Quantum analysis of second-order effects in superconducting travelling-wave parametric amplifiers

Abstract

We have performed a quantum mechanical analysis of travelling-wave parametric amplifiers (TWPAs) in order to investigate five experimental phenomena related to their operations, namely the effect of impedance mismatch, the presence of upper idler modes, the presence of quantum and thermal noise, the generation of squeezed states, and the preservation of pre-squeezed states during amplification. Our analysis uses momentum operators to describe the spatial evolution of quantised modes along a TWPA. We calculate the restriction placed on pump amplitude as well as amplifier gain as a result of impedance mismatch between a TWPA and its external system. We apply our analysis to upper idler modes and demonstrate that they will result in suppressed gain. We show that an ideal TWPA is indeed quantum-limited—i.e. it introduces a half-quantum of zero-point fluctuation which is the minimum possible noise contribution for a phase-preserving linear amplifier. We analyse the thermal noise associated with a TWPA by considering the effect of distributed sources along an amplifier transmission line. Our analysis predicts a doubling of thermal noise in the high gain limit as a result of wave-mixing between signal and idler modes. We study the operation of a TWPA in the presence of a DC bias current, and have shown that highly squeezed states can in principle be generated. However, amplifying a pre-squeezed state using a non-degenerate TWPA generally reduces the squeezing advantage.

Nonlinear mechanisms in Al and Ti superconducting travelling-wave parametric amplifiers

“…altering the thermal noise output by changing the level of dissipation, or by resulting in additional modulation of the noise. Understanding the magnitude of the dissipative nonlinearity is therefore important in determining if a particular TWPA can, in theory, achieve amplification and approach the quantum limit [7]. Lastly, as we shall show in this study, the response time of a nonlinear mechanism imposes a strong constraint on the bandwidth of a TWPA.…”

Modeling of Josephson Traveling Wave Parametric Amplifiers

“…They are due to variable impedance along the transmission line that do not well matches the input and output impedances and generate interference between forward and backward propagating waves undergoing multiple reflections [41] [43]. These ripples have been described as Fabry-Pérotlike resonances [26] [44] with a bandwidth inversely proportional to the waveguide length. Recently, an approach based on the theory of coupled modes [36], successfully predicts the formation of these ripples by considering the interactions of reflected waves [45].…”

Nonlinear mechanisms in Al and Ti superconducting travelling-wave parametric amplifiers

“…altering the thermal noise output by changing the level of dissipation, or by resulting in additional modulation of the noise. Understanding the magnitude of the dissipative nonlinearity is therefore important in determining if a particular TWPA can, in theory, achieve amplification and approach the quantum limit [7]. Lastly, as we shall show in this study, the response time of a nonlinear mechanism imposes a strong restriction on the bandwidth of a TWPA.…”