Three-wave mixing in Josephson travelling-wave parametric amplifiers

This work explores possibilities of building a wide-band, quantum-limited low-noise amplifier by means of three-wave mixing (3WM) in different kinds of Josephson travelling-wave parametric amplifiers (TWPAs). We extend the theory of the continuous three-mode model to include any number of up-converted modes in the small frequency limit where the frequency dispersion is close to linear. We also extend the theory to describe a discrete chain at frequencies close to the spectral cutoff where there is no up-conversion. In both cases we find that the gain is significantly reduced compared to the prediction by the continuous three-mode model. At the high frequencies we cannot pump strongly enough to overcome the increasingly strong dispersion, while in the small frequency limit, the dispersion can be overcome but the gain is then reduced by up-conversion processes. The developed theory is in quantitative agreement with experimental observations.To recover the high gain predicted by the continuous three-mode model, we propose to engineer a TWPA with dispersive features to create a two-band dispersion relation, either by adding resonant phase matching (RPM) features, or by periodically modulating the parameters of the chain. By placing the pump frequency within the upper band, close to the cutoff frequency, while placing the signal in the lower band, we prove that there exists a sweet spot where the signal and the pump are phase matched while the up-conversion is inhibited. We solve the discrete equations for the RPM-based TWPA and show that the gain is expected to grow exponentially with the length of the TWPA

Modeling and Harmonic Balance Analysis of Parametric Amplifiers for Qubit Read-out

Predicting the performance of traveling-wave parametric amplifiers (TWPAs) based on nonlinear elements like superconducting Josephson junctions (JJs) is vital for qubit read-out in quantum computers. The purpose of this article is twofold: (a) to demonstrate how nonlinear inductors based on combinations of JJs can be modeled in commercial circuit simulators, and (b) to show how the harmonic balance (HB) is used in the reliable prediction of the amplifier performance e.g., gain and pump harmonic power conversion. Experimental characterization of two types of TWPA architectures is compared with simulations to showcase the reliability of the HB method. We disseminate the modeling know-how and techniques to new designers of parametric amplifiers.Comment: 13 pages, 15 figure

Quantum efficiency, purity and stability of a tunable, narrowband microwave single-photon source

We demonstrate an on-demand source of microwave single photons with 71–99% intrinsic quantum efficiency. The source is narrowband (300 kHz) and tuneable over a 600 MHz range around 5.2 GHz. Such a device is an important element in numerous quantum technologies and applications. The device consists of a superconducting transmon qubit coupled to the open end of a transmission line. A π-pulse excites the qubit, which subsequently rapidly emits a single photon into the transmission line. A cancellation pulse then suppresses the reflected π-pulse by 33.5 dB, resulting in 0.005 photons leaking into the photon emission channel. We verify strong antibunching of the emitted photon field and determine its Wigner function. Non-radiative decay and 1/f flux noise both affect the quantum efficiency. We also study the device stability over time and identify uncorrelated discrete jumps of the pure dephasing rate at different qubit frequencies on a time scale of hours, which we attribute to independent two-level system defects in the device dielectrics, dispersively coupled to the qubit. Our single-photon source with only one input port is more compact and scalable compared to standard implementations

Three-wave mixing traveling-wave parametric amplifier with periodic variation of the circuit parameters

We report on the implementation of a near-quantum-limited, traveling-wave parametric amplifier that uses three-wave mixing (3WM). To favor amplification by 3WM, we use superconducting nonlinear asymmetric inductive element (SNAIL) loops, biased with a dc magnetic flux. In addition, we equip the device with dispersion engineering features to create a stopband at the second harmonic of the pump and suppress the propagation of the higher harmonics that otherwise degrade the amplification. With a chain of 440 SNAILs, the amplifier provides up to 20 dB gain and a 3-dB bandwidth of 1 GHz. The added noise by the amplifier is found to be less than one photon

Three-wave mixing traveling-wave parametric amplifier with periodic variation of the circuit parameters

We report the implementation of a near-quantum-limited, traveling-wave parametric amplifier that uses three-wave mixing (3WM). To favor amplification by 3WM, we use the superconducting nonlinear asymmetric inductive element (SNAIL) loops, biased with a dc magnetic flux. In addition, we equip the device with dispersion engineering features to create a stop-band at the second harmonic of the pump and suppress the propagation of the higher harmonics that otherwise degrade the amplification. With a chain of 440 SNAILs, the amplifier provides up to 20 dB gain and a 3-dB bandwidth of 1 GHz. The added noise by the amplifier is found to be less than one photon.Comment: 6 pages, 6 figure

A high gain travelling-wave parametric amplifier based on three-wave mixing

We extend the theory for a Josephson junction travelling wave parametric amplifier (TWPA) operating in the three-wave mixing regime and we propose a scheme for achieving high gain. The continuous three-mode model [P. K. Tien, J. Appl. Phys. 29, 1347 (1958)] is on one hand extended to describe a discrete chain of Josephson junctions at high frequencies close to the spectral cutoff where there is no up-conversion. On the other hand, we also develop a continuous multimode theory for the low-frequency region where the frequency dispersion is close to linear. We find that in both cases the gain is significantly reduced compared to the prediction by the continuous three-mode model as the result of increasingly strong dispersion at the high frequencies and generation of up-converted modes at the low frequencies. The developed theory is in quantitative agreement with experimental observations. To recover the high gain, we propose to engineer a chain with dispersive features to form a two-band frequency spectrum and to place the pump frequency within the upper band close to the spectral cutoff. We prove that there exists a sweet spot, where the signal and the pump are phase matched, while the up-conversion is inhibited. This results in a high gain which grows exponentially with the length of the TWPA

Embedding networks for ideal performance of a travelling-wave parametric amplifier

We investigate the required embedding networks to enable ideal performance for a high-gain travelling-wave parametric amplifier (TWPA) based on three-wave mixing (3WM). By embedding the TWPA in a network of superconducting diplexers and hybrid couplers, the amplifier can deliver a high stable gain with near-quantum-limited noise performance, with suppressed gain ripples, while eliminating the reflections of the signal, the idler and the pump as well as the transmission of all unwanted tones. We demonstrate a configuration where the amplifier can isolate. We call this technique Wideband Idler Filtering (WIF). The theory is supported by simulations that predict over 20 dB gain in the band 4-8 GHz with 10 dB isolation for a single amplifier and 30 dB isolation for two cascaded amplifiers. We demonstrate how the WIF-TWPAs can be used to construct switchable isolators with over 40 dB isolation over the full band 4-8 GHz. We also propose an alternative design where the WIF can be implemented without diplexers. Finally we show how, with small modifications, the technique can be implemented for four-wave mixing (4WM) TWPAs as well.Comment: 13 pages, 22 figures, 3 table