Active Cancellation of Servo-Induced Noise on Stabilized Lasers via Feedforward

Lintao Li, William Huie, Neville Chen, Brian DeMarco, and Jacob P. Covey

Phys. Rev. Applied 18, 064005 – Published 2 December 2022

Abstract

Many precision laser applications require active frequency stabilization. However, such stabilization loops operate by pushing noise to frequencies outside their bandwidth, leading to large “servo bumps” that can have deleterious effects for certain applications. The prevailing approach to filtering this noise is to pass the laser through a high-finesse optical cavity, which places constraints on the system design. Here, we propose and demonstrate a different approach where a frequency error signal is derived from a beat note between the laser and the light that passes through the reference cavity. The phase noise derived from this beat note is fed forward to an electro-optic modulator after the laser, carefully accounting for relative delay, for real-time frequency correction. With a hertz-line-width laser, we show $≳ 20 dB$ noise suppression at the peak of the servo bump (approximately $250 kHz$ ) and a noise-suppression bandwidth of approximately $5 MHz$ —well beyond the servo bump. By simulating the Rabi dynamics of a two-level atom with our measured data, we demonstrate substantial improvements to the pulse fidelity over a wide range of Rabi frequencies. Our approach offers a simple and versatile method for obtaining a clean spectrum of a narrow-line-width laser, as required in many emerging applications of cold atoms, and is readily compatible with commercial systems that may even include wavelength conversion.

Received 4 August 2022
Accepted 5 October 2022

DOI:https://doi.org/10.1103/PhysRevApplied.18.064005

Physics Subject Headings (PhySH)

Atomic, optical & lattice clocks Laser-system design Optical coherence Quantum control

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Lintao Li^*, William Huie , Neville Chen, Brian DeMarco, and Jacob P. Covey ^†

Department of Physics, The University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

^*ltli@illinois.edu
^†jcovey@illinois.edu

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Vol. 18, Iss. 6 — December 2022

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Figure 1
An overview of the scheme and the main results. (a) An external-cavity diode laser (ECDL) is locked to a high-finesse optical cavity, which produces “servo bumps” on its spectrum. The light transmitted through the cavity serves as a spectral filter to remove these bumps and the real-time frequency and/or phase deviation of the laser with respect to the cavity-transmitted reference is obtained via a beat note between the two. This signal is then fed forward to an electro-optic modulator (EOM), possibly with an optical-fiber delay line added onto the light, to cancel the frequency deviations. For an ideal cavity with infinitesimal line width, the frequency noise of the laser can be denoted as $Δ ν$ and the single-frequency laser after the cavity is denoted as $ν_{0}$ . (b) Laser spectra with (red and blue) and without (yellow) the feedforward (FF) applied to the laser. The blue (red) data show the case where a 30-m fiber delay line is used (not used) prior to the EOM. The black data show the background noise level, where a fictitious data point at 200 MHz and approximately $35 dB μ V$ due to rf leakage is removed. The inset shows the same data over a wider frequency range. The resolution bandwidth is 100 Hz for all the measurements in this plot. (c) Simulations of driven two-level atoms under the three laser noise cases from (b) using a Rabi frequency of $Ω = 2 π \times 200 kHz$ , which is near the peak of the servo bump.
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Figure 2
A detailed schematic. The clock ECDL is locked to a high-finesse cavity via the standard Pound-Drever-Hall (PDH) technique (not shown). The ECDL light and the cavity-transmitted light are used in two places for our measurements, so each is split with a 50:50 beam splitter (BS). An acousto-optic modulator (AOM) is used to create a 200-MHz beat note between the ECDL and the cavity-transmitted light on photodiode PD1 by interfering them on a BS. This signal is used to cancel frequency deviations from the cavity-transmitted reference through the use of the feedforward phase-correction circuit shown in the teal box. After the AOM, the laser light is sent through an optical-fiber delay line before going to an electro-optic modulator (EOM). The phase signal from the circuit in the teal box is applied to the EOM. Then, this light is interfered with the cavity-transmitted light on a BS and monitored on two PDs. PD2 is used for measurements and represents what would be sent to the atoms. PD3 is used to measure slow fiber-induced frequency drifts, which are then corrected with the fiber-noise-cancellation circuit (green box). This feedback system corrects the frequency applied to the AOM to compensate these slow drifts. The feedback and feedforward work together to maintain the highly coherent peak of the cavity-stabilized laser while simultaneously removing fast noise from the servo bumps.
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Figure 3
The results. (a) Noise-difference spectra $I (f)$ between the case without feedforward engaged and cases with it engaged versus the frequency for several optical-fiber delay lengths $L$ : red, 0 m; purple, 15 m; blue, 30 m. Negative values show reduced noise and positive values show increased noise. The points are measured data while the lines are simulations based on the circuit transfer function (see Appendix pp1). (b) The integrated noise difference $T (f^{'})$ between $f = 0$ and $f^{'}$ for several values of $f^{'} \in {1, \dots, 9} MHz$ versus the optical-fiber delay length $L$ , showing a clear minimum at $L = 30 m$ . (c) The noise spectrum over a narrow range with $L = 30 m$ , with and without feedforward engaged. The main figure shows the case with a slow feedback loop to the AOM to cancel fiber noise, giving a Fourier-limited coherent peak. This indicates that our technique maintains the intrinsic laser line width. The inset shows the case without canceling fiber noise. (d) The laser-intensity noise with and without applying the feedforward, and the background. We see that the feedforward makes the intensity noise higher due to residual-amplitude modulation from the EOM. We show below that this effect is negligible.
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Figure 4
The simulation of a driven two-level atom. The fidelity after a $9 π$ -pulse (the fifth maximum of the population-transfer fraction) of Rabi dynamics with time-dependent drives based on measured noise spectra (see Appendix pp4) is shown for the cases without feedforward (solid yellow) and with feedforward for $L = 0$ and $L = 30 m$ (solid red and blue). We see that the $L = 30 m$ case (blue) has excellent fidelity over the entire bandwidth. The $L = 0 m$ case (red) is improved compared to the no-feedforward case below approximately $1 MHz$ but degrades substantially at higher frequency. The case without feedforward (solid yellow) returns to high fidelity for frequencies well above the servo-bump regime. We also consider the case where intensity noise is included (dashed lines). We see that the intensity noise is negligible compared to the frequency noise.
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Figure 5
The drive circuitry used in the feedforward-noise-canceling setup. (a) The PLL-based phase-detection circuit, which converts the real-time phase deviation of the input beat signal into voltage. (b) The high-bandwidth and high-voltage wide-band amplifier, which amplifies the phase-deviation signal to high voltage that matches the $V_{π}$ of the free-space EOM.
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Figure 6
The circuit simulation of the phase-detection circuit. (a) The Bode plot of the output of the phase-detection circuit versus the phase-variation signal input. (b) The step response of the output of the phase-detection circuit.
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