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Frontiers in Optics

Constraints in Collective State Atomic Interferometry Due to Inhomogeneities in Laser Intensity and Atomic Velocity

Resham Sarkar, May E. Kim, Renpeng Fang, M. S. Shahriar

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We show that in a collective state atomic interferometer, the signal amplitude depends significantly on the transverse spatial variation of laser intensity, and the spread in Doppler shifts due to velocity distribution in the atoms.
DOI
10.1364/fio.2014.jtu3a.27

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Atom interferometry relies on the separation and recombination of atom wavepackets. When the two paths overlap perfectly at the end of the interferometer, the phase is insensitive to the atomic velocity distribution. Here, we show that, when the separation and recombination is performed using a Raman transition there is a displacement of the atomic wavepacket due to a phase shift during light pulses. Because of the variation of the laser intensity seen by the atoms, there is an imperfect cancellation of these displacements. The observation of a velocity-dependent phase shift on the interferometer is the signature of this effect, which has been modeled. Thanks to the signature we have identified, we are able to compensate for this effect by applying laser power ramps during the interferometer to mitigate intensity variations.
The uniformity of the intensity and the phase of laser beams is crucial to high-performance atom interferometers. Inhomogeneities in the laser intensity profile cause contrast reductions and systematic effects in interferometers operated with atom sources at micro-Kelvin temperatures and detrimental diffraction phase shifts in interferometers using large momentum transfer beam splitters. We report on the implementation of a so-called top-hat laser beam in a long-interrogation-time cold-atom interferometer to overcome the issue of inhomogeneous laser intensity encountered when using Gaussian laser beams. We characterize the intensity and relative phase profiles of the top-hat beam and demonstrate its gain in atom-optic efficiency over a Gaussian beam, in agreement with numerical simulations. We discuss the application of top-hat beams to improve the performance of different architectures of atom interferometers.
We have used an echo-type atom interferometer that manipulates laser-cooled atoms in a single ground state to investigate the effect of light scattering from pulsed and continuous-wave light. The interferometer uses two off-resonant standing-wave pulses applied at times t=0t=0t=0 and t=Tt=Tt=T to diffract and recombine momentum states separated by $2\ensuremath{\hbar}k$ at t=2Tt=2Tt=2T. Matter wave interference is associated with the formation of a density grating with period $\ensuremath{\lambda}/2$ in the vicinity of this echo time. The grating contrast is measured by recording the intensity of coherently backscattered light. The interferometer is perturbed by an additional pulse applied at $t=2T\ensuremath{-}\ensuremath{\delta}T$ or by continuous-wave background light. If the additional pulse is a standing wave, the momentum states interfering at t=2Tt=2Tt=2T are displaced and the grating contrast can be completely recovered due to constructive interference. In this case, the contrast shows a periodic modulation at the atomic recoil frequency as a function of $\ensuremath{\delta}T$. In a recent work, it was shown that the atomic recoil frequency can be measured easily and precisely when using coherence functions to model the signal shape. This paper provides an alternative description of the signal shape through an analytical calculation of echo formation in the presence of an additional standing-wave pulse. Using this treatment, it is possible to model the effects of spontaneous emission and spatial profile of the laser beam on the signal shape. Additionally, the theory predicts scaling laws as a function of the pulse area and the number of additional standing-wave pulses. These scaling laws are investigated experimentally and can be exploited to improve precision measurements of the atomic recoil frequency. We also show that coherence functions can be used to make a direct measurement of the populations of momentum states associated with the ground state under conditions where the Doppler-broadened velocity distribution of the sample is much larger than the recoil velocity. These measurements are consistent with Monte Carlo wave-function simulations. If the additional pulse is a traveling wave, we find that the grating contrast measured as a function of $\ensuremath{\delta}T$ can be modeled by a quasiperiodic coherence function as in previous experiments that utilized atomic beams. In this work, we investigate the dependence of the photon scattering rate on the intensity and detuning of the traveling wave. We also study the effects of perturbing the interferometer with continuous-wave light and find that the dependence of the photon scattering rate on the intensity and detuning of the perturbing field is consistent with expectations.
Velocity-selective Raman transitions are widely used in atom interferometers to prepare atomic ensembles with narrowly defined momentum distributions. However, differential light shifts between atomic energy levels generate velocity distributions that are correlated with the Raman beam intensity, and therefore with the position of the atoms within the laser beam. We show that these spatially inhomogeneous velocity distributions interact with detuning-dependent systematic effects in a Bragg diffraction-based simultaneous conjugate Ramsey-Bordé interferometer. These interactions can induce systematic phase shifts of order 10 milliradians in the interferometer phase. We further identify a "magic" detuning for velocity selection and show that operating at this detuning suppresses the systematic phase shift. Magic velocity selection eliminates systematic errors arising from correlations between atom velocity and position, facilitating high-resolution atom interferometry experiments targeting sub-part-per-billion accuracy.