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Physical Review A

Influence of external potentials on optical Ramsey fringes in atomic interferometry

Jürgen Audretsch, Karl-Peter Marzlin

Published May 1, 1993• 10 citations
Publisher

Abstract

The interaction of an atomic beam with four traveling-wave laser beams leads to optically induced Ramsey fringes in the atomic beam. This experimental setup has been used as an optical frequency standard as well as a matter-wave interferometer. We calculate for two-level atoms the shift of the fringes due to the influence of fairly general external forces in lowest order of a perturbation approach. A comparison with the phase shift found in a corresponding WKB treatment of the interaction geometry is made. The consequences of beam reversal and cooling of the atomic beam are studied. As an application, we treat the linear acceleration and rotation of the interferometer and discuss the influence of space-time curvature.

DOI
10.1103/physreva.47.4441

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The interaction of an atomic beam with four traveling-wave laser beams leads to optically induced Ramsey fringes in the atomic beam. This experimental setup has been used as an optical frequency standard as well as a matter-wave interferometer. We calculate for two-level atoms the shift of the fringes due to the influence of fairly general external forces in lowest order of a perturbation approach. A comparison with the phase shift found in a corresponding WKB treatment of the interaction geometry is made. The consequences of beam reversal and cooling of the atomic beam are studied. As an application, we treat the linear acceleration and rotation of the interferometer and discuss the influence of space-time curvature.
We study in a general treatment the influence of a class of perturbations acting on the atoms of an atomic interferometer. An exact expression for the resulting shift of the interference pattern is given for an arbitrary number of laser zones with travelling or standing waves. The assumption made is that the two-level model is appropriate for the description of atoms and that the perturbations can be neglected in the laser zones. As an important application we calculate the influence acceleration, rotation, and space-time curvature on the Ramsey interferometer and the atomic fountain. The measurability of the respective phase shifts is discussed.
The influence of space-time curvature on quantum matter which can be theoretically described by covariant wave equations has not been experimentally established yet. In this paper we analyze in detail the suitability of the Ramsey atom beam interferometer for the measurement of the phase shift caused by the Riemannian curvature of the Earth or alternatively of two parallel oriented lead blocks. It appears that for the lead blocks the detection should be possible with realistic modifications of existing devices within the near future. For the Earth's gravitational field the experimental difficulties are too big. The paper is divided into two parts. The first one is concerned with the derivation of general relativistic correction terms to the Pauli equation starting from the fully covariant Dirac equation and their physical interpretation. The inertial effects of acceleration and rotation are included. The calculation makes use of Fermi coordinates. In the second part we calculate the shift of the Ramsey fringes for the two different sources of curvature and examine various possibilities to enlarge the sensitivity of the apparatus to space-time curvature. Since the two parts may be more or less interesting for physicists with different research fields they are written in such a way that each one may be read without much reference to the other one.
A calcium atomic beam excited in an optical Ramsey geometry was rotated about an axis perpendicular to the plane defined by the laser beams and the atomic beam. A frequency shift of the Ramsey fringes of several kHz has been measured which is proportional to the rotation frequency of the apparatus and to the distance between the laser beams. The results can be interpreted in three equivalent ways as the Sagnac effect in a calcium-atomic-beam interferometer: in the rotating frame of the laser beams either along straight paths or along the curved trajectories of the atoms, or in the inertial atomic frame.
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 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.
Summary form only given. The field of atom interferometry is experiencing rapid progress. Atom interferometers have been used to determine topological phase shifts such as the Aharonov-Bohm or Aharonov-Casher effects. Both two beam and more recently multiple beam atom interferometers have been realized. We report on an investigation of the electric (or scalar) Aharonov-Bohm effect in a multiple beam Ramsey experiment. The topological phase shift leads to collapse and revival of the fringe pattern. In a first interaction region cesium atoms are optically pumped into a dark coherent superposition of the magnetic quantum numbers m/sub F/=-4, -2, 0, 2 and 4 of the 6S/sub 1/2/ (F=4) ground state. The coherent superposition is probed after a time T in a second interaction region. When the atoms are irradiated in between the Ramsey interactions by an additional linearly polarized light field 400 MHz blue detuned to the F=4/spl rarr/F'=4 transition of the cesium D1 line, the induced AC Stark shift increases quadratically with the magnetic quantum number. The laser field coupling to the induced atomic dipole moment causes-in the absence of any classical forces-an electric Aharonov-Bohm phase shift.