Erratum: Parametric amplification in Josephson junction embedded transmission lines [Phys. Rev. B<b>87</b>, 144301 (2013)]

Yaakobi, Oded; Frièdland, L.; Macklin, Chris; Siddiqi, Irfan

doi:10.1103/physrevb.88.219904

Cited by 22 publications

(56 citation statements)

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“…Preliminary results are promising [64]. Similar analysis for a Josephson junction based traveling-wave parametric amplifier could help the current experimental and theoretical effort [65][66][67][68][69]. Finally, while higher-order corrections hinder the performance of the JPA for squeezing and amplification, it can become a feature for other applications of the JPA such as robust cat state preparation and stabilization [70] which can be used for quantum computation [71] and quantum annealing [72].…”

Section: Discussionmentioning

confidence: 96%

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

et al. 2017

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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 Kerr-type quartic term, while the first scheme contains additional cubic terms. In all cases, we find that the corrections are detrimental to squeezing. In addition, we show that the Kerr correction leads to a strongly phase-dependent reduction of the quantum efficiency of a phase-sensitive measurement. Finally, we quantify the departure from ideal Gaussian character of the filtered output field from numerical calculation of third and fourth order cumulants. Our results show that, while a Gaussian output field is expected for an ideal Josephson parametric amplifier, higher-order corrections lead to non-Gaussian effects which increase with both gain and nonlinearity strength. This theoretical study is complemented by experimental characterization of the output field of a flux-driven Josephson parametric amplifier. In addition to a measurement of the squeezing level of the filtered output field, the Husimi Q-function of the output field is imaged by the use of a deconvolution technique and compared to numerical results. This work establishes nonlinear corrections to the standard degenerate parametric amplifier model as an important contribution to Josephson parametric amplifier's squeezing and noise performance.

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Section: Discussionmentioning

confidence: 96%

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

et al. 2017

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“…While the observed large bandwidth was qualitatively explained by a model consisting of a negative resistance 18 coupled to a frequency dependent impedance, no clear prescription on the design principle was provided. A different approach using Josephson non-linear transmission lines 19,20 was recently demonstrated 21,22 with nearly 4 GHz of bandwidth. However, this design requires fabrication of about 2000 nearly identical blocks of oscillator stages, demanding fairly sophisticated fabrication facilities.…”

Section: Josephson Parametric Amplifiers (Jpas) Have Become a Crucialmentioning

confidence: 99%

Broadband parametric amplification with impedance engineering: Beyond the gain-bandwidth product

Roy

Kundu

Chand

et al. 2015

Applied Physics Letters

154

146

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We present an impedance engineered Josephson parametric amplifier capable of providing bandwidth beyond the traditional gain-bandwidth product. We achieve this by introducing a positive linear slope in the imaginary component of the input impedance seen by the Josephson oscillator using a λ/2 transformer. Our theoretical model predicts an extremely flat gain profile with a bandwidth enhancement proportional to the square root of amplitude gain. We experimentally demonstrate a nearly flat 20 dB gain over a 640 MHz band, along with a mean 1-dB compression point of -110 dBm and near quantum-limited noise. The results are in good agreement with our theoretical model.Josephson parametric amplifiers (JPAs) have become a crucial component of superconducting qubit 1 measurement circuitry, enabling recent studies of quantum jumps 2 , generation and detection of squeezed microwave field 3 , quantum feedback 4,5 , real-time tracking of qubit state evolution 6-8 and quantum error detection 9,10 . Although JPAs based on Josephson junctions embedded in a resonator 11-13 regularly achieve 20 dB power gain and quantum-limited noise, typical bandwidth is restricted to 10-50 MHz 11,14 , making them suitable for single qubit measurements only. The rapid progress towards multi-qubit architectures 9 for fault-tolerant quantum computing 15,16 demands an amplifier with much larger bandwidth to enable simultaneous readout of multiple qubits with minimal resources.There have been several attempts in this direction in recent years. One such attempt used a broadband impedance transformer 17 to lower the quality factor of a lumped-element Josephson oscillator which is the main component of a parametric amplifier. While the observed large bandwidth was qualitatively explained by a model consisting of a negative resistance 18 coupled to a frequency dependent impedance, no clear prescription on the design principle was provided. A different approach using Josephson non-linear transmission lines 19,20 was recently demonstrated 21,22 with nearly 4 GHz of bandwidth. However, this design requires fabrication of about 2000 nearly identical blocks of oscillator stages, demanding fairly sophisticated fabrication facilities. Multimode systems utilizing dissipative interactions have also been suggested theoretically as a route for enhancing bandwidth 23 , but have not been realized experimentally. In this Letter, we present a simple technique for enhancing the bandwidth of a JPA and beating the standard gain-bandwidth limit. It involves engineering the imaginary part of the environmental impedance: in particular, we introduce a positive linear slope in the imaginary component of the impedance shunting the JPA, while keeping the real part unchanged at the pump frequency. Our design uses a combination of a λ/4 and a λ/2 impedance transformers which are significantly easier to fabricate than a broadband impedance transformer 17 . Our theoretical model explains why the imaginary part of the impedance plays a crucial role in determining the amplifier bandw...

