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arXiv:1606.06831 · Atoms

Prospects for Precise Measurements with Echo Atom Interferometry

B. Barrett, Adam C. Carew, Hermina C. Beica, Andrejs Vorozcovs, Alexander Pouliot, Anantharaman Kumarakrishnan

Published Jun 27, 2016• 23 citations
arXivHTMLPDF

Abstract

Echo atom interferometers have emerged as interesting alternatives to Raman interferometers for the realization of precise measurements of the gravitational acceleration g and the determination of the atomic fine structure through measurements of the atomic recoil frequency ω q . Here we review the development of different configurations of echo interferometers that are best suited to achieve these goals. We describe experiments that utilize near-resonant excitation of laser-cooled rubidium atoms by a sequence of standing wave pulses to measure ω q with a statistical uncertainty of 37 parts per billion (ppb) on a time scale of ∼50 ms and g with a statistical precision of 75 ppb. Related coherent transient techniques that have achieved the most statistically precise measurements of atomic g-factor ratios are also outlined. We discuss the reduction of prominent systematic effects in these experiments using off-resonant excitation by low-cost, high-power lasers.

DOI
10.3390/atoms4030019

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Echo atom interferometers have emerged as interesting alternatives to Raman interferometers for the realization of precise measurements of the gravitational acceleration g and the determination of the atomic fine structure through measurements of the atomic recoil frequency ω q . Here we review the development of different configurations of echo interferometers that are best suited to achieve these goals. We describe experiments that utilize near-resonant excitation of laser-cooled rubidium atoms by a sequence of standing wave pulses to measure ω q with a statistical uncertainty of 37 parts per billion (ppb) on a time scale of ∼50 ms and g with a statistical precision of 75 ppb. Related coherent transient techniques that have achieved the most statistically precise measurements of atomic g-factor ratios are also outlined. We discuss the reduction of prominent systematic effects in these experiments using off-resonant excitation by low-cost, high-power lasers.
We have developed two configurations of an echo interferometer that rely on standing-wave excitation of a laser-cooled sample of rubidium atoms. Both configurations can be used to measure acceleration aaa along the axis of excitation. For a two-pulse configuration, the signal from the interferometer is modulated at the recoil frequency and exhibits a sinusoidal frequency chirp as a function of pulse spacing. In comparison, for a three-pulse stimulated-echo configuration, the signal is observed without recoil modulation and exhibits a modulation at a single frequency as a function of pulse spacing. The three-pulse configuration is less sensitive to effects of vibrations and magnetic field curvature, leading to a longer experimental time scale. For both configurations of the atom interferometer (AI), we show that a measurement of acceleration with a statistical precision of 0.5% can be realized by analyzing the shape of the echo envelope that has a temporal duration of a few microseconds. Using the two-pulse AI, we obtain measurements of acceleration that are statistically precise to 6 parts per million (ppm) on a 25 ms time scale. In comparison, using the three-pulse AI, we obtain measurements of acceleration that are statistically precise to 0.4 ppm on a time scale of 50 ms. A further statistical enhancement is achieved by analyzing the data across the echo envelope so that the statistical error is reduced to 75 parts per billion (ppb). The inhomogeneous field of a magnetized vacuum chamber limited the experimental time scale and resulted in prominent systematic effects. Extended time scales and improved signal-to-noise ratio observed in recent echo experiments using a nonmagnetic vacuum chamber suggest that echo techniques are suitable for a high-precision measurement of gravitational acceleration ggg. We discuss methods for reducing systematic effects and improving the signal-to-noise ratio. Simulations of both AI configurations with a time scale of 300 ms suggest that an optimized experiment with improved vibration isolation and atoms selected in the mF=0{m}_{F}=0mF​=0 state can result in measurements of ggg statistically precise to 0.3 ppb for the two-pulse AI and 0.6 ppb for the three-pulse AI.
We describe progress toward a precise measurement of the recoil energy of an atom measured using a modified grating-echo atom interferometer (AI) that involves three standing-wave (sw) pulses. With this technique, an additional sw pulse is used to shift the phase of excited momentum states, which produces a modulation in the contrast of the interference pattern. The signal exhibits narrow fringes that revive periodically at twice the two-photon recoil frequency, $2{\ensuremath{\omega}}_{q}$, as a function of the onset time of the pulse. Experiments are performed using samples of laser-cooled rubidium atoms with temperatures $\ensuremath{\lesssim}$5 $\ensuremath{\mu}$K in a nonmagnetic apparatus. We demonstrate a measurement of ${\ensuremath{\omega}}_{q}$ with a statistical uncertainty of 37 parts per 109{10}^{9}109 (ppb) on a time scale of $\ensuremath{\sim}$45 ms in 14 h. Further statistical improvements are anticipated by extending this time scale and narrowing the signal fringe width. However, the total systematic uncertainty is estimated to be $\ensuremath{\sim}$6 parts per 106{10}^{6}106 (ppm). We describe methods of reducing these systematic errors.
