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Journal de Physique II

Atomic quantum phase studies with a longitudinal Stern-Gerlach interferometer

Jacques Robert, Christian Miniatura, O. Gorceix, S. Le Boiteux, V. Lorent, J. Reinhardt, J. Baudon

Published Apr 1, 1992• 28 citations
Publisher

Abstract

A general description of atomic interferometers in terms of the scattering operator is given. The action of a longitudinal interferometer on an atom described by an incident polarized wavepacket is shown to be equivalent to a frame transformation, leading to a “beaded” atom. The special case of a pure longitudinal gradient of magnetic field and that of a spatially precessing field are examined. An experiment using metastable hydrogen atoms is presented and the results obtained in both situations mentioned above are discussed. Properties of beaded atoms produced by relatively strong fields (∼10 G) are investigated by means of the intensity diagram of their electrically induced radiative decay.

DOI
10.1051/jp2:1992155

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Conference on Lasers and Electro-Optics•Aug 29, 2005•0 citations
A general description of atomic interferometers in terms of the scattering operator is given. The action of a longitudinal interferometer on an atom described by an incident polarized wavepacket is shown to be equivalent to a frame transformation, leading to a “beaded” atom. The special case of a pure longitudinal gradient of magnetic field and that of a spatially precessing field are examined. An experiment using metastable hydrogen atoms is presented and the results obtained in both situations mentioned above are discussed. Properties of beaded atoms produced by relatively strong fields (∼10 G) are investigated by means of the intensity diagram of their electrically induced radiative decay.
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.
A quadrupolar static magnetic field used as a phase object in a Stern-Gerlach atom interferometer produces phase shifts proportional to the distance to the zero-field line. As a consequence the transverse intensity profile of the atomic beam beyond the interferometer is modulated by an interference pattern which is a ``phase portrait'' of the field configuration. This pattern---a central bright spot surrounded by annular fringes---can be translated as a whole in any transverse direction by adding a homogeneous field to the quadrupolar field. These effects have been investigated experimentally with a beam of metastable hydrogen atoms H∗(2s),{\mathrm{H}}^{*}(2s),H∗(2s), either by measuring the atom flux through a fixed slit or by scanning the beam profile through a movable hole. The results are in good agreement with the theoretical predictions.
A coherent electric analogue of the Stern-Gerlach experiment has been performed with helium atoms in Rydberg states. The atoms, travelling in pulsed supersonic beams, were prepared in superpositions of Rydberg states with different static electric dipole polarisabilities using pulses of microwave radiation. State-dependent forces were then exerted on them, transverse to their direction of propagation, using inhomogeneous electric fields. These fields were generated between a pair of electrodes in a wedge configuration. The forces applied resulted in the coherent evolution of each atomic wavepacket into a superposition of spatially separated momentum states. The classical paths of least action associated with these momentum states evolved over time up to a separation of ∼2 nm. The coherent evolution of the atoms, and hence the superposition of atomic wavepackets in this ‘half-loop’ electric Rydberg-atom interferometer, was monitored by measuring the internal Rydberg state populations at the end of each measurement cycle. The experimental data are in good quantitative agreement with the results of semiclassical calculations of the phase evolution of the atomic superposition states which account for contributions from Stark shifts, the momentum differences between the classical paths of least action through the apparatus, and the spatial separation of the atomic wavepackets.
A detailed analysis of the classic Stern–Gerlach experiment is presented. An analytical simple solution is presented for the quantum description of the translational and spin dynamics of a silver atom in a magnetic field with a gradient along a single z-direction. This description is then used to obtain an approximate quantum description of the more realistic case with a magnetic field gradient also in a second y-direction. An explicit relation is derived for how an initial off center deviation in the y-direction affects the final result observed at the detector. This shows that the “mouth shape” pattern at the detector observed in the original Stern–Gerlach experiment is a generic consequence of the gradient in the y-direction. This is followed by a discussion of the spin dynamics during the entry of the silver atom into the magnet. An analytical relation is derived for a simplified case of a field only along the z-direction. A central question for the conceptual understanding of the Stern–Gerlach experiment has been how an initially unpolarized spin ends up in a polarized state at the detector. It is argued that this can be understood with the use of the adiabatic approximation. When the atoms first experience the magnetic field outside the magnet, there is in general a change in the spin state, which transforms from a degenerate eigenstate in the absence of a field into one of two possible non-degenerate states in the field. If the direction of the field changes during the passage through the device, there is a corresponding adiabatic change of the spin state. It is shown that an application of the adiabatic approximation in this way is consistent with the previously derived exact relations.
Summary form only given. Spatial coherences are measured by means of a new atom interferometry technique. First, a coherent superposition of the Zeeman components of the atom is built by means of well-controlled magnetic interactions. Second, pulsed inhomogeneous magnetic fields are employed to coherently separate and reunite the atomic substates via the Stern-Gerlach induced forces. Finally, atomic interference fringes are recorded on the state-selected outcoming sample by changing the spatial separation. This method bears strong similarities with the Fourier-transform spectroscopy of light. The interferogram visibility curve yields the atom sample spatial coherences. For example, when the applied magnetic gradients are parallel to the atom trajectory, one gets the coherence length by varying the overlap of the separated wavepackets. Several experiments on cold cesium atoms have been performed and are presented. Furthermore, we have used our magnetic cooling method to prepare the atom cloud upstream from the interferometer. Large enhancements of the coherence length are demonstrated.