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A Collective Excitation Interferometer for Rotation Sensing with a Trapped Bose-Einstein Condensate

G. Edward Marti, Ryan Olf, Dan Stamper-Kurn

Published Sep 28, 2012• 2 citations
OpenAlex

Abstract

Compact inertial sensing schemes using trapped- and guided-atom interferometers have been unable to achieve high precision because of uncontrolled phase errors caused by trapping potentials and interactions. Here, we demonstrate an atom-shot-noise limited acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotations. Our system operates at $10^4 - 10^6$ times higher density and in a volume $10^9$ times smaller than free-falling atom interferometers.

Related papers

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The precision of most compact inertial sensing schemes using trapped- and guided-atom interferometers has been limited by uncontrolled phase errors caused by trapping potentials and interactions. Here we propose an acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotation, and we demonstrate experimentally several key aspects of this type of interferometer. We use spatially patterned light beams to excite counterpropagating sound waves within the condensate and use in situ absorption imaging to characterize their evolution. We present an analysis technique by which we extract separately the oscillation frequencies of the standing-wave acoustic modes, the frequency splitting caused by static imperfections in the trapping potential, and the characteristic precession of the standing-wave pattern due to rotation. Supported by analytic and numerical calculations, we interpret the noise in our measurements, which is dominated by atom shot noise, in terms of rotation noise. While the noise of our acoustic interferometric sensor, at the level of $\ensuremath{\sim}\text{rad}\phantom{\rule{0.16em}{0ex}}{\text{s}}^{\ensuremath{-}1}/\sqrt{\text{Hz}}$, is high owing to rapid acoustic damping and the small radius of the trap, the proof-of-concept device does operate at the high densities and small volumes of trapped Bose-Einstein condensed gases.

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Abstract The coherent manipulation of a quantum wave is at the core of quantum sensing. For instance, atom interferometers require linear splitting and recombination processes to map the accumulated phase shift into a measurable population signal. Although Bose Einstein condensates (BECs) are the archetype of coherent matter waves, their manipulation between trapped spatial modes has been limited by the strong interparticle collisions. Here, we overcome this problem by using BECs with tunable interaction trapped in an innovative array of double-well potentials and exploiting quantum tunneling to realize linear beam splitting. We operate several Mach-Zehnder interferometers in parallel, canceling common-mode potential instabilities by a differential analysis, thus demonstrating a trapped-atom gradiometer. Furthermore, by applying a spin-echo protocol, we suppress additional decoherence sources and approach unprecedented coherence times of one second. Our interferometer will find applications in precision measurements of forces with a high spatial resolution and in linear manipulation of quantum entangled states for sensing with sub shot-noise sensitivity.

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An atom interferometer is a sensitive device that has potential for many useful applications. Atoms are sensitive to electromagnetic fields due to their electric and magnetic moments and their mass allows them to be deflected in a gravitational field, thereby making them attractive for measuring inertial forces. The narrow momentum distribution of Bose-Einstein condensate (BEC) is a great asset in realizing portable atom interferometers. An example is a guided-wave atom interferometer that uses a confining potential to guide the motion of the condensate. Despite the promise of guided-wave atom interferometry with BEC, spatial phase and phase diffusion limit the contrast of the interference fringes. The control of these phases is required for successful development of a BEC-based guided-wave atom interferometer. This thesis analyses the guided-wave atom interferometer, where an atomic BEC cloud at the center of a confining potential is split into two clouds that move along different arms of the interferometer. The clouds accumulate relative phase due to the environment, spatially inhomogeneous trapping potential and atom-atom interactions within the condensate. At the end of the interferometric cycle, the clouds are recombined producing a cloud at rest and moving clouds. The number of atoms in the clouds that emerge depends on the relative phase accumulated by the clouds during propagation. This is investigated by deriving an expression for the probability of finding any given number of atoms in the clouds that emerge after recombination. Characteristic features like mean, standard deviation and cross-correlation function of the probability density distribution are calculated and the contrast of the interference fringes is optimized. This thesis found that optimum contrast is achieved through the control of total population of atoms in the condensate, trap frequencies, s-wave scattering length, and the duration of the interferometric cycle.

