Fig. 4: Characterization of fully-locked comb stability and low-noise microwave generation.
From: Frequency microcomb stabilization via dual-microwave control
a Optical beat frequency between the pump and the stabilized fiber frequency comb (FFC). With both the frep and ξ phase-locked loops engaged, the artificially introduced pump frequency perturbation (red curve) is suppressed and the optical beat frequency remains constant (black curve). The inset plots the corresponding power spectral densities, showing a more than 20 dB pump frequency noise suppression by the stabilization loops. b Free-running comb Allan Deviation (AD) is plotted with black hexagons. The orange and brown circles plot the AD of the pump and ith comb line, respectively, when stabilized with slow feedback to the preamp (yellow path in Fig. 2a). No apparent difference is observed between the ADs of the two comb lines 43 nm apart, indicating a good coherence transfer across the microcomb. Our measured values are close to the local oscillator AD (gray pentagons) used to stabilize frep. For longer gate times, ADs show a characteristic linear dependence on the gate time, attributed to the uncompensated ambient temperature drift. To mitigate this, improved environmental isolation and partial compensation of ambient temperature drift (via green path in Fig. 2a) are implemented and AD of stabilized pump with is plotted in blue squares. The AD is improved to 2 × 10−11 at 20-s gate time, and slope of AD increase is reduced from τ to τ0.23. The shaded region on the right marks the point where slow thermal drift degrades the lock performance. c The setup schematic to generate low-noise microwaves. The pump laser is directly locked to an optical reference, in this case, a fully stabilized FFC referenced to an ultrastable cavity. Subsequently the offset ξ is also locked via feedback to pump power (through the action of the polarization rotator and PBS). The above-mentioned loops indirectly lock frep due to suppression of both pump frequency noise and power fluctuations. Slow feedback is sent to the temperature of the chip mount via a TEC to partially suppress ambient thermal drift. d frep is plotted in the black bars and ξ is plotted in blue. Both frep and ξ are strongly correlated with pump power, with measured correlation greater than 0.997. The absolute and frequency sensitivity to pump power are, respectively, ≈15 and ≈6,700 times larger for ξ than frep. e Locking of both ξ and pump frequency allows for suppression of frep noise (also see Supplementary Note VII). Here, the phase noise of the locked ξ (at 40 MHz) is plotted in black and the measured frep, after engaging both feedback loops (and carried down to 40 MHz), is plotted in blue. We observe a 62 dB suppression of noise at high offset frequencies matching well with our expectations, in the unshaded region to the right; however, at lightly shaded region in the center uncompensated 1/f2 thermal noise (plotted in the dashed red line) begins to dominate and eventually surpasses the locked signal in the shaded region on the left. We can mitigate the effect of this thermal noise via better environmental isolation or passive cavity temperature feedback.
