Parametric resonance in tunable superconducting cavities

We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the SQUID attached to the cavity, and damping due to connection of the cavity to a transmission line are taken into consideration. We study in detail the nonlinear classical dynamics of the cavity field below and above the parametric threshold for the degenerate parametric resonance, featuring regimes of multistability and parametric radiation. We investigate the phase-sensitive amplification of external signals on resonance, as well as amplification of detuned signals, and relate the amplifier performance to that of linear parametric amplifiers. We also discuss applications of the device for dispersive qubit readout. Beyond the classical response of the cavity, we investigate small quantum fluctuations around the amplified classical signals. We evaluate the noise power spectrum both for the internal field in the cavity and the output field. Other quantum statistical properties of the noise are addressed such as squeezing spectra, second order coherence, and two-mode entanglement.Comment: 25 pages, 17 figure

Digitally-Enhanced Software-Defined Radio Receiver Robust to Out-of-Band Interference

A software-defined radio (SDR) receiver with improved robustness to out-of-band interference (OBI) is presented. Two main challenges are identified for an OBI-robust SDR receiver: out-of-band nonlinearity and harmonic mixing. Voltage gain at RF is avoided, and instead realized at baseband in combination with low-pass filtering to mitigate blockers and improve out-of-band IIP3. Two alternative “iterative” harmonic-rejection (HR) techniques are presented to achieve high HR robust to mismatch: a) an analog two-stage polyphase HR concept, which enhances the HR to more than 60 dB; b) a digital adaptive interference cancelling (AIC) technique, which can suppress one dominating harmonic by at least 80 dB. An accurate multiphase clock generator is presented for a mismatch-robust HR. A proof-of-concept receiver is implemented in 65 nm CMOS. Measurements show 34 dB gain, 4 dB NF, and 3.5 dBm in-band IIP3 while the out-of-band IIP3 is + 16 dBm without fine tuning. The measured RF bandwidth is up to 6 GHz and the 8-phase LO works up to 0.9 GHz (master clock up to 7.2 GHz). At 0.8 GHz LO, the analog two-stage polyphase HR achieves a second to sixth order HR > dB over 40 chips, while the digital AIC technique achieves HR > 80 dB for the dominating harmonic. The total power consumption is 50 mA from a 1.2 V supply

High performance photonic reservoir computer based on a coherently driven passive cavity

Reservoir computing is a recent bio-inspired approach for processing time-dependent signals. It has enabled a breakthrough in analog information processing, with several experiments, both electronic and optical, demonstrating state-of-the-art performances for hard tasks such as speech recognition, time series prediction and nonlinear channel equalization. A proof-of-principle experiment using a linear optical circuit on a photonic chip to process digital signals was recently reported. Here we present a photonic implementation of a reservoir computer based on a coherently driven passive fiber cavity processing analog signals. Our experiment has error rate as low or lower than previous experiments on a wide variety of tasks, and also has lower power consumption. Furthermore, the analytical model describing our experiment is also of interest, as it constitutes a very simple high performance reservoir computer algorithm. The present experiment, given its good performances, low energy consumption and conceptual simplicity, confirms the great potential of photonic reservoir computing for information processing applications ranging from artificial intelligence to telecommunicationsComment: non

Transient dynamics of a superconducting nonlinear oscillator

We investigate the transient dynamics of a lumped-element oscillator based on a dc superconducting quantum interference device (SQUID). The SQUID is shunted with a capacitor forming a nonlinear oscillator with resonance frequency in the range of several GHz. The resonance frequency is varied by tuning the Josephson inductance of the SQUID with on-chip flux lines. We report measurements of decaying oscillations in the time domain following a brief excitation with a microwave pulse. The nonlinearity of the SQUID oscillator is probed by observing the ringdown response for different excitation amplitudes while the SQUID potential is varied by adjusting the flux bias. Simulations are performed on a model circuit by numerically solving the corresponding Langevin equations incorporating the SQUID potential at the experimental temperature and using parameters obtained from separate measurements characterizing the SQUID oscillator. Simulations are in good agreement with the experimental observations of the ringdowns as a function of applied magnetic flux and pulse amplitude. We observe a crossover between the occurrence of ringdowns close to resonance and adiabatic following at larger detuning from the resonance. We also discuss the occurrence of phase jumps at large amplitude drive. Finally, we briefly outline prospects for a readout scheme for superconducting flux qubits based on the discrimination between ringdown signals for different levels of magnetic flux coupled to the SQUID.Comment: 15 pages, 9 figure

Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation

Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is identified as the seemingly intractable factor limiting the achievable rate at high launch power. However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear optical channel. Exploiting the integrability of the nonlinear Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing (NFDM) scheme is presented, which directly modulates non-interacting signal degrees-of-freedom under NLS propagation. The main distinction between this and previous methods is that NFDM is able to cope with the nonlinearity, and thus, as the the signal power or transmission distance is increased, the new method does not suffer from the deterministic cross-talk between signal components which has degraded the performance of previous approaches. In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4346--4369, July, 201

Nonlinearities and Parametric Amplification in Superconducting Coplanar Waveguide Resonators

Experimental investigations of the nonlinear properties of superconducting niobium coplanar waveguide resonators are reported. The nonlinearity due to a current dependent kinetic inductance of the center conductor is strong enough to realize bifurcation of the nonlinear oscillator. When driven with two frequencies near the threshold for bifurcation, parametric amplification with a gain of +22.4 dB is observed.Comment: 4 pages, 5 figures, 1 table. In version 2: Added appendix with model description and fits to measurements. Minor corrections and rephrasin