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Random acceleration noise on Stern-Gerlach interferometry in a harmonic trap

Sneha Narasimha Moorthy1,2,*, Andrew Geraci3, Sougato Bose4, and Anupam Mazumdar5

  • *Contact author: snehahema1029@gmail.com
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APS Open Sci. 1, 000106 – Published 25 August, 2026

DOI: https://doi.org/10.1103/3jjv-vwmv

Abstract

We analyze decoherence in a one-loop Stern-Gerlach-type matter-wave interferometer for a massive nanoparticle embedded with a nitrogen-vacancy-centered nanodiamond evolving under an effective harmonic-oscillator dynamics in a magnetic-field gradient. We assume that the Stern-Gerlach interferometer is subjected to an acceleration a⃗ external to the system, which is at an angle θ0 with respect to the direction of the superposition. For a one-loop interferometer, we quantify dephasing from two noise channels: fluctuations in the external acceleration δa(t) and fluctuations in the tilt angle δθ(t). At the level of the action, we treat these two external sources of noise as stochastic inputs, compute the resulting stochastic phase difference between the interferometer arms, and obtain the dephasing rate Γ. We obtain the transfer function of the interferometer for each of the noise sources. We also show explicit results of constraints on the power spectral density of the noise sources for an interferometer that produces a superposition size of Δx∼1nm of a nanodiamond of mass m=10−15kg by considering white-noise statistics and imposing a coherence target Γτ≤1, where τ≃0.015s. We find Saa≲O(10−11)ms−2Hz−1/2 if we take the external acceleration, a=0ms−2 and θ0=0∘ (along the direction of the superposition), and Sθθ≲O(10−10)radHz−1/2 for a=g=9.81ms−2 and θ0=90∘ (superposition direction is perpendicular to the Earth’s gravity). We have also found an operating regime where the acceleration noise can be minimized by either varying θ0 or a for a fixed set of other experimental parameters.

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APS Open Sci. 1, 000106– Published 25 August, 2026
Vol. 1
  • Received 20 March 2026
  • Revised 10 June 2026
  • Accepted 12 August 2026
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