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arXiv:2206.05145

Practical limits for large-momentum-transfer clock atom interferometers

Mauro Chiarotti, Jonathan N. Tinsley, Satvika Bandarupally, Shamaila Manzoor, Sacco, Michele, Leonardo Salvi, N. Poli

Published Jun 10, 2022• 0 citations
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Abstract

Atom interferometry on optical clock transitions is being pursued for numerous long-baseline experiments both terrestrially and for future space missions. Crucial to meeting these experiments' required sensitivities is the implementation of large momentum transfer ($>$10$^3\hbar k$). Here we show that to sequentially apply such a large momentum via $π$ pulses places stringent requirements on the frequency noise of the interferometry laser, finding that the linewidth is required to be considerably lower than has previously been suggested. This is due to imperfect pulse fidelity in the presence of noise and is apparent even for an atom at rest interacting with resonant light, making this a fundamental constraint on operational fidelity for a given laser and pulse sequence. Within this framework, we further present and analyse two high-power, frequency-stabilised laser sources designed to perform interferometry on the $^1$S$_0$ - $^3$P$_0$ clock transitions of cadmium and strontium, respectively operating at 332 nm and 698 nm.

DOI
10.48550/arxiv.2206.05145

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Atom interferometry on optical clock transitions is being pursued for numerous long-baseline experiments both terrestrially and for future space missions. Crucial to meeting these experiments' required sensitivities is the implementation of large momentum transfer (>>>103ℏk^3\hbar k3ℏk). Here we show that to sequentially apply such a large momentum via πππ pulses places stringent requirements on the frequency noise of the interferometry laser, finding that the linewidth is required to be considerably lower than has previously been suggested. This is due to imperfect pulse fidelity in the presence of noise and is apparent even for an atom at rest interacting with resonant light, making this a fundamental constraint on operational fidelity for a given laser and pulse sequence. Within this framework, we further present and analyse two high-power, frequency-stabilised laser sources designed to perform interferometry on the 1^11S0_00​ - 3^33P0_00​ clock transitions of cadmium and strontium, respectively operating at 332 nm and 698 nm.
Clock atom interferometry is an emerging technique in precision measurement, well suited for sensitivity enhancement through large momentum transfer (LMT). Although next-generation sensors aim for LMT factors beyond 10410^4104, their feasibility has been questioned due to potential impacts of laser frequency noise. We address this concern by analyzing the cumulative fidelity of sequential state inversions, showing that population error scales linearly with pulse number, not quadratically. Parasitic interferometer paths from imperfect pulses contribute negligibly, confirming that laser frequency noise is not a practical limitation.
Strontium clock atom interferometry is a promising new technology, with multiple experiments under development around the world to explore its potential for dark matter and gravitational wave detection. In these detectors, large momentum transfer using sequences of many laser pulses is necessary, and thus high-fidelity pulses are important since small errors become magnified. Quantum optimal control (QOC) is a framework for developing control pulse waveforms that achieve high fidelity and are robust against experimental imperfections. Resonant single-photon transitions using the narrow clock transition of strontium involve significantly different quantum dynamics than more established atom interferometry methods based on far-detuned two-photon Raman or Bragg transitions, which leads to new opportunities and challenges when applying QOC. Here, we study in simulation QOC pulses for strontium clock interferometry and demonstrate their advantage over basic square pulses (primitive pulses) and composite pulses in terms of robustness against multiple noise channels. This could improve the scale of large momentum transfer in Sr clock interferometers, paving the way to achieving these scientific goals.
We report the first realization of large momentum transfer (LMT) clock atom interferometry. Using single-photon interactions on the strontium ^{1}S_{0}-^{3}P_{1} transition, we demonstrate Mach-Zehnder interferometers with state-of-the-art momentum separation of up to 141 ℏk and gradiometers of up to 81 ℏk. Moreover, we circumvent excited state decay limitations and extend the gradiometer duration to 50 times the excited state lifetime. Because of the broad velocity acceptance of the interferometry pulses, all experiments are performed with laser-cooled atoms at a temperature of 3 μK. This work has applications in high-precision inertial sensing and paves the way for LMT-enhanced clock atom interferometry on even narrower transitions, a key ingredient in proposals for gravitational wave detection and dark matter searches.
