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arXiv:0810.4455 · Physical Review A

Collisional decoherence in trapped-atom interferometers that use nondegenerate sources

James Stickney, Matthew B. Squires, James Scoville, Paul M. A. Baker, Steven Miller

Published Jan 22, 2009• 6 citations
arXivHTMLPDF

Abstract

The coherence time, and thus sensitivity, of trapped-atom interferometers that use nondegenerate gases are limited by the collisions between the atoms. An analytic model that describes the effects of collisions between atoms in an interferometer is developed. It is then applied to an interferometer using a harmonically trapped nondegenerate atomic gas that is manipulated with a single set of standing wave laser pulses. The model is used to find the optimal operating conditions of the interferometer and direct Monte Carlo simulation of the interferometer is used to verify the analytic model.

DOI
10.1103/physreva.79.013618

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The coherence time, and thus sensitivity, of trapped-atom interferometers that use nondegenerate gases are limited by the collisions between the atoms. An analytic model that describes the effects of collisions between atoms in an interferometer is developed. It is then applied to an interferometer using a harmonically trapped nondegenerate atomic gas that is manipulated with a single set of standing wave laser pulses. The model is used to find the optimal operating conditions of the interferometer and direct Monte Carlo simulation of the interferometer is used to verify the analytic model.
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.
The operation of a BEC based atom interferometer, where the atoms are held in a weakly confining magnetic trap and manipulated with counterpropagating laser beams, is analyzed. A simple analytic model is developed to describe the dynamics of the interferometer. It is used to find the regions of parameter space with high and low contrast of the interference fringes for both single and double reflection interferometers. We demonstrate that for a double reflection interferometer the coherence time can be increased by shifting the recombination time. The theory is compared with recent experimental realizations of these interferometers.
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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.
Atom interferometers using Bose-Einstein condensate that is confined in a waveguide and manipulated by optical pulses have been limited by their short coherence times. We present a theoretical model that offers a physically simple explanation for the loss of contrast and propose the method for increasing the fringe contrast by recombining the atoms at a different time. A simple, quantitatively accurate, analytical expression for the optimized recombination time is presented and used to place limits on the physical parameters for which the contrast may be recovered.
We analyze a Bose-Einstein condensate (BEC)-based free oscillation atom Michelson interferometer in a weakly confining harmonic magnetic trap. A BEC at the center of the trap is split into two harmonics by a laser standing wave. The harmonics move in opposite directions with equal speeds and turn back under the influence of the trapping potential at their classical turning points. The harmonics are allowed to pass through each other and a recombination pulse is applied when they overlap at the end of a cycle after they return for the second time. We derive an expression for the contrast of the interferometric fringes and obtain the fundamental limit of performance of the interferometer in the parameter space.