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Symposium on VLSI Technology

Superconducting parametric devices

Tsuyoshi Yamamoto

Published Jun 1, 2019• 0 citations
Publisher

Abstract

Superconducting parametric amplifier, originally developed more than half a century ago, gained renewed interests in some experiments of superconducting quantum electronics about a decade ago, and now has become an indispensable tool in the field of superconducting quantum information processing. More recently, there are several proposals, where a parametric oscillator, which is a parametric amplifier pumped above the threshold, is used as a quantum bit and the network of the parametric oscillators solve some computational tasks. Here, we briefly introduce the research activity on the development of the superconducting parametric devices, including our results, with some historical backgrounds.

DOI
10.23919/vlsit.2019.8776576

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Superconducting parametric amplifier, originally developed more than half a century ago, gained renewed interests in some experiments of superconducting quantum electronics about a decade ago, and now has become an indispensable tool in the field of superconducting quantum information processing. More recently, there are several proposals, where a parametric oscillator, which is a parametric amplifier pumped above the threshold, is used as a quantum bit and the network of the parametric oscillators solve some computational tasks. Here, we briefly introduce the research activity on the development of the superconducting parametric devices, including our results, with some historical backgrounds.
A parametric oscillator is an oscillating system in which one of the parameters, typically either the resonance frequency or damping, can be modulated by an external pump. Parametric oscillations can be found in a wide variety of systems including radiofrequency circuits, optical and mechanical systems, and even single electrons in a Penning trap. In recent years, interest in parametric oscillators has revived in many areas of physics, ranging from basic physics to applications. For instance, they are being used as quantum-limited amplifiers in an increasingly large number of experiments in quantum information and computing. At the same time, interest in their basic physics in the quantum regime, in which they are a model system for driven, nonlinear systems, has grown commensurately. This chapter gives a largely self-contained introduction to the theoretical description of the dynamics of parametric oscillators, both classical and quantum, and reviews some of the recent experimental work in superconducting circuits.
In this licentiate thesis, I present the design, fabrication, and characterization of superconducting parametric resonators, for use in quantum information processing. These devices are quarter-wavelength coplanar waveguide resonators (~5 GHz), terminated at one end by a non-linear inductance provided by a SQUID (superconducting quantum interference device). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using on-chip transmission lines. The modulation occurs on a timescale much faster than the photon loss out of the resonator. The non-linearity provides several different regimes for operating this device. I focused on the parametric regime, in which the non-linear element was being modulated (pumped) at or near twice the resonant frequency. This pumping can lead to amplification and frequency conversion of an incoming signal. It can also give rise to instabilities and self-oscillations "parametric oscillations" - that is, the generation of an intense electric field in the resonator (the creation of photons). Parametric oscillations set in when the pumping strength exceeds a threshold value, and also depends on the pump-frequency detuning from twice the resonance and on the static flux through the SQUID. I characterized the devices over a wide parameter range by doing homodyne detection of the reflected signal or of the emitted field oscillations. In particular, I investigated the damping and two leading nonlinearities, dominating in different operating regimes, which influence the dynamics of the parametric resonator. First, I extracted the Duffing nonlinearity by studying the line width of the resonator as a function of the input signal (without pumping the SQUID). Second, with high pump amplitude, I extracted the pump-induced nonlinearity by determining the threshold parameters (pump amplitude and detuning) for the onset of parametric oscillations; this nonlinearity leads to the generation of higher-order pump terms that complicate the system dynamics, but can be mitigated now that they have been understood. My results validate a recent theoretical model for the classical, non-linear dynamics of parametric resonance, and helps determine workable design parameters. Finally, I helped develop a linearized model −-− the "pumpistor" - describing this device in terms of a flux-controlled impedance. This will be useful when designing more complex circuits. One goal of this work is to demonstrate single-shot measurements on superconducting qubits (quantum bits of information). We will use the parametric resonator as a threshold discriminator, associating the qubit's two energy eigenstates with the parametric oscillations either turning on or not. This would be a very useful device in the quantum engineer's toolbox when designing systems for quantum information processing and communication.
Nowadays, it is possible to control and measure the quantum state of systems with a few degrees of freedom, whether they are microscopic objects like cold atoms and single photons, or macroscopic objects like superconducting circuits. Such delicate experiments require an interface which bridges the gap of orders of magnitudes in energy between the quantum object and the data acquisition system. This problem is solved by an active device: the amplifier. Although the amplifier is necessary to overcome the noise at the stage of data acquisition, it eventually alters the signal. We have developed an amplifier for microwave signals which adds only the minimum of noise allowed by quantum laws: the equivalent of half a photon of noise referred to the input. Our amplifier is based on a superconducting circuit of Josephson junctions in superconducting resonators. We found a way to make it practical to use by tuning its center frequency over 500 MHz. We are now trying to increase its bandwidth for a given gain using more compact resonators. In this talk, I will show how the amplifier works and also its applications to quantum information processing. This circuit can be used to generate and combine twin microwave photons within an integrated circuit. Finally, I will show that such an amplifier allows real time measurement of the state of a qubit and quantum feedback protocols.
In superconducting quantum computing, qubit state information is conveyed via low-power microwave fields. As such, ultralow-noise microwave amplification plays a central role in measuring these fields to quickly and accurately infer the qubit state. To this end, parametric amplification, once a well-known concept for low-noise amplifiers during the 1960s and 1970s, has become the leading technology for enabling highly efficient microwave measurements of these quantum circuits. While current research efforts have elements in common with much earlier work, there are some important differences that distinguish this new generation of amplifiers. Here, we try to give an overview of what this excitement is about, how these devices work, and where there are opportunities for improvement.
We review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions. We discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for their description. Amplification and frequency conversion are discussed in detail for degenerate and nondegenerate parametric resonance, including quantum noise squeezing and photon entanglement. Experimental advances in this area played decisive role in successful development of quantum limited parametric amplifiers for superconducting quantum information technology. We also discuss nonlinear down-conversion processes and experiments on self-sustained parametric and subharmonic oscillations.
We review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions. We discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for their description. Amplification and frequency conversion are discussed in detail for degenerate and non-degenerate parametric resonance, including quantum noise squeezing and photon entanglement. Experimental advances in this area played decisive role in successful development of quantum limited parametric amplifiers for superconducting quantum information technology. We also discuss nonlinear down-conversion processes and experiments on self-sustained parametric and subharmonic oscillations.