Parametric amplification in Josephson junction embedded transmission lines

Abstract

An electronic transmission line that contains an array of nonlinear elements (Josephson junctions) is studied theoretically. A continuous nonlinear wave equation describing the dynamics of the node flux along the transmission line is derived. It is shown that due to the nonlinearity of the system, a mixing process between four waves with different frequencies is possible. The mixing process can be utilized for amplification of weak signals due to the interaction with a strong pump wave. An analytical solution for the spatial evolution of the wave amplitudes is derived, and found to be in excellent agreement with the results of numerical computations. Simulations of realistic parameters show that the power gain can exceed 20 dB over a bandwidth of more than 2 GHz.

Nonreciprocal Components With Distributedly Modulated Capacitors

“…, and small capacitance modulation index, a small variable approximation can be applied to the sinusoid function in (26), which leads to (27) The length of the transmission-line section between two adjacent variable capacitors in the DMC is assumed to be much shorter than the signal wavelength to assure that both the signal and the carrier operate below the dispersive region. The following approximations are thus valid: (28) where is the capacitance of the transmission-line section between each neighboring pair of varactors.…”

“…The interest, however, diminished later when semiconductor transistors were invented and proven to be an overall better technology when gains and physical dimensions of amplifiers were emphasized. Recently, there has been a resurgence of interest [19]- [26] in utilizing parametric effects for both hybrid circuits and ICs by taking advantage of the intrinsically lower noise characteristics of the reactance-based components over the conductance-based components. Among those works, discrete parametric mixers [19]- [22] are investigated for applications such as frequency converters and multipliers.…”

“…Distributed circuit architectures [23], [24] are developed utilizing the degenerating parametric effects for resonators and narrowband amplifiers. In [25] and [26], Josephson junctions are employed as nonlinear inductors for nonlinear wave propagation or parametric amplification. In this paper, the time-varying transmission line is treated as a distributed parametric amplifier, where the nondegenerating parametric conversion effects are utilized.…”

Resonant Phase Matching of Josephson Junction Traveling Wave Parametric Amplifiers

“…A major challenge in the design of TWPAs, however, is that optimum parametric gain is achieved only when the amplification process is phase matched. TWPAs based on Josephson junctions have been investigated theoretically [22][23][24][25] and experimentally [26-28] but have not demonstrated sufficient gain, in part due to phase-matching limitations, to replace existing semiconductor amplifier technology. TWPAs based on the weaker nonlinear kinetic inductance of thin titanium nitride wires and phase matched through periodic loading have also been demonstrated [29,30], but they require significantly longer propagation lengths and higher pump powers to achieve comparable gain.…”

“…We use a first principles model for the nonlinear dynamics in the Josephson-junction transmission line [24,25], which has been validated by experiments [28]. By making the ansatz that the solutions are traveling waves, taking the slowly varying envelope approximation, and neglecting pump depletion, we obtain a set of coupled wave equations which describe the energy exchange between the pump, the signal, and the idler in the undepleted pump approximation (see Supplemental Material [31] for the derivation): ∂a s ∂x − iκ s a à i e iðΔk L þ2α p −α s −α i Þx ¼ 0;…”