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Bulletin of the American Physical Society

Frequency Comb Generation in Superconducting Resonators

David P. Pappas, Robert P. Erickson, Michael R. Vissers, Hsiang-Sheng Ku

Published Mar 3, 2015• 0 citations
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Cryogenic microwave frequency combs based on quantum paraelectric superconducting resonators

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A frequency comb, known for its precision as an “optical ruler,” features an evenly spaced spectral pattern. While these combs are vital in integrated photonics, their microwave counterparts are now highly sought in cryogenic quantum technologies, including semiconducting and superconducting qubits as well as quantum electrical metrology. However, microwave combs are still largely underexplored. Existing studies mostly rely on complex, high-power optical systems incompatible with the low-power, cryogenic on-chip architecture. In this manuscript, we present an all-electrical, on-chip, cryogenic microwave frequency comb on strontium titanate (SrTiO3), exploiting its Pockels-like effect in its quantum paraelectric phase. Our device utilizes a superconducting microwave cavity to generate the frequency comb via cavity phase modulation enabled by the field-induced effective χ(2) of SrTiO3. The ability to continuously vary the dielectric constant of SrTiO3 by the application of an electric field, in its quantum paraelectric phase, makes it possible to control the comb's operating frequency span. The exceptionally high dielectric constant of SrTiO3, > 20 000 at low temperatures, enables an ultra-miniature design and on-chip integration with cryogenic quantum technologies.

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We have generated frequency combs spanning 0.5 to 20 GHz in superconducting λ/2 resonators at T=3 K. Thin films of niobium-titanium nitride enabled this development due to their low loss, high nonlinearity, low frequency dispersion, and high critical temperature. The combs nucleate as sidebands around multiples of the pump frequency. Selection rules for the allowed frequency emission are calculated using perturbation theory, and the measured spectrum is shown to agree with the theory. Sideband spacing is measured to be accurate to 1 part in 10(8). The sidebands coalesce into a continuous comb structure observed to cover at least several frequency octaves.
Frequency combs are useful in a wide range of applications, such as optical metrology and high-precision spectroscopy. We experimentally study a controllable frequency comb generated in a tunable superconducting coplanar-waveguide resonator in the microwave regime. A two-tone drive is applied on one of the resonance modes of the resonator and comb generation is observed around the resonance frequency of the resonator. Both central frequency and teeth density of the comb are precisely controllable, and the teeth spacing can be adjusted from Hz to MHz. Moreover, we show that a few hundreds of sidebands can be generated using a sufficiently strong drive power and the weakest drive power needed to generate the comb can be reduced to approach the quantum limit. These experimental results can be qualitatively explained via theoretical analysis.
Coplanar waveguide resonators are central to the thriving field of circuit quantum electrodynamics. Recently, we have demonstrated the generation of a broadband microwave-frequency comb spectrum using a superconducting quantum interference device (SQUID) driven by a time-dependent magnetic field. Here, the frequency comb is used to spectroscopically probe a bank of coplanar microwave resonators, inductively coupled to a common transmission line, a standard circuit with a variety of applications. We compare the resonator line shape obtained from signals synthesized at room temperature using conventional electronics with the radiation produced in the cryogenic environment by our source, showing substantial equivalence in the estimation of the resonator quality factors. To measure non-uniformly spaced resonant frequencies, we drive the generator with a bi-chromatic tone to generate intermodulation products. Such a dense frequency comb spectrum enables simultaneous addressing of a few resonators via frequency multiplexing. Finally, we discuss the criteria for achieving effective spectroscopic coverage of a given frequency bandwidth.
A frequency comb, known for its precision as an “optical ruler,” features an evenly spaced spectral pattern. While these combs are vital in integrated photonics, their microwave counterparts are now highly sought in cryogenic quantum technologies, including semiconducting and superconducting qubits as well as quantum electrical metrology. However, microwave combs are still largely underexplored. Existing studies mostly rely on complex, high-power optical systems incompatible with the low-power, cryogenic on-chip architecture. In this manuscript, we present an all-electrical, on-chip, cryogenic microwave frequency comb on strontium titanate (SrTiO3), exploiting its Pockels-like effect in its quantum paraelectric phase. Our device utilizes a superconducting microwave cavity to generate the frequency comb via cavity phase modulation enabled by the field-induced effective χ(2) of SrTiO3. The ability to continuously vary the dielectric constant of SrTiO3 by the application of an electric field, in its quantum paraelectric phase, makes it possible to control the comb's operating frequency span. The exceptionally high dielectric constant of SrTiO3, > 20 000 at low temperatures, enables an ultra-miniature design and on-chip integration with cryogenic quantum technologies.