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Wavefront curvature and transverse atomic motion in time-resolved atom interferometry: Impact and mitigation

Anonymous, Jeremiah Mitchell, V. Gibson, Ulrich Schneider

Published Jul 2, 2026• 0 citations
Publisher

Abstract

Time-resolved atom interferometry, as employed in applications such as gravitational-wave detection and searches for ultralight dark matter, requires precise control over systematic effects. In this work, we investigate phase noise arising from shot-to-shot fluctuations in the atoms’ transverse motion in the presence of the wavefront curvature of the interferometer beam, and analyze its dependence on the laser-beam geometry in long-baseline, large-momentum-transfer atom interferometers. We use a semiclassical framework to derive analytical expressions for the effective phase perturbation in position-averaged measurements and validate them using Monte Carlo simulations. Applied to 100 m and 1 km atom gradiometers representative of next-generation experiments, the model shows that configurations maximizing pulse efficiency also amplify curvature-induced phase noise, requiring micron-level control of the atom cloud's center-of-mass position and submicron-per-second control of its center-of-mass velocity to achieve sub- 10 − 5 rad phase stability. Alternative beam geometries can suppress this noise by up to 2 orders of magnitude, but at the cost of reduced pulse efficiency. To address this limitation, we propose a mitigation strategy based on position-resolved phase-shift readout, which empirically learns and corrects the wavefront-induced bias from measurable quantities such as the phase-shift gradient and final cloud position. This approach restores high-sensitivity operation in the maximum-pulse-efficiency configuration without detailed beam characterization, providing a practical route toward next-generation, time-resolved atom interferometers operating at the 10 − 5 rad noise level.

