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Bulletin of the American Physical Society

A New Technique for Measuring Atomic Recoil Frequency Using Coherence Functions

Scott Beattie, B. Barrett, I. Y. Chan, Carson Mok, Itay Yavin, Anantharaman Kumarakrishnan

Published May 22, 2009• 0 citations
OpenAlex

Abstract

We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency r as a function of the time at which the third pulse is applied, allowing r to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.

Related papers

Technique for measuring atomic recoil frequency using coherence functions

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We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency ${\ensuremath{\omega}}_{r}$ as a function of the time at which the third pulse is applied, allowing ${\ensuremath{\omega}}_{r}$ to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.

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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 $t=0$ and $t=T$ to diffract and recombine momentum states separated by $2\ensuremath{\hbar}k$ at $t=2T$. 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 $t=2T$ 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.

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Contrast Interferometry using Bose-Einstein Condensates to Measure h/m and α

Subhadeep Gupta, Kai Dieckmann, Zoran Hadzibabic +1 more

The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency, using an interferometric technique called "contrast interferometry." Optical standing wave pulses were used to create a symmetric three-path interferometer with a Bose-Einstein condensate. Its recoil phase, measurable with a single shot, varies quadratically with additional recoils and is insensitive to errors from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to 7 ppm precision, using a simple realization of this scheme. Plausible extensions should yield sufficient precision to attain a ppb-level determination of h/m and the fine structure constant alpha.

arXiv:cond-mat/0202452•Physical Review Letters•Sep 10, 2002•165 citations
We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency r as a function of the time at which the third pulse is applied, allowing r to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.
We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency ${\ensuremath{\omega}}_{r}$ as a function of the time at which the third pulse is applied, allowing ${\ensuremath{\omega}}_{r}$ to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.
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 describe progress toward a precise measurement of the recoil energy of an atom measured using a modified grating-echo atom interferometer (AI) that involves three standing-wave (sw) pulses. With this technique, an additional sw pulse is used to shift the phase of excited momentum states, which produces a modulation in the contrast of the interference pattern. The signal exhibits narrow fringes that revive periodically at twice the two-photon recoil frequency, $2{\ensuremath{\omega}}_{q}$, as a function of the onset time of the pulse. Experiments are performed using samples of laser-cooled rubidium atoms with temperatures $\ensuremath{\lesssim}$5 $\ensuremath{\mu}$K in a nonmagnetic apparatus. We demonstrate a measurement of ${\ensuremath{\omega}}_{q}$ with a statistical uncertainty of 37 parts per 109{10}^{9}109 (ppb) on a time scale of $\ensuremath{\sim}$45 ms in 14 h. Further statistical improvements are anticipated by extending this time scale and narrowing the signal fringe width. However, the total systematic uncertainty is estimated to be $\ensuremath{\sim}$6 parts per 106{10}^{6}106 (ppm). We describe methods of reducing these systematic errors.
Echo atom interferometers have emerged as interesting alternatives to Raman interferometers for the realization of precise measurements of the gravitational acceleration g and the determination of the atomic fine structure through measurements of the atomic recoil frequency ω q . Here we review the development of different configurations of echo interferometers that are best suited to achieve these goals. We describe experiments that utilize near-resonant excitation of laser-cooled rubidium atoms by a sequence of standing wave pulses to measure ω q with a statistical uncertainty of 37 parts per billion (ppb) on a time scale of ∼50 ms and g with a statistical precision of 75 ppb. Related coherent transient techniques that have achieved the most statistically precise measurements of atomic g-factor ratios are also outlined. We discuss the reduction of prominent systematic effects in these experiments using off-resonant excitation by low-cost, high-power lasers.
This thesis details the experimental investigation of a new type of atom interferometer using rubidium-85 atoms in the unexplored near-resonant domain. A cold cloud of atoms, all prepared in the same hyperfine ground state, are subjected to temporally periodic pulses of near-resonant standing waves of light. The standing wave pulses are made to act like an absorption grating where only atoms located around the low intensity region about the nodes remain in the initial ground state, the rest are pumped into a dark hyperfine ground state. The output of the atom interferometer is a measure of the fraction of atoms remaining in the initial ground state after N standing wave pulses for different times between the pulses. An increased survival rate is observed for certain times between pulses due to the occurrence of a coherence echo and the matter wave Talbot effect. This feature allows us to use our atom interferometer to make measurements of the Talbot time which is an important parameter in determinations of the fine structure constant alpha.\n\nWe provide a theoretical model to describe the relevant physics behind our atom interferometer that compares well with our empirical results. Design and implementation of the apparatus are discussed along with characterisation of parameters such as pulse duration, pulse number, and frequency. Finally we include a demonstration of how, in principle, our atom interferometer could be used to make precision measurements of the Talbot time along with some of the necessary steps to bring it in line with current leading measurements.
The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency, using an interferometric technique called "contrast interferometry." Optical standing wave pulses were used to create a symmetric three-path interferometer with a Bose-Einstein condensate. Its recoil phase, measurable with a single shot, varies quadratically with additional recoils and is insensitive to errors from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to 7 ppm precision, using a simple realization of this scheme. Plausible extensions should yield sufficient precision to attain a ppb-level determination of h/m and the fine structure constant alpha.