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arXiv:1008.4426 · Physical Review A

Numerical simulation of a multilevel atom interferometer

B. Barrett, Itay Yavin, Scott Beattie, Anantharaman Kumarakrishnan

Published Aug 31, 2010• 7 citations
arXivHTMLPDF

Abstract

We present a comprehensive numerical simulation of an echo-type atom interferometer. The simulation confirms an interesting theoretical description of this interferometer that includes effects due to spontaneous emission and magnetic sublevels. Both the simulation and the theoretical model agree with the results of experiments. These developments provide an improved understanding of several observable effects. The evolution of state populations due to stimulated emission and absorption during the standing-wave interaction imparts a time-dependent phase on each atomic momentum state. This manifests itself as an asymmetry in the signal shape that depends on the strength of the interaction as well as spontaneous emission due to a nonzero population in the excited states. The degree of asymmetry is a measure of a nonzero relative phase between interfering momentum states.

DOI
10.1103/physreva.82.023625

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We present a comprehensive numerical simulation of an echo-type atom interferometer. The simulation confirms an interesting theoretical description of this interferometer that includes effects due to spontaneous emission and magnetic sublevels. Both the simulation and the theoretical model agree with the results of experiments. These developments provide an improved understanding of several observable effects. The evolution of state populations due to stimulated emission and absorption during the standing-wave interaction imparts a time-dependent phase on each atomic momentum state. This manifests itself as an asymmetry in the signal shape that depends on the strength of the interaction as well as spontaneous emission due to a nonzero population in the excited states. The degree of asymmetry is a measure of a nonzero relative phase between interfering momentum states.
We have studied the effects of spontaneous emission (SE) on a single-state time domain atom interferometer (AI) that uses trapped Rb atoms. The AI uses two standing wave pulses separated by time TTT to produce an echo signal at time 2T2T2T due to interference between momentum states. We find that SE influences both the shape of the echo signal and its periodic time-dependent amplitude in a manner consistent with theoretical predictions. The results show that the time-dependent signal from the AI is related to the effective radiative decay rate of the excited state. We also present results that test theoretical predictions for several properties of the echo formation such as the variation in momentum transfer due to the change in the angle between the traveling wave components of the excitation pulses, strength of the atom-field interaction, and the effect of spatial profile of the excitation beams. These studies are important for realizing precision measurements of the atomic fine structure constant and gravity using this interferometer.
We have studied the effects of spontaneous emission (SE) on a single-state time domain atom interferometer (AI) that uses trapped Rb atoms. The AI uses two standing wave pulses separated by time TTT to produce an echo signal at time 2T2T2T due to interference between momentum states. We find that SE influences both the shape of the echo signal and its periodic time-dependent amplitude in a manner consistent with theoretical predictions. The results show that the time-dependent signal from the AI is related to the effective radiative decay rate of the excited state. We also present results that test theoretical predictions for several properties of the echo formation such as the variation in momentum transfer due to the change in the angle between the traveling wave components of the excitation pulses, strength of the atom-field interaction, and the effect of spatial profile of the excitation beams. These studies are important for realizing precision measurements of the atomic fine structure constant and gravity using this interferometer.
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.
We consider the evolution of a single-atom wave function in a time-dependent double-well interferometer in the presence of a spatially asymmetric potential. We examine a case where a single trapping potential is split into an asymmetric double well and then recombined again. The interferometer involves a measurement of the first excited state population as a sensitive measure of the asymmetric potential. Based on a two-mode approximation a Bloch vector model provides a simple and satisfactory description of the dynamical evolution. We discuss the roles of adiabaticity and asymmetry in the double-well interferometer. The Bloch model allows us to account for the effects of asymmetry on the excited state population throughout the interferometric process and to choose the appropriate splitting, holding, and recombination periods in order to maximize the output signal. We also compare the outcomes of the Bloch vector model with the results of numerical simulations of the multistate time-dependent Schr\"odinger equation.
Abstract A new type of atomic interferometer in which the registration is carried out by absorption spectroscopy of probing radiation is theoretically presented. To split the input atomic beam, the interaction with counterpropagating resonant waves is used. In addition, the atom also acquires equal populations at internal energy levels. The interaction with the subsequent traveling wave results in the interference between neighboring momentum states of the atom, and the distribution periodically varies with a strong asymmetry relative to the input momentum value. At the measurement stage, the result of the interference of matter waves is reproduced by the spectral distribution of the probing electromagnetic wave.
A theory of matter-wave interference is developed in which resonant, standing-wave optical fields interact with an ensemble of two-level atoms. If effects related to the recoil the atoms undergo on absorbing or emitting radiation are neglected, the total atomic density is spatially uniform. However, when recoil effects are included, spatial modulation of the atomic density can occur for times that are greater than or comparable to the inverse recoil frequency. In this regime, the atoms exhibit matter-wave interference that can be used as the basis of a matter-wave atom interferometer. Two specific atom-field geometries are considered, involving either one or two field-interaction zones. For each geometry, the recoil-induced spatial modulation of the total atomic density is calculated. In contrast to the normal Talbot and Talbot-Lau effects, the spatially modulated density is nota periodic function of time, owing to spontaneous emission; however, after a sufficiently long time, the contribution from spontaneous processes no longer plays a role and the periodicity is restored. With a suitable choice of observation time and field strengths, the spatially modulated atomic density serves as an indirect probe of the distribution of spontaneously emitted radiation.