Demonstration of improved sensitivity of echo interferometers to gravitational acceleration

Abstract

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 a 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 timescale. 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 timescale. In comparison, using the three-pulse AI, we obtain measurements of acceleration that are statistically precise to 0.4 ppm on a timescale 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 timescale and resulted in prominent systematic effects. Extended timescales and improved signal-to-noise ratio observed in recent echo experiments using a non-magnetic vacuum chamber suggest that echo techniques are suitable for a high precision measurement of gravitational acceleration g. We discuss methods for reducing systematic effects and improving the signal-to-noise ratio. Simulations of both AI configurations with a timescale of 300 ms suggest that an optimized experiment with improved vibration isolation and atoms selected in the mF = 0 state can result in measurements of g statistically precise to 0.3 pbb for the two-pulse AI and 0.6 ppb for the three-pulse AI.

Prospects for Precise Measurements with Echo Atom Interferometry

“…As described in Refs. [32,56,57], two major improvements to our experiment have enabled us to reach time scales of T 60 ms: (i) utilizing a non-magnetizable glass vacuum system, which reduced decoherence effects related to inhomogeneous B-fields [58] and improved the molasses cooling of the sample, and (ii) using large-diameter, chirped excitation beams, which increased the transit time of the atoms in the beam and compensated for the Doppler shift due to gravity 4 .…”

“…Due to the limited bandwidth of two-photon Raman transitions given by the Rabi frequency Ω eff /2π 10 − 100 kHz, and the desire to use only atoms in magnetically "insensitive" m F = 0 states, a large percentage of atoms are lost during the sample preparation process. To give a typical example, a sample of N ∼ 10 8 laser-cooled 87 Rb atoms at a temperature of ∼ 5 µK has an initial velocity spread of σ v 3 cm/s. After preparing the atoms in the |F = 1, m F = 0 state using a sequence of near-resonant push beams and microwave π-pulses, typically 1/3 of the atoms remain.…”

“…Echo AI experiments that have demonstrated sensitivity to this gravitational phase shift are described in Refs. [30,54,55,58,87].…”

“…Most of the progress in both short-term and long-term sensitivity has been achieved using Raman interferometers [8,22,[45][46][47][48]. This AI relies on optical velocity-sensitive two-photon Raman transitions between two long-lived hyperfine ground states in alkali atoms, such as the |F = 1 and |F = 2 states in 87 Rb. Raman AIs were the first implementation of state-labeled interferometer [45], where the coherent exchange of photon momentum between the atoms and the optical fields is associated with a change in the internal atomic state.…”

“…This AI requires only a single excitation frequency, and does not require velocity selection. Recently, this configuration has achieved several milestones, including an extension of the timescale to the transit time limit (∼ 250 ms for experimental conditions) [32], as well as significant improvements in statistical precision relating to measurements of the atomic recoil frequency (related to h/M) [56,57] and the acceleration due to gravity [58]. In what follows, we review recent progress on both atomic recoil (Sec.…”