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Physical Review A

Observation of ground-state Ramsey fringes

M. Weel, Anantharaman Kumarakrishnan

Published Jun 26, 2003• 22 citations
Publisher

Abstract

We have used trapped ${}^{85}\mathrm{Rb}$ atoms to demonstrate an atom interferometric measurement of atomic recoil in the frequency domain. The measurement uses echo techniques to generate a Ramsey fringe pattern. The pattern exhibits recoil components consistent with theoretical predictions. We find the measurement to be insensitive to magnetic field gradients and discuss the prospects for a precision measurement of the recoil frequency.

DOI
10.1103/physreva.67.061602

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We have used trapped 85Rb{}^{85}\mathrm{Rb}85Rb atoms to demonstrate an atom interferometric measurement of atomic recoil in the frequency domain. The measurement uses echo techniques to generate a Ramsey fringe pattern. The pattern exhibits recoil components consistent with theoretical predictions. We find the measurement to be insensitive to magnetic field gradients and discuss the prospects for a precision measurement of the recoil frequency.
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.
We propose a set of experiments in which Ramsey-fringe techniques are tailored to probe transitions originating and terminating on the same ground state level. When pulses of resonant radiation, separated by a time delay $% T, $ interact with atoms, it is possible to produce Ramsey fringes having widths of order 1/T. If each pulse contains two counterpropagating travelling wave modes, the atomic wave function is split into two or more components having different center-of-mass momenta. Matter-wave interference of these components leads to atomic gratings, which have been observed in both spatially separated fields and time separated fields. Time-dependent signals can be transformed into frequency dependent signals, leading to ground state Ramsey fringes (GSRF). The signals can be used to probe many problems of fundamental importance: a precise measurement of the earth gravitational acceleration ggg and residual gravity in a microgravity environment with an accuracy 610−9g;6 10^{-9}g;610−9g; the rotation rate measurement with an accuracy of 6 10^{-3} deg/h; the recoil frequency measurement. Since only transitions originating and terminating on the same ground state are involved, frequency measurements can be carried out using lasers phase-locked by quartz oscillators having relatively low frequency. Our technique may allow one to increase the precision by a factor of 100 (the rf- to quartz oscillator frequencies ratio) over previous experiments based on Raman-Ramsey fringes or reduce on the same factor requirements for frequency stabilization.
We investigate theoretically and by numerical simulations the effects of the atomic recoil on the frequency and fringe contrast of microwave atomic frequency standards. Such effects arise because of the influence of external degrees of freedom on the phases and the spatial positions of the interfering wave packets. We show under which conditions such effects lead to a frequency shift and examine the loss of contrast of the interference signal (Ramsey fringes). We use an interferometric description to model the frequency standards, treating simultaneously internal and external degrees of freedom. We consider multiple momentum exchanges in 3D between the atoms and the standing microwave field inside the cavity leading to a large number of wave packets that leave the cavity with different momenta. At detection, these wave packets interfere giving rise to Ramsey fringes that are modulated by the interference of the external states of the wave packets. Similar treatments have proved efficient when treating ID recoil effects in standing laser waves. We apply this theoretical model numerically to laser cooled atomic fountain frequency standards and investigate the behaviour of the observed signal as a function of the frequency standard parameters (microwave power, launching height, etc.). Finally, we discuss possible experimental methods that could be used to observe such effects.
We report on interference studies in the internal and external degrees of freedom of metastable triplet helium atoms trapped near quantum degeneracy in a $$1.5 \,\upmu {\mathrm{m}}$$ optical dipole trap. Applying a single π/2\pi /2π/2 rf pulse we demonstrate that 50% of the atoms initially in the m=+1m=+1m=+1 state can be transferred to the magnetic field insensitive m=0m=0m=0 state. Two π/2\pi /2π/2 pulses with varying time delay allow a Ramsey-type measurement of the Zeeman shift for a high precision measurement of the 2 3S12\,^3S_123S1​ – 2 1S02\,^1S_021S0​ transition frequency. We show that this method also allows strong suppression of mean-field effects on the measurement of the Zeeman shift, which is necessary to reach the accuracy goal of 0.1 kHz on the absolute transition frequencies. Theoretically the feasibility of using metastable triplet helium atoms in the m=0m=0m=0 state for atom interferometry is studied demonstrating favorable conditions, compared to the alkali atoms that are used traditionally, for a non-QED determination of the fine structure constant.
We present results on a free-space atom interferometer operating on the first order magnetically insensitive |F = 1,mF = 0) --> |F = 2,mF = 0) ground state transition of Bose-condensed (87)Rb atoms. A pulsed atom laser is output-coupled from a Bose-Einstein condensate and propagates through a sequence of two internal state beam splitters, realized via coherent Raman transitions between the two interfering states. We observe Ramsey fringes with a visibility close to 100% and determine the current and the potentially achievable interferometric phase sensitivity. This system is well suited to testing recent proposals for generating and detecting squeezed atomic states.