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Optimisation of superconducting traveling wave parametric amplifiers in the GHz frequency range by circuit simulationsFrequenzbereich durch Schaltungssimulationen


Within the EMPIR project "ParaWave", which is funded by the EU and coordinated by PTB, broadband, low noise traveling wave amplifiers are under development. To optimise the circuit parameters, a software tool allowing for a correct description of Josephson junctions was used.


Modern quantum technology systems, such as quantum computers or multi-channel quantum sensors, require broadband cryogenic amplifiers with significant gain and bandwidth as well as very low noise, which is determined by quantum mechanical principles. Parametric amplifiers using nonlinear reactive components (e.g. Josephson junctions) to convert energy from a pump wave into a signal wave can achieve nearly quantum-limited noise performance.

Together with European project partners, a new kind of parametric amplifier was developed at PTB, consisting of an active microwave transmission line with an embedded series array of single-junction SQUIDs (rf-SQUIDs, where SQUID stands for Superconducting Quantum Interference Device) and using the traveling-wave principle. This circuit design creates a quadratic Josephson non-linearity in contrast to the cubic non-linearity (Kerr effect) used in previous concepts and, thus, allows the use of the advantageous three-wave mixing. Due to the three-wave mixing mode, the pump frequency is separated from the signal band, which significantly reduces the need for output filtering.

First test circuits showed a relatively low signal amplification and a strong generation of the second harmonic of the pump frequency, as well as higher-order mixing products. To analyse these results and to optimise the circuit parameters, circuit simulations were carried out. The software tool used enables the simulation of circuits including Josephson junctions, which cannot be described by a simple current-voltage characteristic. The simulations confirmed that - due to the high bandwidth of the circuit - a large part of the pump energy is converted into the second and higher harmonics and is therefore not available for signal amplification.

A possible solution to this problem is the creation of a tailor-made dispersion relation, which ensures perfect phase matching between the pump and signal waves and at the same time largely prevents the transfer of energy into mixing products above the pump frequency. This can be achieved, e.g., by periodically inserting LC resonators into the active microwave line with resonance frequencies slightly below the pump frequency. At PTB, a technologically simpler approach is being investigated, by generating one or more frequency gaps in the dispersion relation through periodic modulation of the transmission line parameters and, thus, of the impedance (Figure 1). This idea was verified by circuit simulations (Figure 2). Currently, the circuit parameters are being optimised in order to achieve a high gain in a large bandwidth.


Concept of gap engineering in the microwave transmission line

Figure 1: Concept of gap engineering in the microwave transmission line.


Circuit simulation of gain versus frequency for a three-wave mixing parametric amplifier

Figure 2: Circuit simulation of gain versus frequency for a three-wave mixing parametric amplifier with modified dispersion relation by gap engineering. The circuit with 1000 rf-SQUIDs shows a gain of more than 20 dB in a bandwidth of 2.5 GHz.




Department 2.4 “Quantum Electronics”