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arXiv:1707.06834 · Physical Review Applied

Josephson Metamaterial with a Widely Tunable Positive or Negative Kerr Constant

Wenyuan Zhang, W. Huang, M. E. Gershenson, M. T. Bell

Published Nov 13, 2017• 33 citations
arXivHTMLPDF

Abstract

The optical Kerr effect, in which a medium's refractive index is affected by the intensity of the transmitted light, is exploited not only in conventional optics, but also in superconducting circuits. This article reports a Josephson-junction-based metamaterial with a widely tunable Kerr constant that can even change sign. Controlled by an external magnetic field, this material can speed up or slow down the phase velocity of light per the intensity of the propagating electromagnetic wave. Such an engineered medium could be used for phase matching in traveling-wave parametric amplifiers, or in superconducting hardware for encoding or reading out quantum information.

DOI
10.1103/physrevapplied.8.051001

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The optical Kerr effect, in which a medium's refractive index is affected by the intensity of the transmitted light, is exploited not only in conventional optics, but also in superconducting circuits. This article reports a Josephson-junction-based metamaterial with a widely tunable Kerr constant that can even change sign. Controlled by an external magnetic field, this material can speed up or slow down the phase velocity of light per the intensity of the propagating electromagnetic wave. Such an engineered medium could be used for phase matching in traveling-wave parametric amplifiers, or in superconducting hardware for encoding or reading out quantum information.
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.
Josephson meta-materials have recently emerged as very promising platform for superconducting quantum science and technologies. Their distinguishing potential resides in ability to engineer them at sub-wavelength scales, which allows complete control over wave dispersion and nonlinear interaction. In this article we report a versatile Josephson transmission line with strong third order nonlinearity which can be tuned from positive to negative values, and suppressed second order non linearity. As an initial implementation of this multipurpose meta-material, we operate it to demonstrate reversed Kerr phase-matching mechanism in traveling wave parametric amplification. Compared to previous state of the art phase matching approaches, this reversed Kerr phase matching avoids the presence of gaps in transmission, can reduce gain ripples, and allows in situ tunability of the amplification band over an unprecedented wide range. Besides such notable advancements in the amplification performance with direct applications to superconducting quantum computing and generation of broadband squeezing, the in-situ tunability with sign reversal of the nonlinearity in traveling wave structures, with no counterpart in optics to the best of our knowledge, opens exciting experimental possibilities in the general framework of microwave quantum optics, single-photon detection and quantum limited amplification.
We report parametric amplification of a microwave signal in a Kerr medium formed from superconducting qubits. Two mutually coupled flux qubits, embedded in the current antinode of a superconducting coplanar waveguide resonator, are used as a nonlinear element. Shared Josephson junctions provide the qubit-resonator coupling, resulting in a device with a tunable Kerr constant (up to 3 × 10−3) and a measured gain of about 20 dB. This arrangement represents a unit cell which can be straightforwardly extended to a quasi one-dimensional quantum metamaterial with large tunable Kerr nonlinearity, providing a basis for implementation of wide-band travelling 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 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.