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“…A promising approach is to build a TWPA based on the non-linear inductance of the Josephson junction (JJ) [27][28][29][30][31]. This junction TWPA (JTWPA) circuit, shown in Fig.…”

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confidence: 99%

“…Simultaneous amplification of up to five multiplexed tones has been achieved with a JPA [15-17] but was only possible with the Impedance-transformed parametric amplifier [18] (IMPA). This highly engineered JPA provides much larger bandwidth and saturation power but pushes the resonant design to its low Q limit.To extend this frequency multiplexed approach for future experiments, we have adopted the distributed design of the traveling wave parametric amplifier (TWPA) [19]. Fiber-optic TWPAs have already demonstrated high gain, dynamic range, and bandwidth while reaching the quantum-limit of added noise [20,21].…”

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Traveling wave parametric amplifier with Josephson junctions using minimal resonator phase matching

White

Mutus

Hoi

et al. 2015

Applied Physics Letters

166

174

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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 condition between pump, signal, and idler and increase gain. We achieve an average gain of 12 dB across a 4 GHz span, along with an average saturation power of -92 dBm with noise approaching the quantum limit.The Josephson parametric amplifier [1][2][3][4][5][6][7] (JPA) is a critical tool for high fidelity state measurement in superconducting qubits [8][9][10] as it allows parametric amplification with near quantum-limited noise [11]. Despite its success, the JPA has typically been used only for single frequency measurements due to lower bandwidth and saturation power. A promising approach to scaling superconducting qubit experiments is frequency multiplexing [12][13][14], which requires additional bandwidth and dynamic range for each measurement tone. Simultaneous amplification of up to five multiplexed tones has been achieved with a JPA [15-17] but was only possible with the Impedance-transformed parametric amplifier [18] (IMPA). This highly engineered JPA provides much larger bandwidth and saturation power but pushes the resonant design to its low Q limit.To extend this frequency multiplexed approach for future experiments, we have adopted the distributed design of the traveling wave parametric amplifier (TWPA) [19]. Fiber-optic TWPAs have already demonstrated high gain, dynamic range, and bandwidth while reaching the quantum-limit of added noise [20,21]. In this letter we present a microwave frequency TWPA with 4 GHz of bandwidth and an order of magnitude more saturation power than the best JPA. This device is compatible with scaling to much larger qubit systems through multiplexed measurement, and may find applications outside quantum information such as astrophysics detectors [12,22] At microwave frequencies the TWPA can be thought of as a transmission line where the propagation velocity is controlled by varying the individual circuit parameters of inductance or capacitance per unit length [24,25]. This is typically achieved by constructing a signal line with a current dependent (nonlinear) inductance. Like the JPA, a large enough pump tone will modulate this inductance, coupling the pump (ω p ) to a signal (ω s ) and idler (ω i ) tone via frequency mixing such that ω s + ω i = 2ω p . Unlike the JPA however, the TWPA has no resonant structure so gain, bandwidth, and dynamic range are determined by the coupled mode equations of a nonlinear transmission line [23]. In addition to allowing more bandwidth and saturation power...

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Erratum: Parametric amplification in Josephson junction embedded transmission lines [Phys. Rev. B87, 144301 (2013)]

Cited by 22 publications

References 0 publications

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

Broadband parametric amplification with impedance engineering: Beyond the gain-bandwidth product

Traveling wave parametric amplifier with Josephson junctions using minimal resonator phase matching

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