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arXiv:2409.08764

Quadrature amplitude modulation for electronic sideband Pound-Drever-Hall laser frequency locking

Tu, J., Alessandro Restelli, K. Weber, Ian B. Spielman, S. L. Rolston, J. V. Porto, S. Subhankar

Published Sep 13, 2024• 1 citation
arXivHTMLPDF

Abstract

The Pound--Drever--Hall (PDH) technique is routinely used to stabilize the frequency of a laser to a reference cavity. Electronic sideband (ESB) locking, a PDH variant, bridges the frequency gap between the discrete cavity resonances and a desired laser frequency. Here we use quadrature amplitude modulation (QAM), a standard technique in digital communications, to generate the high-quality phase-modulated radio-frequency (rf) drive required for ESB locking. We develop a theoretical framework to analyze how in-phase/quadrature-phase (I/Q) impairments distort the ESB error signal and induce frequency offsets relevant to ultranarrow-linewidth lasers. We then design and implement a direct software-defined radio (SDR) on an UltraScale+ RFSoC platform, frequently adopted across modern quantum-computing systems, to digitally compensate QAM I/Q impairments. Using this device, we generate phase-modulated rf signals with a large phase-modulation index of $1.01$ rad and root-mean-square I/Q errors below $0.3\ \%$ over a carrier-frequency range of $350~\mathrm{MHz}$ to $1.75~\mathrm{GHz}$. Finally, we lock a laser to an ultralow expansion (ULE) reference cavity and demonstrate continuous laser-frequency tuning by ramping the carrier frequency while maintaining lock, validating the continuous tunability of our ESB locking instrument.

DOI
10.48550/arxiv.2409.08764

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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
We have proposed an artificial modulation-free Pound-Drever-Hall (PDH) method for laser frequency stabilization and demonstrated it via two-color polarization spectroscopy of Rydberg electromagnetically induced transparency (EIT) resonance in a room-temperature rubidium vapor. Due to the unique error signal profile, the conventional PDH method owns a large capture range in laser frequency locking. Here we manually construct a PDH error signal via a linear combination of polarization spectroscopies of the Rydberg EIT resonances without and with a magnetic field applied. The artificial modulation-free PDH error signal owns a subnatural linewidth dispersion curve as well as a large capture range with which we successfully stabilize the laser to an absolute atomic frequency reference in a long running time, immune to environmental fluctuation and even manmade impulse perturbation. This method can provide an absolute frequency reference based on atomic transition while keeping similar locking ability to provide corrections for frequency fluctuations over a broad bandwidth as the conventional PDH.
A phase-modulated RF current source is applied to an injection-locked diode laser operating at 780 nm. This produces tunable phase-modulated sidebands of the laser suitable for stabilizing the length of an optical transfer cavity using the Pound-Drever-Hall technique. The Pound-Drever-Hall signal is antisymmetric about the lock point, despite the presence of significant diode laser amplitude modulation. The stabilized optical transfer cavity is used to frequency stabilize a 776 nm external cavity diode laser. The stability and tunability of this transfer cavity locked laser is established by observation of the hyperfine components of the Rb875P3/2−5D5/2 transition in a vapor cell.
\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
Traditional locking techniques, such as PDH (Pound-Drever-Hall), HC (Hansh-Couillaud), spatial mode interference technique, offset sideband locking technique, quantum noise locking, etc., have been widely applied to laser frequency stabilization and precision optical interferometry measurement. Here, a new technique, which we call phase-sensitive heterodyne locking (PSHL), is investigated by use of frequency-synthesized light to obtain a phase-sensitive high-frequency photoelectric readout to lock the phase of a squeezed light. Comparing with above techniques, there are several kinds of advantages for PSHL to be advocated. Frequency-synthesized light, which allows arbitrary control of the amplitudes and phases of the modulation sidebands relative to the carrier, is derived by the AOM (acousto-optic modulator), not the EOM (electro-optic modulator). Interferometic signals coming from a balanced heterodyne detector are high-frequency AC photoelectric current which can easily get rid of low-frequency classical noise and lead to reach or break through the shot noise limit. A theoretical derivation of the PSHL error signal and the associated stability of the squeezed and anti-squeezed lock points will be carried out in this work.
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.