| Summary: | Simultaneous ideal quantum measurements of multiple single-photon-level signals would advance applications in quantum information processing, metrology, and astronomy but require the first amplifier to be simultaneously broadband, quantum limited, and directional. However, conventional traveling-wave parametric amplifiers support broadband amplification at the cost of increased added noise and are not genuinely directional due to non-negligible nonlinear backward-wave generation. In this work, we introduce a new class of amplifiers that encode the information in the Floquet modes of the system. Such Floquet-mode amplifiers prevent information leakage and overcome the trade-off between quantum efficiency (QE) and bandwidth. Crucially, Floquet-mode amplifiers strongly suppress the nonlinear forward-backward wave coupling and are therefore genuinely directional and readily integrable with qubits, clearing another major obstacle toward broadband ideal quantum measurements. Furthermore, Floquet-mode amplifiers are insensitive to out-of-band impedance mismatch, which otherwise may lead to gain ripples, parametric oscillations, and instability in conventional traveling-wave parametric amplifiers. Finally, we show that a Floquet-mode Josephson traveling-wave parametric amplifier implementation can simultaneously achieve >20dB gain and a QE of η/η_{ideal}>99.9% of the quantum limit over more than an octave of bandwidth. The proposed Floquet scheme is also widely applicable to other platforms, such as kinetic inductance traveling-wave amplifiers and optical parametric amplifiers.
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