We investigated both theoretically and experimentally open-ended coplanar waveguide resonators with rf SQUIDs embedded in the central conductor at different positions. These rf SQUIDscan be tuned by an external magnetic field and thus may exhibit the non-centrosymmetric nonlinearity of χ(2) type with suppressed Kerr nonlinearity. We demonstrated that this nonlinearity allows for efficient mixing of λ/2 and λ modes in the cavity and thus enables various parametric effects with three wave mixing. These effects are the second harmonic generation, the half tone generation, the parametric amplification in both degenerate and non-degenerate regimes and deamplification in degenerate regime.
We develop the concept of quasi-phasematching (QPM) in the recently proposed traveling-wave Josephson parametric amplifier (TWJPA) with three wave mixing (3WM). The amplifier is basedon a ladder transmission line consisting of flux-biased radio-frequency SQUIDs possessing non-centrosymmetric nonlinearity of χ(2)-type. Due to design with periodically inverted groups of SQUIDs, giving reversal of sign of this nonlinearity, QPM in 3WM process, ωp=ωs+ωi, for pump (ωp), signal (ωs), and idler (ωi) frequency is achieved. Modeling shows that the TWJPA bandwidth is sufficiently large (ca. 0.4ωp) and flat, while propagating unwanted modes, including ω2p=2ωp, ω+=ωp+ωs, ω−=2ωp−ωs, etc., is suppressed with the help of engineered dispersion.
. The amplifier consists"]of a microwave transmission line formed by a serial array of nonhysteretic one-junction SQUIDs. These SQUIDs are flux-biased in a way that the phase drops across the Josephson junctions are equal to 90 degrees and the persistent currents in the SQUID loops are equal to the Josephson critical current values. Such a one-dimensional metamaterial possesses a maximal quadratic nonlinearity and zero cubic (Kerr) nonlinearity. This property allows phase matching and exponential power gain of traveling microwaves to take place over a wide frequency range. We report the proof-of-principle experiment performed at a temperature of T = 4.2 K on Nb trilayer samples, which has demonstrated that our concept of a practical broadband Josephson parametric amplifier is valid and very promising for achieving quantum-limited operation.
We present an experimental realization of resonance fluorescence in squeezed vacuum. We strongly couple microwave-frequency squeezed light to a superconducting artificial atom and detectthe resulting fluorescence with high resolution enabled by a broadband traveling-wave parametric amplifier. We investigate the fluorescence spectra in the weak and strong driving regimes, observing up to 3.1 dB of reduction of the fluorescence linewidth below the ordinary vacuum level and a dramatic dependence of the Mollow triplet spectrum on the relative phase of the driving and squeezed vacuum fields. Our results are in excellent agreement with predictions for spectra produced by a two-level atom in squeezed vacuum [Phys. Rev. Lett. \textbf{58}, 2539-2542 (1987)], demonstrating that resonance fluorescence offers a resource-efficient means to characterize squeezing in cryogenic environments.