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arXiv:0710.1081 · Physical Review A

Confinement effects in a guided-wave atom interferometer with millimeter-scale arm separation

John H. Burke, Benjamin Deissler, K. J. Hughes, Charles A. Sackett

Published Aug 14, 2008• 48 citations
arXivHTMLPDF

Abstract

Guided-wave atom interferometers measure interference effects using atoms held in a confining potential. In one common implementation, the confinement is primarily two dimensional, and the atoms move along the nearly free dimension after being manipulated by an off-resonant standing wave laser beam. In this configuration, residual confinement along the nominally free axis can introduce a phase gradient to the atoms that limits the arm separation of the interferometer. We experimentally investigate this effect in detail, and show that it can be alleviated by having the atoms undergo a more symmetric motion in the guide. This can be achieved by either using additional laser pulses or by allowing the atoms to freely oscillate in the potential. With these techniques, we demonstrate interferometer measurement times up to $72\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ and arm separations up to $0.42\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ with a well controlled phase, or times of $0.91\phantom{\rule{0.3em}{0ex}}\mathrm{s}$ and separations of $1.7\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ with an uncontrolled phase.

DOI
10.1103/physreva.78.023619

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Guided-wave atom interferometers measure interference effects using atoms held in a confining potential. In one common implementation, the confinement is primarily two dimensional, and the atoms move along the nearly free dimension after being manipulated by an off-resonant standing wave laser beam. In this configuration, residual confinement along the nominally free axis can introduce a phase gradient to the atoms that limits the arm separation of the interferometer. We experimentally investigate this effect in detail, and show that it can be alleviated by having the atoms undergo a more symmetric motion in the guide. This can be achieved by either using additional laser pulses or by allowing the atoms to freely oscillate in the potential. With these techniques, we demonstrate interferometer measurement times up to 72ms72\phantom{\rule{0.3em}{0ex}}\mathrm{ms}72ms and arm separations up to 0.42mm0.42\phantom{\rule{0.3em}{0ex}}\mathrm{mm}0.42mm with a well controlled phase, or times of 0.91s0.91\phantom{\rule{0.3em}{0ex}}\mathrm{s}0.91s and separations of 1.7mm1.7\phantom{\rule{0.3em}{0ex}}\mathrm{mm}1.7mm with an uncontrolled phase.
A Michelson interferometer using Bose-Einstein condensates is demonstrated with coherence times of up to 44ms44\phantom{\rule{0.3em}{0ex}}\mathrm{ms}44ms and arm separations up to $180\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{m}$. This arm separation is larger than that observed for any previous atom interferometer. The device uses atoms weakly confined in a magnetic guide and the atomic motion is controlled using Bragg interactions with an off-resonant standing-wave laser beam.
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.
An atom interferometer using Bose-Einstein condensates has been implemented and is used to measure the dynamic polarizability of 87Rb. An off-resonant standing-wave laser beam is used to manipulate the motion of atomic wavepackets in order to implement splitting and reflection operations. It is demonstrated that these operations can be performed with near unity fidelity. Interferometer times of up to 72 ms as well as arm separations of up to 0.42 mm are achieved experimentally. The primary limitation for guided-wave atom interferometers with a large arm separation is found to be the effect of the confining potential along the waveguide axis. Such a potential causes a spatially varying phase shift on the wavepackets as they propagate in the interferometer. Different parts of the cloud therefore interfere with different phases, leading to a reduction of the interferometer contrast. A model of the phase shifts on the wavepackets agrees well with the experimental data. In a different scheme in which the wavepackets oscillate freely in the confining potential, these phase shifts completely cancel. Interference is observed at times up to 0.9 s in this case, but with a fluctuating overall phase of the output, which is attributed to mechanical instabilities. Finally, the dynamic polarizability of 87Rb is measured. A well-calibrated laser beam is applied to one atomic packet and not the other, inducing a differential phase shift. This technique requires relatively low laser intensity and works for arbitrary optical frequencies. For offresonant light, the ac polarizability is obtained with a statistical accuracy of 3% and a calibration uncertainty of 6%. On resonance, the dispersion-shaped behavior of the Stark shift is observed, but with a broadened linewidth that is attributed to multiple and collective light scattering effects. The resulting nonlinearity may prove useful for the production and control of squeezed quantum states. In general, this work also demonstrates the applicability of condensate interferometry to practical measurements.
A free-oscillation interferometer uses atoms confined in a harmonic trap. Bragg scattering from an off-resonant laser is used to split an atomic wave function into two separated packets. After one or more oscillations in the trap, the wave packets are recombined by a second application of the Bragg laser to close the interferometer. Anharmonicity in the trap potential can lead to a phase shift in the interferometer output. In this paper, analytical expressions for the anharmonic phase are derived at leading order for perturbations of arbitrary power in the position coordinate. The phase generally depends on the initial position and velocity of the atom, which are themselves typically uncertain. This leads to degradation in the interferometer performance, and can be expected to limit the use of a centimeter-scale device to interaction times of about 0.1 s. Methods to improve performance are discussed.
Light Pulse Atom lnterferometryLight Pulse Atom Interferometers (LPAI) utilize Raman or Bragg transitions to coherently split, redirect, and recombine atomic wave packets.1In free space LPAIs, light pulses impart momentum kicks to freely expanding cold atomic clouds released from rest.During the atom-light interaction, the laser phase is imprinted onto the atom's wave function.Atoms experience different phase shifts along each interferometer arm which gives us information about their spatial trajectories and thus their local acceleration.The quadratic dependence of the phase shift on the interrogation time, T, have prompted researchers to increase the system's size.For field use, however, smaller compact devices are desired.Guided atom interferometers confine atoms spatially, increasing the interrogation time while minimizing the laser power needed to drive these systems. Beam 4litterIg,p) Mirror
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.