Precision measurements of gravitational acceleration g have far reaching applications in navigation and sensing as well as for tests of general relativity. Grating-echo atom interferometers (AIs) utilize simple setups and distinctive excitation schemes that involve a single excitation laser, and do not require velocity selection. They have demonstrated measurements of gravity precise to 75 parts per billion (ppb) by dropping laser-cooled atomic samples through ~ 1 cm. Here we describe progress toward realizing a cold atom gravimeter using an echo AI designed for drop heights of ~30 cm. The experimental technique involves illuminating the falling sample of laser-cooled rubidium atoms with two standing wave (sw) pulses separated by time t = T. The sw pulses are composed of two traveling-wave components, each having a wave vector of magnitude k = 2π/λ. Momentum state interference produces one-dimensional density gratings with a period λ/2 immediately after each excitation pulse. These gratings dephase due to the velocity distribution of the sample along the sw axis. The AI uses an echo technique to cancel the effect of velocity dephasing and observe a rephased density grating in the vicinity of the echo time τ = 2Τ. The grating contrast and phase are measured by coherently backscattering a traveling wave readout pulse from the sample. The grating phase, measured with respect to a vibrationally stabilized inertial reference frame, scales as 2kgΤ2. A drawback of echo AIs is the signal-to-noise ratio, which is limited by the contrast of the grating and systematic effects due the refractive index of the sample. Here, we review improvements to the experimental design and investigate methods of improving the signal-to-noise ratio by optimizing the atom-field coupling. We describe progress toward realizing our goals of increasing the grating contrast and the backscattered signal. The improved contrast is expected to allow the experiment to be carried out at a lower density to reduce corrections due to the refractive index. We discuss a variety of excitation schemes for achieving a target precision of a few ppb.
The basic physical principles behind atom interferometers based on optical pulses of light are summarized. This method of atom interferometry is based on measurements in the time and frequency domain and is an inherently precise measurement technique. After a brief discussion of some of the important technical requirements for good fringe accuracy and visibility, we describe an interferometer that has measured the acceleration of an atom due to gravity with a resolution better than one part in 1010. We project that the absolute accuracy of our measurement will be of the order of a few parts in 109. We also describe an interferometer experiment that measures the recoil energy shift of an atom when it absorbs a photon. When combined with the value of the Rydberg constant and the mass ratios MCs/mp and mp/me, one can obtain a value for α, the fine structure constant. Currently, we have an experimental resolution Δα/α ∼ 10-8 after two hours of integration time and are studying the systematic effects that affect the measurement.
This dissertation describes the development of a suite of interlinked techniques for precision metrology with matter wave lattices realized in a ceiling-to-floor non-magnetic atom trapping apparatus. This work involves the development of a single-state atom interferometer that relies on the observation of density gratings formed in the atomic ground state of a laser-cooled sample. These gratings, the result of Kapitza-Dirac diffraction of momentum states following a standing wave optical excitation pulse, typically dephase according to their velocity distribution, and motional properties of the sample, including the local value of gravitational acceleration g, are imprinted on the grating contrast and phase. These features can be extracted by coherently backscattering a travelling wave readout field applied within the thermal coherence time of the sample and measuring the grating free-induction decay. Alternatively, a grating echo, resulting from the application of two standing wave pulses separated by t=T_{21}, can be detected using the same backscattering method in the vicinity of the echo time t=2T_{21} on time scales defined by the transit of cold atoms out of the standing wave beam volume. This dissertation presents five main experimental results that impact a new generation of cold atom quantum sensors. Firstly, we investigate a technique for measuring the magnetic moments and sublevel distributions of laser-cooled gases. Secondly, we study optical channell-ing which can be used to increase the scattering efficiency of optical lattices and the sensitivity of grating-echo interferometers. Thirdly, we describe Bragg scattering of a readout pulse from optical lattices and develop a technique to optimize this process in dilute gas lattices, leading to increased signal strengths in echo interferometers. Fourthly, we demonstrate a novel "Ramsey" velocimeter which can measure sample center-of-mass velocity with a precision of 600 µm/s. Finally, we present a measurement of g which represents the first realization of a frequency domain echo-type gravimeter, with a sensitivity to g of 2 parts per million. We outline the basis for improving the precision of these sensors to realize devices capable of measuring g with a sensitivity of 10 parts per billion and probing velocities more precisely than all other atomic velocimeters.