Ramsey-type spectroscopy of alkali spin coherence in sealed glass cells: Measurement of geometric quantum phases

Abstract

We report on the detection of ground state spin coherence in coated spherical, cylindrical, and toroidal sealed glass cells by pump/probe experiments, where the pump and probe region may be spatially separated. This constitutes an atomic beam situation for the sub-ensemble of atoms which enters the detection region after having left the pump region. The dependence of the recorded spin signals on the optical frequencies of the pump and probe lasers are discussed and simulated by Monte-Carlo calculations involving the effect of wall collisions. As a first application the measurement of topological phase changes of spin quantum states due to a rotation of the magnetic field direction along the path of flight are reported. PACS: 32.30.Dx; 32.80.Bx; 03.65.Bz If atoms are optically polarized in a magnetic field different techniques may be applied to increase the longitudinal and transversal relaxation times, like the confinement in buffer gases [1] or the coating of the wall surface by non-disorienting agents. Time-of-flight effects like diffusion from the pump area may be overcome by separated pump and probe regions. This idea follows Ramsey’s original technique [2] for precisely measuring the atomic magnetic moment in an atomic beam setup by applying two separated oscillating fields which excite transitions between ground state sublevels in a magnetic field. The oscillating fields are light waves in our case exciting sublevel coherences in the alkali ground state transversally to a magnetic field, if modulated optical pumping is in phase with the Larmor precession. In its simplest way atoms are excited by a single pulse short compared to the Larmor period. If narrowband lasers are used (spectral linewidth Doppler broadened absorption width) solely atoms within a small segment of the velocity distribution are pumped. They form the “atomic beam” which is to be probed by a second light wave. Special coating of the cell wall allows the atoms to collide several hundred times with the wall before the spin orientation ∗To whom the correspondence should be addressed. is completely destroyed. These reflections can be directly observed [3] and can give rise to extra resonances in zero-field level crossings [4]. The resonances do not show higher-order Ramsey fringes due to velocity averaging but their width strongly depends on the probability of the coherences being quenched during a collision with the inner surface of the cell. It is not the reflection of the atoms from the wall which makes a Ramsey resonance to appear but the combination with the frequency of the narrow-band lasers which allows to be more sensitive for atoms approaching from a well-defined direction. This paper is divided into three parts, which describe optical pumping and magnetic resonance experiments with separated pump and probe regions like in atomic beam experiments, except that they are performed in coated sealed glass cells. The first part continues earlier experiments on cylindrical cells [3, 4] and extends the theory developed therein to include the laser-frequency dependence of the spin signals when surface reflections are taken into account. A characteristic waveform of the signal due to reflection of the atoms from the wall surface back into the detection region (which overlaps with the pump region) can be detected in a spherical cell if the laser frequencies are properly chosen. The situation can be described by Bell-Bloom type optical pumping [5] with modulation of intensity (or polarization, or laser frequency) resulting in a spatially inhomogeneous distribution of spin magnetization after the pumping process. If spin detection is performed by a narrow optical probe beam the temporal evolution of spin magnetization can be spatially resolved and thus the motion of the atoms carrying the spin can be mapped out. Comparison of experimental findings and Monte-Carlo type calculations allows for a determination of the spin destruction probability on the wall. The second part deals with situations in which pump and detection beams are spatially separated, establishing a glass cell atomic beam with a Maxwellian velocity distribution. This is demonstrated by means of a cylindrical cell. Spinpolarized atoms can be detected without considerable loss of intensity after they have travelled 5 cm along a tube of 1 cm in diameter. The high frequency resolution should allow a precise determination of phase changes, e. g. due to the interaction of