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Beyond the $T^2$ scaling in acceleration-sensitive atom interferometers

Gordon McDonald, C. C. N. Kuhn, Shayne Bennetts, J. E. Debs, Kyle S. Hardman, J. D. Close, Nicholas P. Robins

Published Nov 9, 2013• 0 citations
OpenAlex

Abstract

A Mach-Zehnder atom interferometer can be used to measure acceleration with a $T^2$ scaling in sensitivity as interrogation time $T$ is increased. We predict and experimentally measure the acceleration-sensitive phase shift of a large-momentum-transfer atom interferometer based upon Bloch oscillations. Using this novel interferometric scheme we demonstrate an improved scaling of sensitivity which will approach $T^3$ in the limit of large interrogation time. This enhanced scaling will allow an increase in bandwidth for acceleration-sensitive atom interferometers.

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Beyond the T2T^2T2 scaling in acceleration-sensitive atom interferometers
A Mach-Zehnder atom interferometer can be used to measure acceleration with a T2T^2T2 scaling in sensitivity as interrogation time TTT is increased. We predict and experimentally measure the acceleration-sensitive phase shift of a large-momentum-transfer atom interferometer based upon Bloch oscillations. Using this novel interferometric scheme we demonstrate an improved scaling of sensitivity which will approach T3T^3T3 in the limit of large interrogation time. This enhanced scaling will allow an increase in bandwidth for acceleration-sensitive atom interferometers.
Atom interferometers have been used to measure acceleration with at best a T2T^2T2 scaling in sensitivity as the interferometer time TTT is increased. This limits the sensitivity to acceleration which is theoretically achievable by these configurations for a given frequency of acceleration. We predict and experimentally measure the acceleration-sensitive phase shift of a large-momentum-transfer atom interferometer based upon Bloch oscillations. Using this novel interferometric scheme we demonstrate an improved scaling of sensitivity which will scale as T3T^3T3. This enhanced scaling will allow an increase in achievable sensitivity for any given frequency of an oscillatory acceleration signal, which will be of particular use for inertial and navigational sensors, and proposed gravitational wave detectors. A straight forward extension should allow a T4T^4T4 scaling in acceleration sensitivity.
We demonstrate phase sensitivity in a horizontally guided, acceleration-sensitive atom interferometer with a momentum separation of $80\ensuremath{\hbar}k$ between its arms. A fringe visibility of 7% is observed. Our coherent pulse sequence accelerates the cold cloud in an optical waveguide, an inherently scalable route to large momentum separation and high sensitivity. We maintain coherence at high momentum separation due to both the transverse confinement provided by the guide and our use of optical $\ensuremath{\delta}$-kick cooling on our cold-atom cloud. We also construct a horizontal interferometric gradiometer to measure the longitudinal curvature of our optical waveguide.
To increase the measured phase of an atom interferometer and improve its sensitivity, researchers attempt to increase the enclosed space-time area using two methods: creating larger separations between the interferometer arms and having longer evolution times. However, increasing the evolution time reduces the bandwidth that can be sampled, whereas decreasing the evolution time worsens the sensitivity. In this paper, we attempt to address this by proposing a setup for high-bandwidth applications, with improved overall sensitivity. This is realized by accelerating and holding the atoms using optical dipole traps. We find that accelerations of up to 103–105{10}^{3}\text{--}{10}^{5}103–105 m/s2{\mathrm{m/s}}^{2}m/s2 can be achieved using acousto-optic deflectors to move the traps. By comparing the sensitivity of our approach to acceleration as a baseline to traditional atom interferometry, we find a substantial improvement to the state of the art. In the limit of appropriate beam and optics stabilization, sensitivities approaching ${10}^{\ensuremath{-}14}$ (m/s2{\mathrm{m/s}}^{2}m/s2)/Hz\sqrt{\mathrm{Hz}}Hz​ may be achievable at 1 Hz, while detection at 1 kHz with a sensitivity an order of magnitude better than traditional free-fall atom interferometers is possible with today's systems.
The best performance of a Mach-Zehnder interferometer is achieved with the input state $\ensuremath{\mid}{N}_{T}∕2+1⟩\ensuremath{\mid}{N}_{T}∕2\ensuremath{-}1⟩+\ensuremath{\mid}{N}_{T}∕2\ensuremath{-}1⟩\ensuremath{\mid}{N}_{T}∕2+1⟩$, NT{N}_{T}NT​ being the total number of atoms or photons. This gives (i) a phase-shift error confidence ${C}_{68%}=2.67∕{N}_{T}$ with (ii) a single interferometric measurement. Different input quantum states can achieve the Heisenberg scaling $\ensuremath{\sim}1∕{N}_{T}$ but with higher prefactors and at the price of a statistical analysis of two or more independent measurements.
Bloch oscillations of atoms in optical lattices are a powerful technique that can boost the sensitivity of atom interferometers to a wide range of signals by large momentum transfer. To leverage this method to its full potential, an accurate theoretical description of losses and phases is needed going beyond existing treatments. Here, we present a comprehensive theoretical framework for Bloch-oscillation-enhanced atom interferometry and verify its accuracy through comparison with an exact numerical solution of the Schrödinger equation. Our approach establishes design criteria to reach the fundamental efficiency and accuracy limits of large momentum transfer using Bloch oscillations. We compare these limits to the case of current state-of-the-art experiments and make projections for the next generation of quantum sensors.