Compact optical waveform generator with digital feedback

TL;DR

This work tackles the challenge of delivering precise phase- and amplitude-controlled laser pulses on sub-microsecond timescales for quantum technologies, where hardware distortions threaten gate fidelity. The authors present a compact optical waveform generator that combines a double-pass AOM and an optical heterodyne detector within a small breadboard, coupled to a digital feedback loop that estimates the system transfer function and pre-distorts inputs. By employing a truncated Volterra-series model and Levenberg-Marquardt optimization, the system compensates for nonlinear and quadrature distortions, achieving distortion-corrected pulses as short as $180\,\text{ns}$ with a residual error around $10^{-3}$. The approach is demonstrated with in situ pulse shaping and robust hardware design, offering a scalable path toward high-fidelity, time-dependent quantum control in compact, multi-channel architectures.

Abstract

A key requirement for quantum technologies based on atoms, ions, and molecules, is the ability to realize precise phase- and amplitude-controlled quantum operations via coherent laser pulses. However, for generating pulses on the sub-microsecond timescale, the characteristics of the optical and electronic components can introduce unwanted distortions that have a detrimental effect on the fidelity of quantum operations. In this paper, we present a compact arbitrary waveform generator that integrates a double-pass acousto-optic modulator for user-specified laser amplitude and phase modulations. Additionally, the module integrates an optical heterodyne detector to extract the precise laser pulse shape in real-time. The measured pulse shape is then fed into a digital feedback loop used to estimate the complex-valued transfer function and pre-distorted input pulses. We demonstrate the performance by generating shaped laser pulses suitable for realizing quantum logic gates with durations down to 180\,ns, requiring only a small number of feedback iterations.

Figures (6)

• Figure 1: Compact optical modulator and laser pulse correction feedback loop. (a) The compact optical modulator contains three parts, AOM double pass (blue), heterodyne detection (brown), and spatial filter (yellow), (b) the beam splitter (BS) combines the two beams for generating the beat note signal, from which the temporal profile of laser's phase and amplitude are extracted. The extracted laser phase and amplitude are measured and subsequently sent to the control computer. An iterative algorithm is used to estimate the system's impulse response function. This estimated function is then used to generate a pre-distorted pulse, enabling simultaneous compensation for both amplitude and phase distortions in the laser.
• Figure 2: The phase distortion induced from AOM. (a) To generate fast laser pulses with short rise time by AOM, we focus a laser beam with central wavevector $k_0$ traveling through AOM. The diffraction light with wavevector $k_0'$ results from interaction between incoming laser beam and the acoustic wave which is modulated by $P(t)$ with wavenumber $q$ driving AOM crystal, $k_1$ and $k_2$ represent the range of wavevectors present in the focused Gaussian beam due to its angular spectrum, while $k_3$ and $k_4$ are the corresponding range of wavevectors in the diffracted beam that satisfy the tolerance of AOM Bragg condition. The phase of the laser is extracted from the cases of pure AOM amplitude modulation, and the corresponding analytical simulation based on Eq. \ref{['eq:quadraturephase']} is shown in (b).
• Figure 3: The uncorrected and corrected amplitude and phase of the laser pulse shape. In the upper row of (a), we show the uncorrected optimal two-qubit gate pulse from Ref. jandura2022time with a 180 ns pulse duration. The slight dip observed at the peak of the amplitude envelope coincides with the moment where the phase gradient is largest likely exceeding the bandwidth of the optical AWG. The lower row of (a) shows the corrected laser amplitude and phase respectively. In (b), we show both the corrected (upper row) and uncorrected (lower row) 1$\mu s$ Gaussian pulse (pure amplitude modulation) used to implement the STIRAP process. The imperfect correction presumably comes from the shot-to-shot variations in the experiment.
• Figure 4: Offline iterations algorithm for pulse correction
• Figure 5: Comparison of iterative closed-loop correction performance: (a) transfer function-based and (b) transfer function-free method for 180 ns and 500 ns pulse durations with identical laser pulse envelope shapes (see Fig. \ref{['fig:experimental_result']}(a)). The transfer function-free method achieves convergence in under four iterations for the 500 ns pulse.