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Physical Review Letters

Subharmonic pumping of a Josephson-parametric amplifier and the pitchfork instability

Roman Movshovich, B. Yurke, A. D. Smith, Arnold H. Silver

Published Sep 9, 1991• 5 citations
Publisher

Abstract

We report the observation of substantial amplification due to multiwave (more than four) mixing in a Josephson-parametric amplifier. Amplification was achieved with subharmonic pumping at 2/3, 2/5, and 2/7 of the signal frequency near 19 GHz. The processes reponsible for the amplification were, correspondingly, five-, seven-, and nine-wave mixing. For the case of five-wave mixing we have observed amplification in excess of 35 dB and noise referred to input of a few degrees kelvin before the amplifier undergoes a pitchfork instability. The noise rise at the pitchfork bifurcation was also studied and compared with theory.

DOI
10.1103/physrevlett.67.1411

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We report the observation of substantial amplification due to multiwave (more than four) mixing in a Josephson-parametric amplifier. Amplification was achieved with subharmonic pumping at 2/3, 2/5, and 2/7 of the signal frequency near 19 GHz. The processes reponsible for the amplification were, correspondingly, five-, seven-, and nine-wave mixing. For the case of five-wave mixing we have observed amplification in excess of 35 dB and noise referred to input of a few degrees kelvin before the amplifier undergoes a pitchfork instability. The noise rise at the pitchfork bifurcation was also studied and compared with theory.
We have investigated the performance of a resistive rf SQUID as a 9 GHz parametric amplifier and oscillator. It was coupled to a low impedance microstrip transformer. Stable Josephson oscillations were obtained for βLQ =2eI0ZL/hf <1.1–1.8. Oscillation linewidth (830 kHz) and output power (−74 dBm) were measured. The four-photon internally pumped amplifier produced large single sideband (ssb) noise temperatures, typically around 50 K, due to the broad flanks of the pump. The best performance was achieved in the three- and four-photon externally pumped modes. Both modes gave signal gains of about 10 dB and negligible noise power contributions. A hot/cold measurement on the four-photon amplifier yielded Gdsb =13 dB (dsb=double sideband) and Tdsb =3±4 K over a bandwidth of 310 MHz. For larger values of βLQ , subharmonics 1/2 and 1/3, as well as noninteger ‘‘excitations’’ of the Josephson oscillation, were observed. The subharmonic oscillations were not tunable in frequency with unchanged linewidth. Amplification close to an excitation also produced gain but with ssb noise temperatures of ∼20 K.
We have developed a Josephson parametric amplifier comprising a superconducting coplanar-waveguide resonator terminated by a dc superconducting quantum interference device (SQUID). An external field (the pump, ∼20 GHz) modulates the flux threading of the dc SQUID and, therefore, the resonant frequency of the cavity field (the signal, ∼10 GHz), which leads to the 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 temperature is estimated to be less than 0.87 K.
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, ∼20\sim 20∼20 GHz) modulates the flux threading the dc SQUID, and, thereby, the resonant frequency of the cavity field (the signal, ∼10\sim 10∼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 temperature is estimated to be less than 0.87 K.
We present the theory of a Josephson parametric amplifier employing two-pump sources. Our calculations are based on input-output theory, and can easily be generalized to any coupled system involving parametric interactions. We analyze the operation of the device, taking into account the feedback introduced by the reaction of the signal and noise on the pump power, and in this framework, compute the response functions of interest---signal and idler gains, internal gain of the amplifier, and self-oscillation signal amplitude. To account for this back action between signal and pump, we adopt a mean-field approach and self-consistently explore the boundary between amplification and self-oscillation. The coincidence of bifurcation and self-oscillation thresholds reveals that the origin of coherent emission of the amplifier lies in the multiwave mixing of the noise components. Incorporation of the back action leads the system to exhibit hysteresis, dependent on parameters such as temperature and detuning from resonance. Our analysis also shows that the resonance condition itself changes in the presence of back action and this can be understood in terms of the change in plasma frequency of the junction. The potential of the double-pump amplifier for quantum-limited measurements and as a squeezer is also discussed.
The high-frequency amplification properties of transformer coupled, resistively shunted Josephson tunnel junctions have been investigated. The importance of the shunt loop inductance is stressed. It allows a high cutoff frequency, of significance for good high-frequency performance. The self-pumped parametric amplifier showed none of the excessive noise rise, which has hitherto plagued the development of externally pumped Josephson junction amplifiers. Around 10 GHz, we estimated a noise temperature less than 30 K for an amplifier pumped by a Josephson oscillation with a frequency well above twice the signal frequency. The corresponding gain of 5 dB may be increased in a better impedance matched circuit. The gain was very stable against variations in the bias conditions. A gain-bandwidth product as high as 0.3 was registered. The experimental results agreed well with the established theory for self-pumped parametric Josephson amplifiers. It should be possible to extend the low noise amplification by this device to mm wave frequencies. A relaxation oscillation occurred at a subharmonic of the Josephson frequency when the shunt loop inductance became large. The amplification in this mode followed closely the predictions of a simple model, where the signal modulated the switching of the sawtooth-like (relatively low frequency) relaxation current. Gains of about 15 dB were measured around 10 GHz, but the amplification was sensitive to bias conditions and noisy in this case where the relaxation frequency fell well below the signal frequency. Much improved properties were registered when the inductance was decreased so that the relaxation frequency approached the Josephson frequency and exceeded twice the signal frequency. The behavior then resembled that of a Josephson mode parametric amplifier, but the high content of harmonics of a relaxation oscillation meant that the amplifier became noisier due to converted noise from the many idler frequencies.
The recent developments in quantum technologies, as well as advanced detection experiments, have raised the need to detect extremely weak signals in the microwave frequency spectrum. To this aim, the Josephson travelling wave parametric amplifier, a device capable of reaching the quantum noise limit while providing a wide bandwidth, has been proposed as a suitable cryogenic front-end amplifier. This work deals with the numerical study of a Josephson travelling wave parametric amplifier, without approximations regarding the nonlinearity of the key elements. In particular, we focus on the investigation of the system of coupled nonlinear differential equations representing all the cells of the Josephson travelling wave parametric amplifier, with proper input and output signals at the boundaries. The investigation of the output signals generated by the parametric amplification process explores the phase-space and the Fourier spectral analysis of the output voltage, as a function of the parameters describing the pump and signal tones that excite the device. Beside the expected behavior, i.e., the signal amplification, we show that, depending on the system operation, unwanted effects (such as pump tone harmonics, incommensurate frequency generation, and noise rise), which are not accounted for in simple linearized approaches, can be generated in the whole nonlinear system.