Kerr-Microresonator Soliton Frequency Combs at Cryogenic Temperatures

We investigate the accessibility and projected low-noise performance of single-soliton Kerr frequency combs in silicon nitride microresonators enabled by operating at cryogenic temperatures as low as 7 K. The resulting 2-orders-of-magnitude reduction in the thermorefractive coefficient relative to room temperature enables direct access to single bright Kerr soliton states through adiabatic frequency tuning of the pump laser while remaining in thermal equilibrium. Our experimental results, supported by theoretical modeling, show that single solitons are easily accessible at temperatures below 60 K for the microresonator device under study. We further demonstrate that the cryogenic temperature primarily impacts the thermorefractive coefficient. Other parameters critical to the generation of solitons, such as quality factor, dispersion, and effective nonlinearity, are unaltered. Finally, we discuss the potential improvement in thermorefractive noise resulting from cryogenic operation. The results of this study open up new directions in advancing chip-scale frequency-comb optical clocks and metrology at cryogenic temperatures.

Figure 1

(a) A schematic of the microring studied, where a single-frequency continuous-wave laser at the input results in a soliton microcomb at the output due to the ${\chi }^{(3)}$ nonlinearity of the resonator: RW, ring width; $G=\mathrm{gap}$; $R$, radius; $L_c$, coupling length. (b) The thermal accessibility of soliton states. The black line shows the LLE-simulated comb power (i.e., the integrated power in the comb with the pump line filtered out) as a function of the laser-pump-mode detuning, while the red and blue dashed lines represent a range of solutions to the thermorefractive model as the temperature (and hence $\mathrm{\partial }n/\mathrm{\partial }T$) is decreased. The intersection of the thermal model solution and the soliton step of the LLE simulation determines whether that soliton state is thermally stable. MI, modulation instability.

Figure 2

(a) A photograph of the cryostat interior with input and output fiber coupling to the ${\mathrm{Si}}_3{\mathrm{N}}_4$ chip. The coupling to the ring is made with two waveguides to extract different portions of the comb spectrum and they are combined before the output port through an on-chip dichroic element. The chip sits on a copper mount affixed to a feedback-controlled heater stage that enables the temperature to be varied from 6 K to 90 K without adjusting the cooling power to the cryostat. The inset is a scanning-electron-microscopy image of an individual microring resonator. (b) The experimental setup for soliton generation at cryogenic temperature: OSA, optical spectrum analyzer; PD, photodiode; PC, polarization controller; EDFA, erbium-doped fiber amplifier.

Figure 3

(a) The spectral shift of the microring resonator pump mode with temperature. The dashed line corresponds to the exponential fit used to retrieve $\mathrm{\partial }n/\mathrm{\partial }T$. The inset represents the measured resonance profile, a doublet that is fitted using the model from Ref. [24]. (b) Variation of the thermorefractive coefficient of the system with temperature. The dashed line corresponds to the exponential trend. The uncertainties are within the size of the markers.

Figure 4

(a) The linear transmission of the ring resonator at 60 K. The crosses mark the first-order mode family of interest for broad soliton comb generation. (b) The integrated dispersion obtained from the linear transmission data such as that in (a) as a function of the mode number and at different temperatures. For the frequency range considered, the dispersion is nearly quadratic. The inset corresponds to the change in the extracted FSR with temperature. The uncertainties are within the size of the markers. (c) The behavior of the intrinsic (blue) and coupling (orange) quality factor with temperature. The error bars represent $95\mathrm{\%}$ confidence intervals from a nonlinear least-squares fit to the data. (d) The threshold power $P_{\mathrm{th}}$ for optical parametric oscillation (OPO) as a function of temperature, where the error bars are one-standard-deviation values due to variation in the fiber insertion loss. The inset corresponds to the optical spectrum of the first OPO side bands obtained at $P_{\mathrm{th}}$.

Figure 5

(a) The measured (blue) and simulated (orange) single-soliton frequency combs obtained at $T\approx$ 7 K with a pump power of 100 mW in the waveguide. The spectrum is acquired using two optical-spectrum analyzers. The noise floor of the instrument for acquiring the lower-frequency section is about 20 dB higher than that which acquires the higher-frequency section. (b) The comb power versus the detuning ${\nu }_0-{\nu }_{\mathrm{pmp}}$ obtained at different temperatures. The black line corresponds to the LLE simulation. (c) The measured soliton step length (blue) versus temperature, compared to theoretical values assuming nominal parameters from the experiment (solid orange line). In addition, we plot a range of theoretical values (dashed orange lines) defined by $\pm 1$ dB variation in the pump power, which represents the observed fluctuation in insertion loss during the experiment.

Figure 6

The calculation of (a) the fractional spectral density of optical-frequency fluctuations $\sqrt{S_{\nu }}/{\nu }_0$ and (b) the ratio of the spectral density of the soliton-comb carrier-envelope offset frequency fluctuations $S_{\mathrm{FCEO}}$ at a given temperature to the value at room temperature. We assume the experimental values of $\mathrm{\partial }{\nu }_0/\mathrm{\partial }T$ from Fig. 3 and other parameters from Ref. [23].