconducting parametric amplifiers (paramps) enable readout of superconducting qubits with unparalleled speed and efficiency. A variety of amplifier designs have been successfully used for readout; however, the most widely used devices require additional microwave components between qubit and paramp, limiting measurement efficiency and scalability. Our work aims to integrate qubit and amplifier on-chip, exploiting two-mode operation of the paramp to minimize measurement backaction on the qubit. To this end, we have developed a flux-pumped, high dynamic range amplifier compatible with qubit integration, and characterized the combined qubit-paramp circuit. We will discuss device design considerations and fabrication, studies of measurement-induced qubit dephasing in the presence of amplification, and prospects for enhanced weak, continuous measurements as well as strong, projective readout.   

Broadband Kinetic Inductance Based Traveling Wave Amplifier for Qubit Readout.

A broadband quantum-limited amplifier is desirable for multiplexed readout of superconducting qubits and detectors. The kinetic inductance traveling-wave parametric amplifier (KIT) is a new type of amplifier that utilizes the intrinsic dissipationless nonlinearity of kinetic inductance of superconductors like NbTiN and TiN for parametric amplification. The amplifier consists of a several meter long CPW transmission line fabricated from a 20nm NbTiN film on an intrinsic Si wafer. The transmission line is dispersion engineered with impedance loadings to achieve the ideal phase matching which leads to broadband gain. We measure over 20dB of gain across several GHz of bandwidth with a high gain-saturation power and dynamic range.   

A dispersion-engineered Josephson junction-based travelling wave parametric amplifier with low loss dielectric

Travelling wave parametric amplifiers (TWPAs) promise wide-band performance with high saturation power for amplifying microwave frequency signals. Designing a TWPA requires a careful balance of many parameters in order to approach quantum-limited noise performance with sufficient gain and saturation power. We present a design based on an LC-ladder transmission line of Josephson junctions and parallel plate capacitors using low-loss amorphous silicon dielectric. Crucially, we have inserted $\lambda/4$ resonators at regular intervals along the transmission line in order maintain the phase matching condition between pump, signal and idler in order to increase gain. The design and performance of the device will be presented, demonstrating high-gain, wide bandwidth and high dynamic range.   

Enhancing bandwidth of Josephson parametric amplifiers with impedance engineering

Josephson parametric amplifiers (JPAs) are a crucial component of superconducting quantum information processing systems since they enable fast, high-fidelity measurement of qubits. However, JPAs based on a single SQUID oscillator suffer from two major drawbacks -- narrow bandwidth and gain saturation at low signal powers, and are typically suited to single qubit experiments only. With the rapid development of multi-qubit systems, there is a practical need to develop an amplifier with larger bandwidth and signal handling capacity, while maintaining gain and noise performance. We will describe a new method to enhance the bandwidth by introducing a frequency dependent shunting impedance for the JPA. To prevent gain saturation, we also replace the single SQUID with a SQUID array. With an appropriate choice of device parameters, numerical calculations indicate the possibility of obtaining 20 dB gain with 700 MHz of bandwidth and near quantum limited noise performance. We will present experimental results demonstrating bandwidth enhancement and discuss strategies for optimizing overall amplifier performance.   

Superinductor Based Traveling Wave Parametric Amplifier

A traveling wave parametric amplifier (TWPA) composed of a transmission line made from a ``superinductor'' element [1] is proposed. The unique nature of this transmission line is that the nonlinearity can be tuned with an external magnetic flux and can even change sign. This feature of the transmission line can be used to perform phase matching in a degenerate four-wave mixing process which can be utilized for parametric amplification of a weak signal in the presence of a strong pump. Numerical simulations of the TWPA design have shown that with tuning, phase matching can be achieved and an exponential gain as a function of the transmission line length can be realized. The proposed TWPA design is well suited for multiplexed readout of quantum circuits or astronomical detectors in a compact configuration which can foster on-chip implementations.\\[4pt] [1] M. Bell et al., ``Quantum Superinductor with Tunable Nonlinearity,'' PRL 109, 137003 (2012).