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Q: Fachverband Quantenoptik und Photonik

Q 58: Quantum Technologies – Color Centers I

Q 58.2: Vortrag

Donnerstag, 5. März 2026, 14:45–15:00, P 5

Exact Computation of Lock-In Amplifier Outputs for Arbitrary Frequency Modulations Using Gauss-Chebyshev Quadrature — •Dennis Lönard, Stefan Johansson, Alena Erlenbach, Jonas Gutsche, and Artur Widera — Department of Physics and State Research Center OPTIMAS, University of Kaiserslautern-Landau, 67663 Kaiserslautern, Germany

Lock-in detection is everywhere, from precision sensing to quantum experiments, but the theoretical treatment of frequency-modulated signals often relies on approximations for small modulation deviations. These approximations are especially prominent in fields like nitrogen-vacancy-center magnetometry and laser spectroscopy, where frequency modulation is used to generate an error signal for locking. These approximations break down precisely in the regime where optimal sensitivity is achieved, leading to inaccurate predictions of optimal modulation depth, lineshape, and ultimately experimental performance.

In this talk, we introduce an approximation-free numerical method based on Gauss-Chebyshev quadrature that computes lock-in amplifier outputs for any modulation waveform, modulation function, signal shape, or deviation. This method is exact, fast, and simple to implement, making it applicable to all lock-in-based experiments.

We demonstrate the approach using nitrogen-vacancy-center magnetometry, which reveals the true optimal modulation parameters beyond the commonly assumed small-modulation regime. An open-source Python package accompanies our work, providing a ready-to-use reference implementation.

Keywords: nitrogen vacancy center; magnetometry; lock in amplification; frequency modulation; laser spectroscopy