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Atomic quantum sensors are a major breakthrough in the technology of time and frequency standards as well as ultra-precise sensing and monitoring of accelerations and rotations. They apply a new kind of optics based on matter waves. Today, atomic clocks are the standard for time and frequency measurement at the highest precisions. Inertial and rotational sensors using atom interferometers have already shown similar potential for replacing state-of-the-art sensors in other fields. With Bose-Einstein condensates, also refered as atom lasers, the traditional experiments with atom interferometers can be greatly improved. Testing of fundamental principles, studies of atomic properties, applications as inertial sensors, and measurements of fundamental constants can benefit from the brightness (intensity and small momentum spread) of these coherent sources. In addition, the coherence properties of condensates may also allow BEC based atom interferometers to approach the Heisenberg detection limit. This corresponds to a measurement precision which scales like 1/N for N atoms and not like 1 / N as for independent measurements on N atoms.

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Rotation Sensing with an Atom Interferometer

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We have measured the phase shift induced by rotation of an atom interferometer at rates of $\ensuremath{-}2$ to $+2$ earth rates and obtained $1%$ agreement with the predicted Sagnac phase shift for atomic matter waves. The rotational rms noise of our interferometer was $42$ milliearth rates for $1$ sec of integration time, within $9%$ of shot noise. The high sensitivity and agreement of predicted and measured behavior suggest useful future scientific applications of atom interferometers as inertial sensors.

