Relaxation of atomic polarization in para+n-coated alkali-metal vapor cells

Relaxation of atomic polarization in paraﬃn-coated alkali-metal vapor cells M. T. Graf, D. F. Kimball, S. M. Rochester, K. Kerner, C. Wong, and D. Budker ∗ Department of Physics, University of California at Berkeley, Berkeley, California 94720-7300 E. B. Alexandrov and M. V. Balabas S. I. Vavilov State Optical Institute, St. Petersburg, 199034 Russia V. V. Yashchuk Advanced Light Source Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (Dated: December 3, 2004) The relaxation of atomic polarization in buﬀer-gas-free, paraﬃn-coated cesium vapor cells is studied using a variation on Franzen’s classic technique of “relaxation in the dark” [Franzen, Phys. Rev. 115, 850 (1959)]. In the present experiment, narrow-band, circularly polarized pump light, resonant with the Cs D2 transition, orients atoms along a longitudinal magnetic ﬁeld, and time- dependent optical rotation of linearly polarized probe light is measured to determine the relaxation rates of the atomic orientation of a particular hyperﬁne level. The change in relaxation rates during light-induced atomic desorption (LIAD) is studied. No signiﬁcant change in the spin relaxation rate during LIAD is found beyond that expected from the faster rate of spin-exchange collisions due to the increase in Cs density. PACS numbers: PACS. 32.80. Bx, 34.50. Dy, 79.20. La I. INTRODUCTION Coating the walls of an alkali-metal vapor cell with paraﬃn wax reduces the relaxation rate of atomic polar- ization by up to four orders of magnitude [1–4]. Long- lived atomic polarization (relaxation times of ∼ 1 s has been observed) enables extremely sensitive measurements of magnetic ﬁelds [3–7], enhances nonlinear optical eﬀects at low light powers (see the review [8] and references therein), and may make possible precision tests of fun- damental symmetries [9–11]. Paraﬃn-coated cells have drawn attention in the study of light propagation dynam- ics [12, 13], for the generation of spin-squeezed states [14], and the creation and study of high-rank polarization mo- ments [15]. There has also been renewed interest in the application of paraﬃn-coated cells in miniaturized atomic clocks [16]. In spite of their wide and varied application and several detailed studies of their spin-relaxation prop- erties [2, 17–22], there is still much to learn about the causes of spin relaxation in paraﬃn-coated cells. In this study, we use a variation on Franzen’s classic technique of relaxation in the dark [23] to elucidate the mechanisms for spin-relaxation of cesium atoms in buﬀer- gas-free, paraﬃn-coated cells (prepared in the manner described in Ref. [24]). A circularly polarized laser beam (the pump beam), tuned to resonance with one of the hyperﬁne components of the D2 transition, propagates along the direction of an applied magnetic ﬁeld (ˆ ) and z polarizes the Cs atoms. The pump beam is abruptly blocked by a shutter and the decay of the atomic polariza- tion is monitored by measuring optical rotation of a weak, linearly polarized probe beam (propagating collinearly with the pump beam). A key challenge in the interpretation of the measure- ∗ Electronic address: budker@socrates.berkeley. edu ments is to determine the physical meaning of the optical signal, in particular how it relates to the atomic polariza- tion in the cell. In the usual implementation of Franzen’s technique, in which transmission of a circularly polarized probe is measured to determine the relaxation of atomic polarization, the observed signal depends on two quanti- ties [2, 29]: the longitudinal electronic polarization S z and the population diﬀerence between the two ground- state hyperﬁne levels S · I (here S represents the elec- tron spin and I represents the nuclear spin). The relation of the optical signal to the relaxation of S z and S · I depends on the spectral properties and polarization of the probe light [2]. Furthermore, the quantities S z and S · I can relax with several diﬀerent time constants depending on the relaxation mechanisms (e.g., spin-exchange collisions be- tween Cs atoms, electron-randomization collisions with the cell walls, relaxation due to exchange of atoms be- tween a metal sample in the stem of the cell and the vapor phase in the volume of the cell – known as the “reservoir eﬀect” [2]). Consequently, when narrow-band laser light is used, the observed signal in Franzen’s method relaxes with multiple rates that can be diﬃcult to distinguish. In contrast (as discussed in Sec. II A), by observing op- tical rotation of a linearly polarized probe beam as we do in the present experiment, under the magnetic ﬁeld con- ditions of our experiments (where for most measurements B < 10 G) the observed signal is well described with only two exponentials. Furthermore, the amplitudes of the ro- tation associated with the two exponentials turn out to be opposite in sign, allowing a clear distinction between the associated rates. We analyze our experimental re- sults using the concepts of atomic polarization moments (see, for example, Refs. [8, 25–28]), and ﬁnd that under appropriate conditions the optical signal is sensitive only to the rank-one multipole moment (orientation). We have used this technique of relaxation in the dark observed via optical rotation (RIDOVOR) to study the change in the relaxation rates of atomic polarization