We introduce a transparency-engineered rf-SQUID cell for Kerr-free three-wave-mixing Josephson metamaterials. This design replaces the conventional tunnel-junction element with an effective Josephson element formed by two junctions in series, yielding a non-sinusoidal energy-phase relation that can be used as a tunable nonlinear design resource. We show that the asymmetry between the two series junctions and the applied flux bias provide independent control over the local expansion of the rf-SQUID potential, enabling operating points where the leading quartic Kerr term is suppressed while the cubic nonlinearity remains finite. We derive the corresponding Kerr-free condition, identify the resulting operating ridge in parameter space, and analyze the local stability and passive-matching constraints that bound its physically accessible portion. Our results provide a compact unit-cell design principle for three-wave-mixing Josephson metamaterials and suggest a route toward Kerr-suppressed Josephson traveling-wave parametric amplifiers.
We introduce a transparency-engineered rf-SQUID cell for Kerr-free three-wave-mixing Josephson metamaterials. This design replaces the conventional tunnel-junction element with an effective Josephson element formed by two junctions in series, yielding a non-sinusoidal energy-phase relation that can be used as a tunable nonlinear design resource. We show that the asymmetry between the two series junctions and the applied flux bias provide independent control over the local expansion of the rf-SQUID potential, enabling operating points where the leading quartic Kerr term is suppressed while the cubic nonlinearity remains finite. We derive the corresponding Kerr-free condition, identify the resulting operating ridge in parameter space, and analyze the local stability and passive-matching constraints that bound its physically accessible portion. Our results provide a compact unit-cell design principle for three-wave-mixing Josephson metamaterials and suggest a route toward Kerr-suppressed Josephson traveling-wave parametric amplifiers.
We develop a novel concept of a Josephson traveling-wave parametric amplifier with three-wave mixing. The proposed amplifier consists of a microwave transmission line formed by a serial array of nonhysteretic one-junction SQUIDs. These SQUIDs are flux-biased such that the phase drops across the Josephson junctions are equal to 90°. This one-dimensional metamaterial possesses large quadratic nonlinearity and minimal cubic (Kerr-like) nonlinearity. This property allows phase matching and exponential power gain in a wide frequency range. The proof-of-principle measurements performed at temperature T = 4.2 K on Nb trilayer samples have demonstrated the validity of our concept of a practical Josephson parametric amplifier with great promise for quantum-limited performance.
We develop a concept of traveling-wave Josephson parametric amplifier based on a ladder-type superconducting transmission line containing serial array of one-junctions SQUIDs. The circuit operates in a three-wave mixing mode and exploits both quadratic and cubic (Kerr) nonlinearities in the current-phase relation of the SQUIDs controlled by external magnetic flux. These two types of nonlinearities allow efficient three-wave mixing and perfect phase matching, respectively. The transmission line exhibits a power gain with exponential dependence on its length (number of cells N) in the widest frequency range, 0≲fs,fi≲fp, where fs, fi and fp are the signal, idler and pump frequencies, respectively, obeying relation fs+fi=fp. Estimation of the amplifier characteristics with typical experimental parameters, number of cells N = 700, length of 28 mm and pump frequency of 12.5 GHz yields a flat (-3 dB) gain of about 20 dB in the bandwidth from 3.35 GHz to 9.15 GHz and a saturation power of -90 dBm.
Abstract A Josephson traveling-wave parametric amplifier (JTWPA) is indispensable for the high-fidelity readout of superconducting qubits, owing to its broadband gain and near-quantum-limited noise performance. Conventional JTWPAs implemented with 0-Josephson junctions (0-JTWPAs) avoid magnetic-flux bias but rely on Kerr nonlinearity, which leads to pump-power-dependent phase mismatch, gain ripple, and a limited dynamic range. More recently, three-wave-mixing (3WM) JTWPAs employing flux-biased rf-SQUIDs have been proposed to suppress Kerr effects. However, these designs require a significant external flux bias per unit cell, which complicates cryogenic hardware, introduces sensitivity to flux noise, and limits scalability in large arrays. In this study, we propose and analyze a π -junction-based JTWPA ( π -JTWPA) in which the intrinsic π phase shift of the junction effectively displaces the operating point of the current–phase relation. This approach aims to realize 3WM-type nonlinearity with reduced flux bias while preserving broadband amplification, thereby simplifying flux-bias distribution, enhancing robustness against flux noise, and providing a pathway toward scalable, multiplexed quantum readout architectures. In addition, we examine the potential applicability of the π -JTWPA in four-wave-mixing (4WM) operation.
