Mitigating back-action in parametric quantum amplifiers

Parametric quantum amplifiers are of paramount importance for quantum information processing with superconducting circuits. A promising route to design quantum amplifiers is based on parametric modulation of coupled modes, where the required mode-mixing processes are realized by utilizing Josephson junction-based tunable couplers. All designs face the challenge of higher-order nonlinearities, resulting in a limitation of the dynamical range of the amplifier. However, even without any higher-order nonlinearities, the amplification process is itself nonlinear, e.g., it involves the mixing of three waves: the pump, the idler and the signal. Only for weak enough signal intensity the pump can be considered stiff and the amplification process becomes linear. Once the signal strength grows this approximation does not hold true anymore. The nonlinear nature of the mixing process leads to back-action, limiting the dynamical range of the amplifier.Here we present possible ways to face these challenges, and how to avoid unwanted back-action effects in engineered quantum systems. Furthermore, we discuss routes for optimizing the design of quantum-limited parametric amplifiers that one can avoid pump-depletion effects completely.