Atomic Stern-Gerlach interferences with time-dependent magnetic fields

Abstract

In atomic Stern-Gerlach (polarization) interferometry with time-dependent magnetic fields both the spatial and temporal parts of the atomic phase are generally affected. This leads to a total energy shift and to an inelastic momentum transfer. Some of the related effects are studied using a beam of metastable hydrogen atoms. In particular the scalar Aharonov-Bohm effect and its nondispersivity are considered, in addition to other phase shift effects occurring where the field gradient differs from zero. PACS numbers: 03.75.0g, 03.65.Bz The Stern-Gerlach -or polarization -interferometric method has proven to be a simple and versatile tool to investigate momentum distributions, coherence [I], and quantum phase properties of beams of neutral particles with nonzero spin such as neutrons [2,3] and atoms [4].For atoms, only time-independent magnetic fields have been used so far. In such experiments, the total energy is conserved, which means that the phase shifts accumulated by the different Zeeman states (labeled by M) essentially deal with the spatial part of the phase. As a consequence, the interference phenomenon involves elements of the density matrix in momentum space with momenta of equal magnitude (elastic scattering by the magnetic potentials). In this respect, longitudinal Stern-Gerlach (LSG) interferometry [5] provides direct information about the longitudinal coherence length of the beam.More recently, using transverse magnetic gradients, our group has investigated angular coherence properties [6].A completely diff'erent situation is encountered when time-dependent fields are used. In the general case where spatial dependence (field gradients) and time dependence coexist, both the spatial and temporal parts of the phase are affected. In other words, for each Zeeman state M, the total energy is changed and a net momentum transfer is allowed to occur. As will be shown later, when a pulsed magnetic 6eld is used different results are obtained according to the spatial dependence of the 6eld "seen" by the particle during the pulse. In order to clarify this point one may first notice that when thermal kinetic energies are considered there is no contradiction in assuming AK p(K, z, t) = -dt'W z -(I -t') h(t'), (la) A« Nl which for times larger than to+ T may be written as 8 fp+T p(K, z, t) = -dt'W z-4 fp (t -r') . (Ib) This (localized) phase perturbation propagates at a group velocity of AK/m. For a specific Zeeman state M, an incoming wave packet with a momentum distribution C(K) evolves into an outgoing wave packet for t & to+ T given by that (i) the size of the wave packet describing the external motion is small at the macroscopic scale defined by the field profile and (ii) it is large compared to the de Broglie wavelength.Second, in the frequency range of the time variation of the fields typically used here (f & GHz) propagation effects are negligible. We will assume that the magnetic field keeps a fixed direction throughout the paper as this is the case experimentally. Hence the Zeeman interaction is diagona...

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“…This effect-now called the scalar Aharonov-Bohm effect-was originally proposed for electrons in a time-varying electric field, but is practically verified using neutral particles with a magnetic moment in a time-varying magnetic field (for example, neutrons [8] and hydrogen atoms [9]). In a Ramsey atom interferometer under a time-varying scalar potential, the phase of the Ramsey fringe shifts, since atoms with different magnetic quantum numbers are subjected to different scalar Aharonov-Bohm effects.…”