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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Ramsey interferometry with two frequencies

D. Seidel, Juan Gonzalo Muga, Ion Lizuain

Published Jun 7, 2007• 1 citation
Publisher

Abstract

The interference fringes of an atomic Ramsey interferometer may be narrowed if the two separated fields have different frequencies and their phase difference is controlled. For spatially separated fields, their width depends inversely on the free flight time of ground state atoms before entering the first field region in addition to the time between the fields. The narrowing effect is stable with respect to velocity fluctuations and for realistic mode functions. We also show that systematic phase shifts and phase fluctuations do not aggravate the frequency offset of the standard (one-frequency) Ramsey method.

DOI
10.1117/12.724279

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The interference fringes of an atomic Ramsey interferometer may be narrowed if the two separated fields have different frequencies and their phase difference is controlled. For spatially separated fields, their width depends inversely on the free flight time of ground state atoms before entering the first field region in addition to the time between the fields. The narrowing effect is stable with respect to velocity fluctuations and for realistic mode functions. We also show that systematic phase shifts and phase fluctuations do not aggravate the frequency offset of the standard (one-frequency) Ramsey method.
We investigate Ramsey interferometry for two separated fields oscillating with different frequencies. It is shown that the interplay between average and relative detuning leads to interference effects not present in the standard, single-frequency setup. For a large free-flight time of ground-state atoms before entering the first field region, the Ramsey fringes with respect to the relative detuning become much narrower than the usual ones. The stability of these effects with respect to phase or velocity fluctuations is discussed.
In a Ramsey atom interferometer excited by two electromagnetic fields, if atoms are under a time-varying scalar potential during the interrogation time, the phase of the Ramsey fringes shifts owing to the scalar Aharonov–Bohm effect. The phase shift was precisely examined using a Ramsey atom interferometer with a two-photon Raman transition under the second-order Zeeman potential, and a formula for the phase shift was derived. Using the derived formula, the frequency shift due to the scalar Aharonov–Bohm effect in the frequency standards utilizing the Ramsey atom interferometer was discussed.
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.
Implications of field quantization on Ramsey interferometry are discussed and general conditions for the occurrence of interference are obtained. Interferences do not occur if the fields in two Ramsey zones have precise number of photons. However in this case we show how two atom (like two photon) interferometry can be used to discern a variety of interference effects as the two independent Ramsey zones get entangled by the passage of first atom. PACS number(s): 03.75.Dg, 03.65.Ud, 42.50.-p Typeset using REVTEX 1 The method of using spatially separated fields as proposed by Ramsey has been proved to be very useful for high resolution work. It was originally proposed as a technique in the microwave domain [1] which was then extended to studies in optical domain [2]. More recently this technique has been used very successfully in the studies of quantum entanglement resulting from the interaction of atoms with radiation in a high quality cavity. In this context Ramsey technique enables one to study the entanglement in different basis of states
Abstract We study the Ramsey interference pattern of ultracold atoms crossing two electromagnetic fields, taking into account quantum motion effects. It is shown that quantum reflection and transmission at the fields lead to a modification of the standard fringes. The implications on present frequency standards are discussed. For weak coupling, the difference between the exact quantum result and the semiclassical result is small but results in a central peak shift that may become important for future accuracies of atomic clocks. In the strong coupling regime, a resonance structure with respect to the detuning is observed and the Ramsey setup acts as a matter‐wave Fabry‐Perot device. Our results question the advantage of using increasingly lower velocities in frequency standards because the peak shift and the resonance positions depend sensitively on very minor variations of the atomic velocity and are difficult to control.