We describe how the transient behavior of a tuned and matched resonator circuit and a ringdown suppression pulse may be integrated into an optimal control theory (OCT) pulse-design algorithm to derive control sequences with limited ringdown that perform a desired quantum operation in the presence of resonator distortions of the ideal waveform. Inclusion of ringdown suppression in numerical pulse optimizations significantly reduces spectrometer deadtime when using high quality factor (high-Q) resonators, leading to increased signal-to-noise ratio (SNR) and sensitivity of inductive measurements. To demonstrate the method, we experimentally measure the free-induction decay of an inhomogeneously broadened solid-state free radical spin system at high Q. The measurement is enabled by using a numerically optimized bandwidth-limited OCT pulse, including ringdown suppression, robust to variations in static and microwave field strengths. We also discuss the applications of pulse design in high-Q resonators to universal control of anisotropic-hyperfine coupled electron-nuclear spin systems via electron-only modulation even when the bandwidth of the resonator is significantly smaller than the hyperfine coupling strength. These results demonstrate how limitations imposed by linear response theory may be vastly exceeded when using a sufficiently accurate system model to optimize pulses of high complexity.
We present a simple, high-duty-cycle, cavity-enhanced optical absorption measurement technique based on delay-limited Pound-Drever-Hall (PDH) sideband locking. The chosen circuit naturally provides realtime readout of the amplitude quadrature of the PDH error signal, which can be mapped onto the cavity’s internal loss rate while using the phase quadrature to lock sideband frequency to the cavity mode. Our proofof-concept device comprises a 5-cm-long Fabry-Perot cavity with a 450 kHz bandwidth (finesse 6800, 350 ns power ringdown), and a feedback bandwidth of several MHz, limited primarily by the group delay of our electronics. This technique could readily be applied to other optical resonators such as fiber cavities, with potential applications in radiation dosimetry.
We study measurement-based feedback control of a damped harmonic oscillator, motivated by optomechanical and interferometric position measurements, in which feedback is synthesized from a displacement measurement. For a band-limited derivative controller, the loop shapes the mechanical susceptibility and reinjects measurement noise, creating a tradeoff between stabilization and noise amplification. We present a compact classical formulation that isolates this tradeoff in the closed-loop displacement spectrum and identifies the parameters governing resonance suppression versus noise-driven actuation. We then extend the same topology to a quantum-limited position detector, enforcing the imprecision-backaction constraint and introducing finite measurement bandwidth that regularizes high-frequency noise reinjection and adds phase lag in the feedback path. In the high-
Q regime we obtain an analytic design rule for the optimal feedback gain at fixed controller and measurement bandwidths and compare it with full-spectrum calculations. The comparison shows that a high mechanical quality factor alone does not guarantee quantitative agreement: the accuracy of the near-resonant approximation depends strongly on the controller and measurement bandwidths. Because finite measurement bandwidth changes both the magnitude and phase of the feedback loop, the analysis separates the near-resonant damping contribution from imprecision-noise reinjection and shows that positive near-resonant feedback damping requires the product of the controller cutoff and measurement bandwidth to exceed the square of the mechanical resonance frequency. Finally, we present a dimensionless map of the gain-optimized high-
Q occupation and compare its predictions with full-spectrum optimization. All analytical gains evaluated in this map satisfy the full closed-loop stability criterion for these parameters.