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arXiv:1311.2143 · Europhysics Letters (EPL)

A faster 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 Mar 1, 2014• 27 citations
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Abstract

Atom interferometers have been used to measure acceleration with at best a $T^2$ scaling in sensitivity as the interferometer time $T$ 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 $T^3$. 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 $T^4$ scaling in acceleration sensitivity.

DOI
10.1209/0295-5075/105/63001

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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.
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.
Exploiting the quantum nature of atoms through the use of matter-wave interferometry has lead to the development of devices sensitive to, among other things, the local gravitational acceleration. Measurements of the gravitational acceleration have applications ranging from detection of subterranean density di erences to observation of general relativistic e ects. Light-pulse atom interferometers provide an absolute measurement of the gravitational acceleration with a sensitivity competitive and even surpassing the performance of classical sensors. The advantages of atom interferometers as inertial measurement devices have lead to e orts in increasing sensitivity and decreasing the physical dimensions of the measurement head, allowing them to be more transportable for eld use applications. With increasing sensitivity, it becomes more critical to address the noise source limitations a ecting the measurement, speci cally the in uence of ground motion on measurements. Vibrations coupling into the inertial reference add a time varying phase shift uncommon to the paths of the interferometer. This limitation is especially pertinent to transportable atom gravimeters measuring in the eld where inertial noise is typically far higher than in relatively quiet laboratory environments. Within this work, implementation and demonstration of inertial noise post-correction in an atom interferometer is shown within low inertial noise environments and simulated strong motion environments. For a high pulse separation time atom interferometer (T = 78 ms) post-correction yielded an increase in the short term stability from 4.4 x 10 ̄6 m/s2/√Hz to 9.2 x 10 ̄7 m/s2/√Hz. This method was reproduced with a di erent motion sensor to perform post-correction in a high motion environment, generated by introducing additional movement onto the inertial reference. By performing post-correction in the high motion environment, we were able to show an increase of short term stability of γ = 73.8. Current limitations to the post-correction resulted from self noise resolution limitations and spectral resolutions limitations. Beyond corrections with commercially available sensors, this work demonstrates the rst post-correction with a next generation compact optomechanical sensor. This optomechanical sensor is formed from monolithic fused silica capable of sensitively measuring accelerations of a harmonic oscillator test mass, which can be read-out optically. This novel motion sensor has the advantage to any previously shown sensor used for post-correction in the capacity that it is vacuum compatible, insensitive to magnetic elds and has the potential to be implemented directly into the inertial reference. In this work, inertial noise post-correction in a simulated high motion environment is shown, correcting from a short term stability of 8 x 10 ̄3 m/s2/√Hz to 5 x 10 ̄4 m/s2/√Hz. Post-correction was limited by the parasitic cavities within the ber required for optical read-out of the harmonic oscillator displacement and intensity noise uctuations of the source laser. The results shown within this work are congruent with previous works on atom chip gravimeters, both of which help move towards portable hand-held gravimeter measurement heads capable of sensitive inertial measurement.
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.
The exquisite precision of atom interferometers has sparked the interest of a large community for uses ranging from fundamental physics to geodesy and inertial navigation. However, their implementation for onboard applications is still limited, not least because rotation and acceleration are intertwined in a single phase shift, which makes the extraction of a useful signal more challenging. Moreover, the spatial separation of the wave packets due to rotations leads to a loss of signal. We present an atom interferometer operating over a large range of random angles, rotation rates and accelerations. A model of the expected phase shift allows us to untangle the rotation and acceleration signals. We also implement a real-time compensation system using fiber-optic gyroscopes and a rotating reference mirror to maintain the full contrast of the interferometer. We demonstrate a single-shot sensitivity to acceleration of 24 μg for rotation rates reaching 14° s−1. Cold atoms inertial sensors offer great precision and sensitivity, yet their use in mobile applications has been hindered by the effects of rotations on their measurements. Here, authors demonstrate an atom interferometer operating over a wide range of orientations and rotation rates, thanks to hybridisation with accelerometers and gyroscopes.
Matter-wave interferometry has enabled high precision measurements of inertial forces such as gravity and the Coriolis force. This is facilitated by the long-term stability of the physical properties of atoms and lasers. Recent experiments have demonstrated the operation of portable, robust sensors using atom interferometry. This has potential uses in the context of inertial navigation, where conventional devices suffer from long-term drifts due to bias instability. Furthermore, determining position via dead reckoning requires minimisation of dead time between measurements. This thesis presents the development of an atom interferometer for measuring horizontal accelerations. In this configuration, gravity induces motion across the laser wavefront, which constrains the tolerable level of wavefront distortions. Effective control of the experiment allows the interferometer to be operated at a rate of 4 Hz. A cold ensemble of 10^6 atoms in the same internal state is prepared in 150 ms. The interferometer operates using a sequence of three laser pulses separated by T= 25 ms to achieve sensitivity to horizontal accelerations. Combining this with a classical accelerometer provides a method of correcting for vibration-induced noise, as well as determining the interferometer fringe order. After an integration time of 40 s, the sensitivity to horizontal accelerations is better than 3^-6 m s^-2. Effects which limit this sensitivity are discussed.
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.