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arXiv:2505.23921 · AVS Quantum Science

Diffraction-phase-free Bragg atom interferometry

V. J. Martínez-Lahuerta, Jan-Niclas Kirsten-Siemß, Klemens Hammerer, Naceur Gaaloul

Published Mar 1, 2026• 1 citation
arXivHTMLPDF

Abstract

Bragg diffraction of matter waves is an established technique used in the most accurate quantum sensors. It is also the method of choice to operate large-momentum-transfer, high-sensitivity atom interferometers. It suffers, however, from an intrinsic multi-path character. Optimal control theory (OCT) has recently led to an improved robustness of atom interferometers to a range of challenging environmental effects such as vibrations or platform accelerations. In this theoretical work, we apply OCT protocols to control the Bragg diffraction phase shifts, thereby enhancing the metrological accuracy of the interferometer. We show a minimization of the diffraction phase for realistic conditions of finite temperature of the incoming wavepacket in a multi-path, high-order Bragg interferometer in a Mach–Zehnder configuration. We study input states with different momentum widths and find that our approach mitigates diffraction phases below the microradian level in the case of 1% of the photon recoil, thereby eliminating one of the leading systematic effects in atom interferometry.

DOI
10.1116/5.0307499

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•Jan 1, 2016•2 citations
Bragg diffraction of matter waves is an established technique used in the most accurate quantum sensors. It is also the method of choice to operate large-momentum-transfer, high-sensitivity atom interferometers. It suffers, however, from an intrinsic multi-path character. Optimal control theory (OCT) has recently led to an improved robustness of atom interferometers to a range of challenging environmental effects such as vibrations or platform accelerations. In this theoretical work, we apply OCT protocols to control the Bragg diffraction phase shifts, thereby enhancing the metrological accuracy of the interferometer. We show a minimization of the diffraction phase for realistic conditions of finite temperature of the incoming wavepacket in a multi-path, high-order Bragg interferometer in a Mach–Zehnder configuration. We study input states with different momentum widths and find that our approach mitigates diffraction phases below the microradian level in the case of 1% of the photon recoil, thereby eliminating one of the leading systematic effects in atom interferometry.
Abstract Multi-photon Bragg diffraction is a powerful method for fast, coherent momentum transfer of atom waves. However, laser noise, Doppler detunings, and cloud expansion limit its efficiency in large momentum transfer (LMT) pulse sequences. We present simulation studies of robust Bragg pulses developed through numerical quantum optimal control. Optimized pulse performance under noise and cloud inhomogeneities is analyzed and compared to analogous Gaussian and adiabatic rapid passage pulses in simulated LMT Mach–Zehnder interferometry sequences. The optimized pulses maintain robust population transfer and phase response over a broader range of noise, resulting in superior contrast in LMT sequences with thermal atom clouds and intensity inhomogeneities. Large optimized LMT sequences use lower pulse area than Gaussian pulses, making them less susceptible to spontaneous emission loss. The optimized sequences maintain over five times better contrast with tens of ℏ k momentum separation and offer more improvement with greater LMT. Such pulses could allow operation of Bragg atom interferometers with unprecedented sensitivity, improved contrast, and hotter atom sources.
We propose high-contrast Mach–Zehnder atom interferometers based on double Bragg diffraction (DBD) operating under external acceleration. To mitigate differential Doppler shifts and experimental imperfections, we introduce a tri-frequency laser scheme with dynamic detuning control. We evaluate four detuning-control strategies—conventional DBD, constant detuning, linear detuning sweep (DS-DBD), and a hybrid protocol combining detuning sweep with optimal control theory (OCT)—using exact numerical simulations and a five-level S-matrix model. The OCT strategy provides the highest robustness, maintaining contrast above 95% under realistic conditions, while the DS-DBD strategy sustains contrast above 90% for well-collimated Bose–Einstein condensates. These results offer practical pathways to high-contrast, large-momentum-transfer DBD-based interferometers for precision quantum sensing and fundamental physics tests.
