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Applied Physics Letters

Nonlinear response of a superconducting filter to a wide band excitation

M. I. Salkola

Published Feb 6, 2006• 0 citations
Publisher

Abstract

Passive superconducting filters are inherently nonlinear devices that distort information-bearing signals and give rise to spectral broadening. Wide band signals efficiently probe both the causes and effects of filter nonlinearities. In particular, a coherent pulse may evaluate the power spectrum of a distortion signal and the nonlinear transmission coefficient in a single measurement. The nonlinear response depends on the bandwidth of the probing signal and implicitly on the data rate.

DOI
10.1063/1.2172067

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Passive superconducting filters are inherently nonlinear devices that distort information-bearing signals and give rise to spectral broadening. Wide band signals efficiently probe both the causes and effects of filter nonlinearities. In particular, a coherent pulse may evaluate the power spectrum of a distortion signal and the nonlinear transmission coefficient in a single measurement. The nonlinear response depends on the bandwidth of the probing signal and implicitly on the data rate.
Nonlinearities in passive superconducting filters give rise to gain and intermodulation distortions that can diminish their ability to attenuate large interfering signals. It is shown that the departure from gain linearity depends on the phase of a nonlinear interaction. If the nonlinear interaction arises from the kinetic inductance of a superconducting state, the signal frequency determines whether the superconducting filter exhibits gain expansion or compression. The absence of gain expansion is a signature of the nonlinear interaction that is mainly resistive.
Superconducting filter technology enables highly selective and sensitive base-station receivers for wireless communications. The performance analysis of a superconducting receiver, which is inherently a nonlinear system, is simplified by introducing the concept of an effective frequency response. With this approach, superconducting filters are shown to be ideal for applications that require steep rejection at the edges of a communication band. In contrast, filter nonlinearities decrease the order of the effective frequency response of a cascaded bandpass filter, thus reducing its stop-band rejection.
The authors evaluate the frequency dependence of the nonlinear response in high-temperature superconductor YBa2Cu3O7−x thin films by simultaneously measuring the nonlinear intermodulation products and harmonic generation in broadband superconducting transmission lines at 76K. The frequencies of the two-tone incident signal are set to produce spurious signals from 1to21GHz. They extract a nonlinear term ∣ΔR2+jωΔL2∣ by applying a model of spurious signal generation in superconducting transmission lines to their measurement results. They found that this nonlinear term follows a linear dependence on frequency, indicating a dominant contribution of the nonlinear inductance ΔL2 over the nonlinear resistance ΔR2, (ωΔL2⪢ΔR2), for the superconducting nonlinear response.
We report on a technique for extracting an accurate value of the nonlinear inductance in superconducting transmission lines. This novel technique assesses the frequency dependence of the transmission line's nonlinear response. A wideband nonlinear measurement system was used to simultaneously measure the third-order spurious signals at 2f1- f2,2f2- f1+ f2, 2f2+ f1, 3f1, and 3f2frequencies. Measurements for different values of the fundamental frequencies f1and f2allow us to study the spurious signal generation from 1 to 21 GHz. We demonstrate this technique by measuring several superconducting YBa2Cu3O7-xcoplanar waveguide transmission line geometries patterned in a single chip at 80 K. The results show a linear frequency dependence of the nonlinear response, indicating a dominant contribution of the nonlinear inductance over the nonlinear resistance omegaDeltaL(i) Gt DeltaR(i). The experimentally obtained nonlinear inductances are then used to determine device-independent measures of the linearity of the thin-film material in order to provide the foundation for modeling the nonlinear response of specific devices.
The simplest model of nonlinear response of a superconducting thin film is used for modeling the nonlinear phenomena in a superconducting transmission line and a microstrip resonator. The specified characteristic power of the transmission line is suggested to use as a fitting parameter for numerical description of the microstrip line nonlinearity at microwaves. Quantitative agreement of simulated and experimental data has been obtained for the incident power dependent transmission coefficient of a microstrip line section and a high quality microstrip resonator. Numerical results have also been obtained for the power of the third harmonic radiated from the nonlinear resonator.
Filtering is commonly used in quantum optics to reject noise photons, and also to enable interference between independent photons. However, filtering the joint spectrum of photon pairs can reduce the inherent coincidence probability or loss-independent heralding efficiency. Here we investigate filtering for multiphoton applications based on entanglement and interference (e.g., quantum teleportation). We multiplex C-band entangled photons and C-band classical communications into the same long-distance fibers, which enables scalable low-loss quantum networking but requires filtering of spontaneous Raman scattering noise from classical light. Using tunable-bandwidth filters, low-jitter detectors, and polarization filters, we distribute wavelength-degenerate time-bin entangled photons in the C band (1536.5 nm) over 25 km/25 km standard fibers (50 km) each carrying 10 Gbit/s C-band classical data signals. Narrow filtering enables milliwatt-level C-band power, which exceeds the power achieved by comparable studies by roughly an order of magnitude and could feasibly support terabit per second classical rates. We evaluate how performance depends on pump and filter bandwidths, multipair emission, filter shapes, loss, phase matching, and how quantum information is measured. We find a trade-off between reducing noise impact and increasing single-mode purity, and discuss mitigation methods toward optimal multiphoton applications. Importantly, these results apply to noise in free space and in quantum devices (sources, frequency converters, switches, detectors, etc.) and provide insight into filter-induced degradation of single-photon purity and rates even in noise-free environments.