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Israel Journal of Chemistry

Quantum Motion Effects in Atom Interferometry

Dirk Seidel, Juan Gonzalo Muga

Published Dec 1, 2007• 1 citation
Publisher

Abstract

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.

DOI
10.1560/ijc.47.1.67

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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.
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.
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.
Fundamental low-energy limits to the accuracy of quantum clock and stopwatch models in which the clock hand motion is activated by the presence of a particle in a region of space have been studied in the past, but their relevance for actual atomic clocks had not been assessed. In this work we address the effect of slow atomic quantum motion on Rabi and Ramsey resonance fringe patterns, as a perturbation of the results based on classical atomic motion. We find the dependence of the fractional error of the corresponding atomic clocks on the atomic velocity and interaction parameters.
We investigate the nonlinear Ramsey interferometry of a bosonic Josephson junction coupled to an optical cavity by applying two identical pumping field pulses separated by a holding field in the time domain. When the holding field is absent, we show that the atomic Ramsey fringes are sensitive to both the cavity-pump detuning and the initial state, and their periods can encode the information on both the atom-field coupling and the atom-atom interaction. For a weak holding field, we find that the fringes characterized by the oscillation of the intra-cavity photon number can completely reflect the frequency information of the atomic interference due to the weak atom-cavity coupling. This finding allows a nondestructive observation of the atomic Ramsey fringes via the cavity transmission spectra.
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 theoretically study the effects of elastic collisions on the determination of frequency standards via Ramsey-fringe spectroscopy in optical-lattice atom clocks. Interparticle interactions of bosonic atoms in multiply occupied lattice sites can cause a linear frequency shift, as well as generate asymmetric Ramsey-fringe patterns and reduce fringe visibility due to interparticle entanglement. We propose a method of reducing these collisional effects in an optical lattice by introducing a phase difference of $\ensuremath{\pi}$ between the Ramsey driving fields in adjacent sites. This configuration suppresses site-to-site hopping due to interference of two tunneling pathways, without degrading fringe visibility. Consequently, the probability of double occupancy is reduced, leading to cancellation of collisional shifts.