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Physical Review A

Optimization of Bragg scattering from atomic gratings for echo interferometry

Gehrig Carlse, Jaskaran Randhawa, Eduardo Ramos, Thomas Vacheresse, Alexander Pouliot, Adam C. Carew, Anantharaman Kumarakrishnan, B. Barrett

Published Oct 8, 2024• 5 citations
Publisher

Abstract

We investigate the characteristics of near resonant Bragg scattering, the underlying process that produces a signal in a grating-echo atom interferometer. We explore how the density modulation produced in an atomic sample by momentum state interference and optical channeling can be optimally read out using a coherently Bragg-scattered traveling-wave electric field. When both the channeling and Bragg scattering processes are optimized, we report a 20-fold increase in scattering efficiency. Our results suggest that a quantitative understanding of the atomic confinement achievable by channeling is possible through an analysis of reflectivity spectra.

DOI
10.1103/physreva.110.043306

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Physical Review Letters•Oct 9, 1995•218 citations
We investigate the characteristics of near resonant Bragg scattering, the underlying process that produces a signal in a grating-echo atom interferometer. We explore how the density modulation produced in an atomic sample by momentum state interference and optical channeling can be optimally read out using a coherently Bragg-scattered traveling-wave electric field. When both the channeling and Bragg scattering processes are optimized, we report a 20-fold increase in scattering efficiency. Our results suggest that a quantitative understanding of the atomic confinement achievable by channeling is possible through an analysis of reflectivity spectra.
We investigate channeling oscillations in the contrast of a density grating formed by exposing a sample of ultracold atoms to an optical standing-wave pulse. We show that these dynamics can be imprinted on the free-induction decay signal following standing wave excitation as well as on the echo signal associated with a two-pulse atom interferometer (Carlse et al. Phys. Rev. A, 109, 043307 (2024)). Experimental results are supported by a simple model, which describes the grating contrast as the combination of two separate physical effects, namely, matter-wave interference and classical optical channeling resulting in Pendellösung-like oscillations. We also investigate the characteristics of near resonant Bragg scattering (Carlse et al. Phys. Rev. A. 110, 043306 (2024)), the underlying process that produces the echo signal. We explore how the density modulation produced in an atomic sample by momentum state interference and optical channeling can be optimally read out using a coherently Bragg-scattered traveling-wave electric field. When both the channeling and Bragg scattering processes are optimized, we report a 20-fold increase in scattering efficiency.
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 investigate channeling oscillations in the contrast of a density grating formed by exposing a sample of ultracold atoms to an optical standing-wave pulse. We show that these dynamics can be imprinted on the echo signal associated with a two-pulse atom interferometer. Experimental results are supported by a simple model, which describes the grating contrast as the combination of two separate physical effects, namely, matter-wave interference and classical optical channeling resulting in Pendell\"osung-like oscillations. We discuss the enhancement in signal strength of echo interferometers that can be achieved by relying on these oscillations.
This dissertation describes the development of a suite of interlinked techniques for precision metrology with matter wave lattices realized in a ceiling-to-floor non-magnetic atom trapping apparatus. This work involves the development of a single-state atom interferometer that relies on the observation of density gratings formed in the atomic ground state of a laser-cooled sample. These gratings, the result of Kapitza-Dirac diffraction of momentum states following a standing wave optical excitation pulse, typically dephase according to their velocity distribution, and motional properties of the sample, including the local value of gravitational acceleration g, are imprinted on the grating contrast and phase. These features can be extracted by coherently backscattering a travelling wave readout field applied within the thermal coherence time of the sample and measuring the grating free-induction decay. Alternatively, a grating echo, resulting from the application of two standing wave pulses separated by t=T_{21}, can be detected using the same backscattering method in the vicinity of the echo time t=2T_{21} on time scales defined by the transit of cold atoms out of the standing wave beam volume. This dissertation presents five main experimental results that impact a new generation of cold atom quantum sensors. Firstly, we investigate a technique for measuring the magnetic moments and sublevel distributions of laser-cooled gases. Secondly, we study optical channell-ing which can be used to increase the scattering efficiency of optical lattices and the sensitivity of grating-echo interferometers. Thirdly, we describe Bragg scattering of a readout pulse from optical lattices and develop a technique to optimize this process in dilute gas lattices, leading to increased signal strengths in echo interferometers. Fourthly, we demonstrate a novel "Ramsey" velocimeter which can measure sample center-of-mass velocity with a precision of 600 µm/s. Finally, we present a measurement of g which represents the first realization of a frequency domain echo-type gravimeter, with a sensitivity to g of 2 parts per million. We outline the basis for improving the precision of these sensors to realize devices capable of measuring g with a sensitivity of 10 parts per billion and probing velocities more precisely than all other atomic velocimeters.
We have studied sub-optical wavelength atomic gratings generated by the interference of atomic de Broglie waves in a time-domain interferometer. Three short optical standing- wave pulses, detuned from resonance with a cloud of approximately 100 (mu) K 85Rb atoms, act as phase gratings for atomic matter waves. Shortly after the first pulse, a modulation in the atomic density containing spatial harmonics of period (lambda) /2N appears ((lambda) is the optical wavelength, and N is any integer) and then rapidly vanishes due to the atomic thermal motion. The cloud maintains phase memory of this modulation, however, and the second pulse (applied at time T after the first one) results in a temporal sequence of atomic density gratings of periods (lambda) /2N. The appearance of a grating is referred to as an echo. The third pulse (and a subsequent traveling wave pulse) is used to detect these gratings. By this technique, we have created and detected in real time a grating with period (lambda) /4 at time 1.5T after the first pulse and observed new types of `echoes' caused by interaction of the de Broglie waves with all three phase gratings. This ability to produce sub-wavelength structures makes our techniques applicable to atomic beam lithography.
We observe coherently enhanced reflection (Bragg scattering) of a near resonant laser beam from cesium atoms ordered by a periodic array of optical potential wells known as an optical lattice. The reflected light is enhanced by a factor of $\ensuremath{\sim}{10}^{5}$ over scattering from a disordered atomic sample. We measure the magnitude of the reflectivity and its detuning dependence as functions of the density and the degree of localization of the atoms. The change in lattice constant due to the frequency-dependent effective index of refraction seen by the lattice light field is observed.