Precise measurement of the resonance frequencies of microwave and optical cavities is a foundational capability across quantum technologies. One of the highest-performance methods currently available is Pound-Drever-Hall (PDH) spectroscopy, which relies on a three-tone interrogation and eliminates sensitivity to path-length fluctuations. However, PDH is known to suffer from systematic offsets due to residual amplitude modulation and demodulation-phase errors. Here we leverage an optimal linear combination of the phases of the three interrogation tones to implement a method for robust cavity metrology which eliminates significant systematic-error sensitivities of PDH. We experimentally demonstrate robust cavity measurements in both the optical and microwave frequency regime, showing insensitivity to sideband imbalance and demodulation phase, as well as demonstrating single-shot readout of a cavity-coupled superconducting qubit.
Precise measurement of the resonance frequencies of microwave and optical cavities is a foundational capability across quantum technologies. One of the highest-performance methods currently available is Pound-Drever-Hall (PDH) spectroscopy, which relies on a three-tone interrogation and eliminates sensitivity to path-length fluctuations. However, PDH is known to suffer from systematic offsets due to residual amplitude modulation and demodulation-phase errors. Here we leverage an optimal linear combination of the phases of the three interrogation tones to implement a method for robust cavity metrology which eliminates significant systematic-error sensitivities of PDH. We experimentally demonstrate robust cavity measurements in both the optical and microwave frequency regime, showing insensitivity to sideband imbalance and demodulation phase, as well as demonstrating single-shot readout of a cavity-coupled superconducting qubit.
We present a cavity-enhanced optical absorption measurement technique based on high-bandwidth Pound-Drever-Hall (PDH) sideband locking, which naturally provides a real-time, resonant amplitude quadrature readout that can be mapped onto the cavity’s internal loss rate. Cavity-enhancement is widely used in the detection of small signals -- an optical cavity traps photons between two highly reflective mirrors, thereby enhancing the effective path length through the absorber [Romanini et al., 2014]. Most of the available techniques, however, probe transmission signals and/or do not provide the stability required for the detection of fast signals.To ensure optimal enhancement of absorption sensitivity, probe light must be locked on resonance with the cavity. PDH locking relies on phase modulation of a laser beam, creating two sidebands on the original carrier frequency [Black, 2001]. Upon reflection from a cavity, this modulated light produces a heterodyne signal (beat note) that can be detected and demodulated. We use the phase quadrature of the beat note to lock the cavity on resonance with one of the sidebands, achieving a locking bandwidth in the MHz range that keeps cavity and probe light resonant for hours [Reinhardt et al., 2017]. Simultaneously, we monitor the amplitude quadrature, which provides a continuous, real-time, heterodyne-amplified readout of the cavity’s internal absorption. Our PDH sideband cavity-enhanced absorption readout technique (SideCAR) ensures high sensitivity without reaching saturation limits in the intracavity medium by keeping a relatively low intracavity power, since only one of the sidebands is allowed to enter the cavity, but the signal is boosted above the detector noise by heterodyne detection (using the carrier as a local oscillator).This thesis presents the theoretical formulation of the sensing technique together with the expressions for the sensitivity limit (ultimately given by the laser quantum noise), and the experimental results from a test cavity setup. Probing a proof-of-concept 5-cm-long Fabry-Perot cavity with a coupled power of 160 uW, we measure an absorption sensitivity of 7*10^(-11) cm^(-1)/sqrt(Hz) at 100 kHz (roughly the cavity bandwidth), a factor of 11 from the shot-noise limit. This technique allows the detection of small, transient signals against absorptive backgrounds with sensitivity close to the shot noise limit using a reflection-based measurement in a fairly simple setup, opening the possibility of developing new microscopic single-port real-world sensors for transients, for example using micron-scale optical fiber cavities
Suppressing high-frequency laser phase noise, particularly at frequencies near and beyond typical feedback bandwidths of a few MHz, is a critical yet challenging task in many advanced applications. Feedforward-based methods generally outperform feedback in high-frequency range, but their performances are more susceptible to perturbations. In this work, we focus on the Pound-Drever-Hall (PDH)-feedforward method we demonstrated recently [Yu-Xin Chao et al., Optica 11(7), 945-950 (2024)] and analyze the factors that affect its long-term stability. By constructing a simple circuit allowing for adaptive control of the feedforward gain in response to power fluctuations of cavity transmission, we demonstrate a robust ≥40 dB suppression of laser phase noise around 2 MHz and a noise suppression bandwidth up to 50 MHz. In comparison, when using normal PDH feedback, robust noise suppression of over 40 dB can only occur for frequencies below tens of kHz in most setups. Our findings may pave the way for general usage of PDH feedforward and allow for simple construction of low-noise lasers for precise quantum controls and precision metrology.
Atom interferometers, as precision gravity sensors, encounter inherent miniaturization challenges due to constraints like interference time and laser pulse intensity. Optical cavities address these limitations through wavefront purification, spatial mode filtering, and resonance-enhanced amplification, significantly enhancing interferometer stability and performance for compact quantum sensing applications. This study develops a fiber-integrated four-mirror cavity locking system based on the Pound-Drever-Hall (PDH) technique combined with modulation transfer spectroscopy (MTS), designed for cavityenhanced Raman resonance control in atom interferometry. The system utilizes a fiber-based electro-optic modulator (EOM) for red-detuned frequency shifting, with MTS stabilization applied to lock the cavity to the +1st-order sideband while maintaining the carrier as the locking beam. A fiber-optic circulator architecture in the PDH feedback loop eliminates environmental disturbances (stray light and vibrations) on dispersion-based error signals. Experimental implementation demonstrates continuous cavity locking for over 2 hours with transmitted power fluctuations below 2%. Validation using pulsed Raman beams (400μs duration) confirms the scheme's compatibility with cavity-enhanced atom interferometry, establishing a methodological framework for multi-beam quantum interference experiments in optical cavity.
As opposed to feedback, feedforward methods bring new opportunities to suppress high-frequency laser phase noise, but their performance is more susceptible to environmental perturbations, hindering broad application. Tackling the key factors for long-term stability of feedforward based on Pound-Drever-Hall (PDH) detection, the authors construct a compact circuit to adaptively control feedforward gain in response to power variations of cavity transmission. This design achieves robust suppression beyond 40 dB for megahertz noise frequencies. The compact scheme may promote the general use of reliable PDH feedforward in simple, inexpensive lasers for precision quantum control and metrology.
\nWe 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.\n
We present a simple, continuous, cavity-enhanced optical absorption measurement technique based on high-bandwidth Pound-Drever-Hall (PDH) sideband locking. The technique provides a resonant amplitude quadrature readout that can be mapped onto the cavity's internal loss rate, and is naturally compatible with weak probe beams. With a proof-of-concept 5-cm-long Fabry-Perot cavity, we measure an absorption sensitivity of 6.6×10−11cm−1/Hz at 100 kHz (roughly the cavity bandwidth) and ∼10−10cm−1/Hz from 30 kHz to 1 MHz, with 38μW collected from the cavity's circulating power.