DOI
10.17863/cam.131544

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Time-resolved atom interferometry, as employed in applications such as gravitational-wave detection and searches for ultralight dark matter, requires precise control over systematic effects. In this work, we investigate phase noise arising from shot-to-shot fluctuations in the atoms’ transverse motion in the presence of the wavefront curvature of the interferometer beam, and analyze its dependence on the laser-beam geometry in long-baseline, large-momentum-transfer atom interferometers. We use a semiclassical framework to derive analytical expressions for the effective phase perturbation in position-averaged measurements and validate them using Monte Carlo simulations. Applied to 100 m and 1 km atom gradiometers representative of next-generation experiments, the model shows that configurations maximizing pulse efficiency also amplify curvature-induced phase noise, requiring micron-level control of the atom cloud's center-of-mass position and submicron-per-second control of its center-of-mass velocity to achieve sub- 10 − 5 rad phase stability. Alternative beam geometries can suppress this noise by up to 2 orders of magnitude, but at the cost of reduced pulse efficiency. To address this limitation, we propose a mitigation strategy based on position-resolved phase-shift readout, which empirically learns and corrects the wavefront-induced bias from measurable quantities such as the phase-shift gradient and final cloud position. This approach restores high-sensitivity operation in the maximum-pulse-efficiency configuration without detailed beam characterization, providing a practical route toward next-generation, time-resolved atom interferometers operating at the 10 − 5 rad noise level.
Wavefront distortions are a leading source of systematic uncertainty in light-pulse atom interferometry, limiting absolute measurements of gravitational acceleration at the 30 nm/s^{2} level. Here, we demonstrate in situ spatially resolved measurement of the interferometer phase in a Mach-Zehnder atom interferometer as a tool to characterize and correct wavefront bias. By introducing controllable curvature of the Raman light using an adjustable collimation retro-reflector, we show that the bias due to parabolic wavefront curvature can be measured with 1 mrad uncertainty and that finite-size corrections impact the measured phase curvature. This measurement process could be adopted in optimized atom interferometer gravimeters to reduce wavefront bias uncertainty below the nm/s^{2} level.
Light-pulse atom interferometers serve as tools for high-precision metrology and are targeting measurements of relativistic effects. This development is facilitated by extended interrogation times and large-momentum-transfer techniques generating quantum superpositions of both interferometer arms on large distances. Due to the finite speed of light, diffracting light pulses cannot interact simultaneously with both arms, inducing phase perturbations that compromise the accuracy of the sensor -- an effect that becomes progressively important as spatial separations increase. For a consistent framework, we develop a theory for finite-speed-of-light effects in atom interferometers alongside with other relativistic effects such as the mass defect. Our analysis shows that their magnitude depends crucially on the diffraction mechanism and the specific interferometer geometry. We demonstrate that the velocity of the atomic cloud at the mirror pulse of a Mach-Zehnder interferometer is less critical than the precise tuning of the lasers for resonant diffraction. Finally, we propose an experiment to test our predictions based on recoilless transitions and discuss mitigation strategies to reduce the bias in gravimetric applications.
One of the main residual limitations of inertial sensors based on atom interferometry stems from laser beam distortions, which cause parasitic phase shifts and non-homogeneous matter-light couplings. Here we present numerical simulations, accompanied by analytical calculations, which quantify the impact of these effects in a cold atom gradiometer. We demonstrate that the propagation of interferometric laser beam aberrations, combined with initial asymmetry and significant time-of-flight expansion of the the two atomic sources, limit the common-mode rejection of phase noise in a differential configuration. The resulting deviations in gravitational acceleration and its gradient are within reach of current experimental devices. Our study allows us to evaluate the surface quality requirements for retroreflective optics in cold-atom gradiometers of various baselines, and can be extended to other sensors based on different interferometer geometries.
Abstract Light pulse atom interferometers (AIFs) are exquisite quantum probes of spatial inhomogeneity and gravitational curvature. Moreover, detailed measurement and calibration are necessary prerequisites for very-long-baseline atom interferometry (VLBAI). Here we provide a theoretical analysis of the phase resulting in a complex gravitational environment and introduce a novel interferometer geometry which singles out the phase shift proportional to the curvature of the gravitational potential. The scale factor depends only on well controlled quantities, namely the photon wave number, the interferometer time and the atomic recoil, which allows the curvature to be accurately inferred from a measured phase. As a case study, we numerically simulate such a gradiometric interferometer in the context of the Hannover VLBAI facility and prove the robustness of the phase shift in gravitational fields with complex spatial dependence. We define an estimator of the gravitational curvature for non-trivial gravitational fields and calculate the trade-off between signal strength and estimation accuracy with regard to spatial resolution. As a perspective, we discuss the case of a time-dependent gravitational field and corresponding measurement strategies.
This report presents the results of the 2012-2013 NASA Institute for Advanced Concepts (NIAC) Phase 1 Atom Interferometry for Detection of Gravitational Waves project. The origin of this GW (Gravitational Wave) detection concept using atoms can be traced to theoretical work that first appeared in 2008 and also to a satellite mission-focused followup study that was done in 2011. The goal of the current project was to explore both theoretical and technical issues surrounding the implementation of this idea, as well as to begin performing proof-of-concept experiments to validate critical aspects of the proposal.The top level trade space for the detector design is driven by the strategy employed to mitigate laser frequency noise, which, if uncontrolled, can mask GW signatures. One of the advantages of the atom interferometric approach is the possibility of single baseline detection (Fig. 1.1), even in the presence of laser noise. This is enabled by the differential measurement between the two ensembles of atoms, which can result in substantial laser noise suppression. The details of this suppression depend on the atomic physics techniques used to implement the atom interferometry. Specifically, we considered the effect on noise suppression that results from using traditional two-photon Raman transitions (with alkali atoms) and also single-photon transitions (with alkaline earth-like atoms).The interferometers shown in Fig 1.1(b) take advantage of single-photon transitions (as opposed to traditional Raman transitions) because using light pulses from one direction at a time allows for near perfect common-mode cancellation of laser phase noise, even for long baselines. This calls for the use of atomic transitions with an (ideally large) optical energy level difference with a long (greater than 1 second) lifetime, such as high-transitions routinely used for optical atomic clocks in species like Sr, Ca and Yb. Notably, large momentum transfer (LMT) atom optics - and the sensitivity enhancement they confer – can still be realized by simply adding additional pairs of alternating pulses to each beam splitter process. Section 3 reports on the theoretical work we performed to justify this GW detection protocol using single-photon transitions. This approach represents a new method for GW detection using atoms that is distinct from the original proposal from 2008. At the system level, we evaluated three architectures, each of which implements a different solution to the laser frequency noise issue. The first two designs are based on two-photon Raman transitions with Rb atoms. One of these is a three-satellite, multiple baseline design while the other is a two-satellite, single baseline design. The third proposal is a two-satellite, single baseline design that uses single-photon transitions with Sr atoms. These three architectures are described in more detail in Section 2. There are a number of known technical issues that we have started to address using ground-based experiments. These issues include atom technology development needs such as, for example, lower ensemble temperature requirements and large momentum transfer (LMT) atom optics. To this end, we have built a 10-meter scale atom drop tower, where we can perform proof-of-principle demonstrations of the proposed AGIS detector in an environment that permits more than 2.5 seconds of free-fall time. This facility allows for demonstration of atom interferometry with long interrogation time (seconds) and large atom wavepacket
Matter-wave interferometry has enabled high precision measurements of inertial forces such as gravity and the Coriolis force. This is facilitated by the long-term stability of the physical properties of atoms and lasers. Recent experiments have demonstrated the operation of portable, robust sensors using atom interferometry. This has potential uses in the context of inertial navigation, where conventional devices suffer from long-term drifts due to bias instability. Furthermore, determining position via dead reckoning requires minimisation of dead time between measurements. This thesis presents the development of an atom interferometer for measuring horizontal accelerations. In this configuration, gravity induces motion across the laser wavefront, which constrains the tolerable level of wavefront distortions. Effective control of the experiment allows the interferometer to be operated at a rate of 4 Hz. A cold ensemble of 10^6 atoms in the same internal state is prepared in 150 ms. The interferometer operates using a sequence of three laser pulses separated by T= 25 ms to achieve sensitivity to horizontal accelerations. Combining this with a classical accelerometer provides a method of correcting for vibration-induced noise, as well as determining the interferometer fringe order. After an integration time of 40 s, the sensitivity to horizontal accelerations is better than 3^-6 m s^-2. Effects which limit this sensitivity are discussed.