Spin squeezing in atomic ensembles enables atom interferometry with sensitivities below the shot-noise limit, but the associated entanglement is highly susceptible to loss, making imperfections in atom optics a central limitation. Bragg diffraction is an established technique for driving transitions between atomic momentum states and enables large-momentum transfer through higher-order diffraction while preserving the internal state. However, it is intrinsically limited by two competing mechanisms: Short light pulses induce parasitic diffraction into off-resonant orders beyond an effective two-level description, while long pulses face velocity selectivity. We derive analytical expressions in a second-quantized framework for the atom optics and phase uncertainty of a Mach-Zehnder interferometer including these effects. We demonstrate that sub-shot-noise scaling is achieved only in a regime of intermediate pulse duration. Furthermore, we show that deleterious effects of higher-order diffraction are partially mitigated by optimizing the input quantum state.
Bragg diffraction has been used in atom interferometers because it allows signal enhancement through multiphoton momentum transfer and suppression of systematics by not changing the internal state of atoms. Its multiport nature, however, can lead to parasitic interferometers, allows for intensity-dependent phase shifts in the primary interferometers, and distorts the ellipses used for phase extraction. We study and suppress these unwanted effects. Specifically, phase extraction by ellipse fitting and the resulting systematic phase shifts are calculated by Monte Carlo simulations. Phase shifts arising from the thermal motion of the atoms are controlled by spatial selection of atoms and an appropriate choice of Bragg intensity. In these simulations, we found that Gaussian Bragg pulse shapes yield the smallest systematic shifts. Parasitic interferometers are suppressed by a ``magic'' Bragg pulse duration. The sensitivity of the apparatus was improved by the addition of ac Stark shift compensation, which permits direct experimental study of sub-part-per-billion (ppb) systematics. This upgrade allows for a $310\ensuremath{\hbar}k$ momentum transfer, giving 6.6 Mrad measured in a Ramsey-Bord\'e interferometer.
We present a theoretical model and numerical optimization of double Bragg diffraction, a widely used technique in atom interferometry. We derive an effective two-level-system Hamiltonian based on the Magnus expansion in the so-called quasi-Bragg regime, where most Bragg-pulse atom interferometers operate. Furthermore, we extend the theory to a five-level description to account for Doppler detuning. Using these derived effective Hamiltonians, we investigate the impacts of AC-Stark shift and polarization errors on the double Bragg beam splitter, along with their mitigations through detuning control. Notably, we design a linear detuning sweep that demonstrates robust efficiency exceeding 99.5% against polarization errors up to 8.5%. Moreover, we develop an artificial-intelligence-aided optimal detuning control protocol, showcasing enhanced robustness against both polarization errors and Doppler effects. This protocol achieves an average efficiency of 99.92% for samples with a finite momentum width of 0.05 ℏ k L within an extended polarization error range of up to 10%. Published by the American Physical Society 2024
We experimentally and theoretically study Bragg diffraction as a tool for large-momentum transfer beam splitters in atom interferometry. A theoretical framework is developed to quantify the diffraction phase systematic caused by Bragg diffraction and experiments are performed to confirm these predictions using a Ramsey-Bord\\'e atom interferometer. We then develop methods to systematically cancel and reduce the diffraction phase systematic by carefully selecting Bragg diffraction parameters and utilizing Bloch oscillations. These techniques are then applied to an ongoing precision measurement of $h/m_\\text{Cs}$ for cesium, with the end goal of measuring the fine structure constant alpha\\alphaalpha. We demonstrate a high contrast simultaneous conjugate Ramsey-Bord\\'e interferometer using 5th order Bragg diffraction and 25 common mode Bloch oscillations which achieves 2.5times1062.5\\times 10^62.5times106 radians of phase. We also demonstrate an interferometer with a statistical uncertainty of deltaalpha/alpha=0.25\\delta \\alpha/\\alpha=0.25deltaalpha/alpha=0.25 ppb after 25 hours of integration time that has diffraction phase systematic error of around 1 ppb. Other sources of systematic uncertainty are also thoroughly explored and determined to better than 0.1 ppb. The techniques and theories developed in this thesis will hopefully help enable future precision measurements based on Bragg diffraction.