PHYSICAL REVIEW A VOLUME 50, NUMBER 6 DECEMBER 1994 Dispersive and nondispersive phase shifts in atomic Stern-Gerlach interferometry O. Gorceix, J. Robert, S. Nic Chormaic, Ch. Miniatura, and J. Baudon Laboratoire de Physique des Lasers, Universite Paris — Nord, Avenue J. B. Clement, 93430 Villetaneuse, France (Received 15 March 1994) We present experimental results on metastable hydrogen-beam Stern-Gerlach interferometry using ei- ther static magnetic fields or time-dependent magnetic fields. The shared experimental scheme is presented. The dispersive behavior of the induced phase shift in the static situation is evidenced. The time-dependent (pulsed) scheme has provided experimental evidence for an external wave-function phase shift in atom force-free dynamical evolution. This so-called scalar Bohm-Aharonov (SAB) effect is thoroughly investigated. As opposed to the static field case, the nondispersive behavior of the SAB effect is validated. Experiments that mix static and pulsed magnetic fields are performed to reach the pro- visional goal to test nontrivial phase additivity. In all cases, experimental results are shown to be con- sistent with theoretical predictions derived from a tentative model including the deterministic magnetic phase shifts as well as additional random shifts due to experimental imperfections. PACS number(s): 03. 75. Dg, 03. 65. Bz I. INTRODUCTION Atom interferometry has attracted increased research interest in recent years with the realization of several practical devices. Such interferometers have already been used for studies of interaction effects acting on atomic motion as well as for fundamental tests of quan- tum theory [1]. In previous papers [2,3], we showed that a device based on the longitudinal Stern-Gerlach effect gives opportunities for atom phase investigations. There, static magnetic-field gradients were being used both for the realization of the interferometer elements and for the phase object. The present paper is aimed at providing ex- perimental evidence that time-dependent magnetic fields can be used as well. As shown in an earlier paper [4], substantially different results are obtained with pulsed fields as compared to static fields. The present paper is an extension of this work; it involves a detailed validation of the scalar Bohm-Aharonov (SAB) effect in atomic in- terferometry. The paper is organized as follows. In Sec. II, the basic Stern-Gerlach interferometry (SGI) experimental method is described. In Sec. III, we list a summary of experimen- tally observed interference patterns with static magnetic phase objects. Then, we turn to pulsed magnetic fields and show that, contrary to the static case, the coherence length of the beam does not impose any limitation on the number of visible fringes. Nevertheless, it is argued that uncontrolled (though limited) experimental imperfections impinge on the interference pattern visibility. Finally, we report experimental results involving the superposition of static and time-dependent phase objects. A11 reported ob- servations are consistent with the previously published theoretical description [2 — 5]. In Sec. IV, the results are discussed with emphasis on the prospects for realization of a longitudinal, as well as a transverse Stern-Gerlach in- terferometer using a succession of four magnetic-field pulses. This type of device will be very similar to the atom interferometers that use the mechanical effect of light to split the atom wave packet [6 — 9]. II. EXPERIMENTAL METHOD On the one hand, the eff'ects induced by magnetic fields on Zeeman state populations and coherences have been known for a long time and are used in many applications. On the other hand, the (historical) Stern-Gerlach experi- mental scheme demonstrates how magnetic-field gra- dients can influence the external motion of atoms [10]. It is only recently that it has been realized how the inter- play between internal and external degrees of freedom might be used to build and operate atomic SGI [11, 12, 5]. The principle of our interferometer relies on Zeeman state preparation of a thermal beam of metastable 2s, &z hydrogen atoms and bears similarities with optical and neutron polarization interferometers [13, 14]. The experi- mental apparature has already been described in detail in previous publications [2 — 5, 15]. It is schematically shown in Fig. 1. The beam of metastable hydrogen atoms H'(2s) is produced by a 100-eV electronic bombardment 'Permanent address: St. Patrick's College, Maynooth, Ireland. FIG. 1. Experimental setup; G, electron gun: P, A; polarizer and analyzer; M, M', mixers: p; magnetic shield: R; magnetic profile region (phase object): D; detector. 1050-2947/94/50(6)/5007(7)/$06. 00 50 5007 1994 The American Physical Society