Frequency Comb Generation in Superconducting Resonators

We have generated frequency combs spanning 0.5 to 20 GHz in superconducting $\lambda /2$ resonators at $T=3\mathrm{K}$. 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.

Figure 1

Photograph of superconducting frequency comb chip. The 25 cm long, $\lambda /2$ resonator is made in a coplanar waveguide (CPW) geometry with input (output) port at top left (bottom right). The CPW has a $2\mu \mathrm{m}$ wide center strip and $2\mu \mathrm{m}$ wide gap and is coupled to ports by interdigitated capacitors. The device is made from NbTiN (Au color) on a $2\mathrm{cm}\times 2\mathrm{cm}$ intrinsic Si ($>20\mathrm{k}\mathrm{\Omega }$) substrate.

Figure 2

Panel (a) depicts model circuit while (b) shows sideband spectrum predicted by second-order perturbation theory. Illustrated are fundamental $f_0$ and pump $f_P$ frequencies, as well as initially generated sideband frequencies, spaced $2f_0$ apart, as dictated by the selection rule.

Figure 3

Evolution of emission spectrum as difference, $\mathrm{\Delta }F=f_P-f_{\text{crit}}$, between pump frequency $f_P$ and critical bifurcation frequency, $f_{\text{crit}}=1254.7\mathrm{MHz}$, is decreased. The pump is close to the $N=21$ multiple of the resonator fundamental, $f_0$. Sample is held at $T=3\mathrm{K}$, with pump power of feedline held constant at $-28\mathrm{dBm}$. Traces are offset vertically for clarity. Signal has been amplified by 30 dB. (Finer detail as $\mathrm{\Delta }F\to 0$ may be found in successive frames of the video of the Supplemental Material [22], where each frame is equivalent to a trace of above stack plot.)

Figure 4

Time domain response of 60 MHz nonlinear resonator driven above the 147th harmonic, at 8820 MHz. Movies depicting the evolution of the above time series, as well as the corresponding frequency response, with decreasing detuning, are included as video in the Supplemental Material [22].