Abstract Large-scale atom interferometers promise unrivaled strain sensitivity to mid-band gravitational waves, and will probe a new parameter space in the search for ultra-light scalar dark matter. These proposals require gradiometry with kilometer-scale baselines, a momentum separation above 104ℏk between interferometer arms, and optical transitions to long-lived clock states to reach the target sensitivities. Prohibitively high optical power and wavefront flatness requirements have thus far limited the maximum achievable momentum splitting. Here we propose a scheme for optical cavity enhanced atom interferometry, using circulating, spatially resolved pulses, and intracavity frequency modulation to meet these requirements. We present parameters for the realization of 20 kW circulating pulses in a 1 km interferometer enabling 104ℏk splitting on the 698 nm clock transition in 87Sr. This scheme addresses the presently insurmountable laser power requirements and is feasible in the context of a kilometer-scale atom interferometer facility.
This thesis contributes to the debate over the viability of using Bose-condensed sources to improve the sensitivity of atom interferometers. Specifically, we present theoretical investigations into (1) the effect of source momentum width on large momentum transfer (LMT) atom interferometry with Bragg pulses, and (2) the prospect of stabilising a high flux, narrow linewidth, continuously pumped atom laser via measurement-based feedback control of the BEC that forms the lasing mode of the atom laser. To begin, this thesis considers the effect of the atomic source's momentum width on the phase sensitivity of Bragg pulse atom interferometers in the Mach-Zehnder configuration. We show that an atomic cloud's momentum width places a fundamental upper bound on the maximum transfer efficiency of a Bragg mirror pulse, and furthermore limits the phase sensitivity of a Bragg pulse atom interferometer. We quantify these momentum width effects and precisely compute how mirror efficiencies and interferometer phase sensitivities vary as functions of Bragg order and source type. In particular, we show that narrow momentum width Bose-condensed sources give comparable sensitivities to broad momentum width thermal sources, even after incorporating the lower atom flux of Bose-condensed sources. Coupled with other favourable properties of Bose-condensed sources, such as their high tolerance to classical noise due to optical wavefront aberrations and the Coriolis effect, this suggests that LMT Bragg atom interferometry with Bose-condensed sources should yield improved sensitivities over current inertial sensors. Furthermore, our results and methodology allow for the efficient optimisation of Bragg pulses, which will help in the design of LMT Bragg mirrors and beamsplitters for atom-interferometer-based inertial sensors, irrespective of source type. In the second part of this thesis, we investigate the prospect of measurement-based feedback control of a BEC, with the aim of reducing density fluctuations by cooling the condensate to a stable spatial mode. Firstly, we consider the effects of experimental imperfections on the estimation-based feedback control of a weakly-interacting BEC undergoing continuous position measurement. These limitations violate the assumption that the estimator (i.e., filter) accurately models the underlying system, thus requiring a separate analysis of the system and filter dynamics. We show that the control scheme is robust to detector inefficiency, time delay, technical noise and miscalibrated parameters. These results imply that reasonable experimental imperfections do not limit the feasibility of cooling a BEC by continuous measurement and feedback. Secondly, we designed a feedback-control scheme for a trapped condensate, with interatomic interactions of any strength, based on a phase-contrast imaging setup. We derive the filtering equation for the system, and show that it gives a continuous measurement of the condensate's density. A semiclassical analysis of this control scheme shows that feedback-cooling of an interacting BEC is also possible, and that the interatomic interactions actually increase the effectiveness of the control. Therefore, measurement-based feedback control can stabilise the spatial mode of a BEC, which is a requirement for the high flux, narrow linewidth, continuously pumped atom laser sources that could potentially give inertial measurement sensitivities orders of magnitude beyond current state-of-the-art devices.