A quantum model for Josephson-based metamaterials working in the three-wave mixing (3WM) and four-wave mixing (4WM) regimes at the single-photon level is presented. The transmission line taken into account, namely Josephson traveling wave parametric amplifier (JTWPA), is a bipole composed of a chain of rf-SQUIDs, which can be biased by a DC current or a magnetic field to activate the 3WM or 4WM nonlinearities. The model exploits a Hamiltonian approach to analytically determine the time evolution of the system both in the Heisenberg and interaction pictures. The former returns the analytic form of the gain of the amplifier, while the latter allows recovering the probability distributions vs time of the photonic populations, for multimodal Fock and coherent input states. The dependence of the metamaterial's nonlinearities is presented in terms of circuit parameters in a lumped model framework while evaluating the effects of the experimental conditions on the model validity.
We have developed active metamaterials based on macroscopic quantum effects capable of quickly tuning their electrical and magnetic responses over a wide frequency range. These metamaterials are based on superconducting elements to form low insertion loss, physically and electrically small, highly tunable structures for the next generation rf electronics. The meta-atoms are rf superconducting quantum interference devices (SQUIDs) that incorporate the Josephson effect. RF SQUIDs have an inductance which includes a contribution from the Josephson inductance of the junction. This inductance is strongly tunable with dc and rf magnetic fields and currents. The rf SQUID metamaterial is a richly nonlinear effective medium introducing qualitatively new macroscopic quantum phenomena into the metamaterials community, namely magnetic flux quantization and the Josephson effect. The coherence of the metamaterials is strongly sensitive to the environment and measurement conditions. The metamaterials also display a unique form of transparency whose development can be manipulated through multiple parametric dependences. Further features such as breathers, superradiance, and self-induced transparency, along with entry into the fully quantum limit, will yield qualitatively new metamaterial phenomena. This work is supported by the NSF-GOALI and OISE Programs through Grant No. ECCS-1158644 and the Center for Nanophysics and Advanced Materials (CNAM).
Metamaterials are artificially designed materials to exhibit properties not available in natural materials by engineering the constituting elements at sub-wavelength scales, enabling unique interactions of matter with electromagnetic waves or coupling modes of electromagnetic waves. Examples of such novel optics phenomenons include negative index of refraction, cloaking, and super-resolution imaging. The study of superconducting metamaterials operating in the microwave frequency domain has recently generated significant interest in the framework of quantum technologies due to a wide range of direct applications, e.g., exploration of novel quantum optics phenomena, non-destructive quantum sensing, quantum-limited amplification, quantum information processing, and quantum illumination. In contrast to their normal metal and semiconducting counterparts, superconducting metamaterials offer some unique advantages. The most relevant of these for Josephson junction based metamaterials are low losses, flux quantization, and Josephson effects. The Josephson effect in a superconducting loop can also be exploited to exact more control over the nonlinearities of the meta-material.In this thesis, we present Josephson junction based metamaterials with in-situ tunability of second and third-order (Kerr) nonlinearities. We optimized the Josephson junction composites SNAILs, well-known in the superconducting circuits community, for the specific use case of building blocks for an impedance-matched nonlinear meta-material. In such devices, the strong third-order (Kerr) nonlinearity can be tuned from positive to negative values. To demonstrate the efficacy of this phenomenon, we have shown a use case of the meta-material as a TWPA with a new phase-matching mechanism: reversed Kerr phase matching, which utilizes the sign reversal of the Kerr nonlinearity to correct for the dispersion curvature of such devices arising due to its finite plasma. The meta-material operated as reversed Kerr TWPA exhibits up to 4 GHz wide combined amplification band with 8 GHz dynamic band tunability, -98 dBm saturation (1 dB compression point) around 20 dB gain, and amplifier added noise close to the standard quantum limit. The absence of any gaps in the transmission can provide a continuous amplification band with significantly lower gain ripples in contrast to the previously demonstrated TWPAs with dispersion engineering.We also present the generation of entanglement utilizing the metamaterials to demonstrate their versatility and further emphasize their potential in the general framework of nonlinear microwave quantum optics. Due to their large bandwidth, these devices have been identified as promising for generating two-mode squeezing and broadband entanglement. With a device optimized for the generation of broadband entanglement, we observed entanglement between two modes separated by up to 400 MHz. We measured logarithmic negativity between 0.27 and 0.51, and the collective quadrature squeezing below the vacuum limit between 1.5 and 2.1 dB. The presented proof-of-principle results can pave the way towards the implementation of Josephson junction based metamaterials in novel applications, including non-destructive single-photon detection, single-photon measurement and control in c-QED, photon-based quantum computing, precision sensing, the detection of dark matter, and quantum illumination.