Robust Quantum Control for Bragg Pulse Design in Atom Interferometry

TL;DR

This work tackles the challenge of designing high-fidelity, robust Bragg pulses for atom interferometry by marrying robust quantum control with a Legendre-polynomial spectral representation of parameter variability. The authors develop a two-stage, minimum-energy optimization that first achieves near-perfect state transfer and then minimizes pulse energy while preserving fidelity, using adaptive linearization and a quadratic programming framework with explicit control constraints. They demonstrate unprecedented momentum-transfer capabilities up to $|\\pm 40\\hbar k\\rangle$ with fidelity robust to $10\\%-40\\%$ variations in initial momentum dispersion and intensity, validated by laboratory experiments in a guided $^{87}$Rb system. The Legendre expansion outperforms direct sampling in both robustness and computational efficiency, and the approach is accompanied by public code, highlighting practical relevance for deployable quantum sensing and interferometry.

Abstract

We formulate a robust optimal control algorithm to synthesize minimum energy pulses that can transfer a cold atom system into various momentum states. The algorithm uses adaptive linearization of the evolution operator and sequential quadratic programming to iterate the control towards a minimum energy pulse that achieves optimal target state fidelity. Robustness to parameter variation is achieved using Legendre polynomial approximation over the domain of variation. The method is applied to optimize the Bragg beamsplitting operation in ultra-cold atom interferometry. Even in the presence of 10-40% variability in the initial momentum dispersion of the atomic cloud and the intensity of the optical pulse, the algorithm reliably converges to a control protocol that robustly achieves unprecedented momentum levels with high fidelity for a single-frequency multi-photon Bragg diffraction scheme (e.g. $|\pm 40\hbar k\rangle$). We show the advantages of our method by comparison to stochastic optimization using sampled parameter values, provide detailed sensitivity analyses, and performance of the designed pulses is verified in laboratory experiments.

Figures (5)

• Figure 1: Convergence of the iterative algorithm for selected target momenta $|\pm 2n_0 \hbar k\rangle$.
• Figure 2: Pulse intensity and total time integration for momentum states from $|\pm 2 \hbar k\rangle$ to $|\pm 40 \hbar k\rangle$.
• Figure 3: Probability of selected target momenta $|\pm 2n_0 \hbar k\rangle$ corresponding to IIR filtered control pulses defined by the cutoff frequency in terms of the sampling frequency $f_s$.
• Figure 4: Beamsplitting from $|0\hbar k\rangle$ to $|\pm 2n_0 \hbar k\rangle$, for $n_0=1,\;5,\;10$. Control and probability refer to the quantities $u/\omega_r$ and $||+2n \hbar k\rangle|^2+||-2n \hbar k\rangle|^2$. Error refers to the evaluation of $1-||+2n_0 \hbar k\rangle|^2-||-2n_0 \hbar k\rangle|^2$ at $t= T$, i.e., the probability that the momentum state is in energy levels other than the target state $2n_0$.
• Figure 5: Diffraction from $|0\hbar k\rangle$ into momentum states $|\pm 2 \hbar k\rangle$, $|\pm 10 \hbar k\rangle$, and $|\pm 20 \hbar k\rangle$.