Physical Review Letters•Feb 3, 1997•198 citations
Compact inertial sensing schemes using trapped- and guided-atom interferometers have been unable to achieve high precision because of uncontrolled phase errors caused by trapping potentials and interactions. Here, we demonstrate an atom-shot-noise limited acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotations. Our system operates at 104−10610^4 - 10^6104−106 times higher density and in a volume 10910^9109 times smaller than free-falling atom interferometers.
The precision of most compact inertial sensing schemes using trapped- and guided-atom interferometers has been limited by uncontrolled phase errors caused by trapping potentials and interactions. Here we propose an acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotation, and we demonstrate experimentally several key aspects of this type of interferometer. We use spatially patterned light beams to excite counterpropagating sound waves within the condensate and use in situ absorption imaging to characterize their evolution. We present an analysis technique by which we extract separately the oscillation frequencies of the standing-wave acoustic modes, the frequency splitting caused by static imperfections in the trapping potential, and the characteristic precession of the standing-wave pattern due to rotation. Supported by analytic and numerical calculations, we interpret the noise in our measurements, which is dominated by atom shot noise, in terms of rotation noise. While the noise of our acoustic interferometric sensor, at the level of $\ensuremath{\sim}\text{rad}\phantom{\rule{0.16em}{0ex}}{\text{s}}^{\ensuremath{-}1}/\sqrt{\text{Hz}}$, is high owing to rapid acoustic damping and the small radius of the trap, the proof-of-concept device does operate at the high densities and small volumes of trapped Bose-Einstein condensed gases.
Abstract The coherent manipulation of a quantum wave is at the core of quantum sensing. For instance, atom interferometers require linear splitting and recombination processes to map the accumulated phase shift into a measurable population signal. Although Bose Einstein condensates (BECs) are the archetype of coherent matter waves, their manipulation between trapped spatial modes has been limited by the strong interparticle collisions. Here, we overcome this problem by using BECs with tunable interaction trapped in an innovative array of double-well potentials and exploiting quantum tunneling to realize linear beam splitting. We operate several Mach-Zehnder interferometers in parallel, canceling common-mode potential instabilities by a differential analysis, thus demonstrating a trapped-atom gradiometer. Furthermore, by applying a spin-echo protocol, we suppress additional decoherence sources and approach unprecedented coherence times of one second. Our interferometer will find applications in precision measurements of forces with a high spatial resolution and in linear manipulation of quantum entangled states for sensing with sub shot-noise sensitivity.
An atom interferometer is a sensitive device that has potential for many useful applications. Atoms are sensitive to electromagnetic fields due to their electric and magnetic moments and their mass allows them to be deflected in a gravitational field, thereby making them attractive for measuring inertial forces. The narrow momentum distribution of Bose-Einstein condensate (BEC) is a great asset in realizing portable atom interferometers. An example is a guided-wave atom interferometer that uses a confining potential to guide the motion of the condensate. Despite the promise of guided-wave atom interferometry with BEC, spatial phase and phase diffusion limit the contrast of the interference fringes. The control of these phases is required for successful development of a BEC-based guided-wave atom interferometer. This thesis analyses the guided-wave atom interferometer, where an atomic BEC cloud at the center of a confining potential is split into two clouds that move along different arms of the interferometer. The clouds accumulate relative phase due to the environment, spatially inhomogeneous trapping potential and atom-atom interactions within the condensate. At the end of the interferometric cycle, the clouds are recombined producing a cloud at rest and moving clouds. The number of atoms in the clouds that emerge depends on the relative phase accumulated by the clouds during propagation. This is investigated by deriving an expression for the probability of finding any given number of atoms in the clouds that emerge after recombination. Characteristic features like mean, standard deviation and cross-correlation function of the probability density distribution are calculated and the contrast of the interference fringes is optimized. This thesis found that optimum contrast is achieved through the control of total population of atoms in the condensate, trap frequencies, s-wave scattering length, and the duration of the interferometric cycle.
Precision interferometry with atomic wavepackets confined in a one-dimensional optical lattice is an emergent paradigm in quantum sensing of forces and fields, with applications in gravimetry, accelerometry, geophysics, and fundamental physics tests. We report on the realization of a lattice-trapped interferometer where the two arms are sourced from a weakly-interacting ytterbium Bose-Einstein condensate, coherently split and trapped by pulsed optical standing waves before recombination. We directly observe atomic interactions through contrast changes and phase shifts of the interferometer. By changing either the atom number or the sample volume to vary the density, we demonstrate control over interactions and optimize interferometer performance. Our observations are effectively captured by a mean-field theoretical model of the system. This work experimentally probes the boundary where improved performance from source brightening through higher phase space density transitions into a regime beyond single-atom physics in lattice-trapped atom interferometry, and opens a door to incorporating many-body effects for metrological advances in such platforms.
Atomic quantum sensors are a major breakthrough in the technology of time and frequency standards as well as ultra-precise sensing and monitoring of accelerations and rotations. They apply a new kind of optics based on matter waves. Today, atomic clocks are the standard for time and frequency measurement at the highest precisions. Inertial and rotational sensors using atom interferometers have already shown similar potential for replacing state-of-the-art sensors in other fields. With Bose-Einstein condensates, also refered as atom lasers, the traditional experiments with atom interferometers can be greatly improved. Testing of fundamental principles, studies of atomic properties, applications as inertial sensors, and measurements of fundamental constants can benefit from the brightness (intensity and small momentum spread) of these coherent sources. In addition, the coherence properties of condensates may also allow BEC based atom interferometers to approach the Heisenberg detection limit. This corresponds to a measurement precision which scales like 1/N for N atoms and not like 1 / N as for independent measurements on N atoms.
We have measured the phase shift induced by rotation of an atom interferometer at rates of $\ensuremath{-}2$ to +2+2+2 earth rates and obtained 11%1 agreement with the predicted Sagnac phase shift for atomic matter waves. The rotational rms noise of our interferometer was 424242 milliearth rates for 111 sec of integration time, within 99%9 of shot noise. The high sensitivity and agreement of predicted and measured behavior suggest useful future scientific applications of atom interferometers as inertial sensors.