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Physical Review A

Multistep preparation into a single Zeeman sublevel in a Rb87 vapor cell: Theory and experiment

Salvatore Micalizio, Aldo Godone, Filippo Levi, Claudio Eligio Calosso

Published Aug 24, 2009• 16 citations
Publisher

Abstract

In this paper we propose a pumping scheme to concentrate nearly all the atoms of an alkali-metal vapor into one of the ground-state Zeeman sublevels. We report theory and experiment for the case of $^{87}\text{R}\text{b}$ in a cell with buffer gas but the technique easily applies to other alkali-metal atoms. The pumping scheme consists of a suitable sequence of laser and microwave pulses after which a large fraction of atoms is transferred into the desired level. The efficiency of this technique depends mainly on the laser power and on the relaxation effects taking place inside the cell; in principle, more than 95% of the atoms can be prepared in a well-defined quantum state. Diagnostic of the resulting population distribution is made observing the free-induction decay signal at the output of a microwave cavity. This multistep laser-microwave pumping technique is particularly suited for compact vapor-cell frequency standards working in pulsed regime or in experiments where it is necessary to maintain the cylindrical symmetry of the experimental arrangement.

DOI
10.1103/physreva.80.023419

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In this paper we propose a pumping scheme to concentrate nearly all the atoms of an alkali-metal vapor into one of the ground-state Zeeman sublevels. We report theory and experiment for the case of 87Rb^{87}\text{R}\text{b}87Rb in a cell with buffer gas but the technique easily applies to other alkali-metal atoms. The pumping scheme consists of a suitable sequence of laser and microwave pulses after which a large fraction of atoms is transferred into the desired level. The efficiency of this technique depends mainly on the laser power and on the relaxation effects taking place inside the cell; in principle, more than 95% of the atoms can be prepared in a well-defined quantum state. Diagnostic of the resulting population distribution is made observing the free-induction decay signal at the output of a microwave cavity. This multistep laser-microwave pumping technique is particularly suited for compact vapor-cell frequency standards working in pulsed regime or in experiments where it is necessary to maintain the cylindrical symmetry of the experimental arrangement.
A scheme for concentrating a large fraction (\ensuremath{\sim}100%) of the alkali-metal atoms in an atomic vapor in any single magnetic sublevel of the ground state is developed. This is experimentally demonstrated in the 87Rb^{87}\mathrm{Rb}87Rb vapor. The atomic vapor is optically pumped to a high degree of spin polarization after which two radio-frequency \ensuremath{\pi} pulses are applied to transfer the atomic population from the (2,2) or (2,-2) (F,MF{\mathit{M}}_{\mathit{F}}MF​) state to the (2,0) sublevel of the ground state. The resulting distribution is diagnosed using a microwave field tuned to the hyperfine transition (6834 MHz).
We present a multilevel theoretical approach to describe the behavior of a pulsed optically pumped (POP) 87Rb^{87}\mathrm{Rb}87Rb frequency standard based on a microwave cavity-vapor cell arrangement. The full Zeeman manifold of the ground-state hyperfine levels is then considered, and the dynamics induced among them by relaxation processes (buffer gas, spin exchange, and cell-walls collisions) is taken into account. The model includes as well the absorption of the pumping laser along the cell and the cavity feedback on the atoms; the effects related to a nonuniform excitation of the atomic sample are also discussed. Theoretical predictions are proven with a laboratory prototype of POP passive maser in which the clock transition is excited by means of the Ramsey technique. The agreement between theory and experiment is very satisfactory from both a quantitative and qualitative point of view, in terms of the shape of the Ramsey fringes, microwave power delivered by the atoms, and short-term frequency stability. In particular, a frequency stability of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at one second has been measured, in very good agreement with the expected value. On this basis, the model has been extended to predict the short-term frequency stability of a POP frequency standard operating with optical detection. A shot-noise limited frequency stability (Allan deviation) of ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$ is foreseen. This value can be degraded by microwave phase noise and laser fluctuations so that the overall predicted clock stability is ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$.
The distribution of population in the ground-state sublevels of an optically pumped alkali-metal vapor has been found to be strongly dependent on the mechanism assumed responsible for relaxation. Two modes of optical pumping zero mixing and complete mixing in the excited state, and three modes of alkali relaxation, uniform, Zeeman, and electron randomization, are considered. Calculations of the sublevel relative populations are made in terms of experimentally measurable parameters for all six combinations of pumping and relaxation modes. Optical-pumping transient signals are then used to demonstrate that alkali relaxation due to wall collisions is of the low-frequency "Zeeman" variety, while relaxation due to alkali-rare-gas collisions takes place through randomization of the spin of the alkali valence electron. Equations for the rate of change of the electronic spin polarization are derived for all cases, and are found to be nonexponential, in contrast with the case of an alkali of zero nuclear spin.
Abstract Incorporating the rate equations of the laser pumped atomic system, the population evolution of the Cesium Zeeman sublevels is calculated and discussed when a specific sequence of laser pulses irradiate the Cesium vapor. In this scheme, after the equalization of the sublevel populations by a magnetically resonant RF pulse, using a left (right) circularly polarized laser pulse the whole atomic population transfer to high (low) projection numbers. Then by irradiating a right (left) polarized laser pulse with appropriate duration and intensity, the desired population distribution could be obtained. The effects of different sequence parameters on the population distribution of Zeeman sublevels are investigated and it is shown that by proper process adjustment it is possible to arbitrary engineer the population distribution. Preparing the desired distribution of the population in the atomic sublevels is substantially important in different light–matter interaction experiments.
It is experimentally demonstrated that, using diode lasers for optical pumping and RF /spl pi/-pulses for population transfer, nearly all of the ground state Rb atoms in a vapor cell can be concentrated into one of the two M/sub F/ = 0 sublevels. The fractional population difference /spl Delta/ between the two M/sub F/ = 0 levels can be made as high as 1. This should result in a very significant improvement (about a factor of 100) in the S/N over the conventional discharge-lamp-pumped rubidium frequency standards (RFSs). This would lead to a substantial improvement in the short-term stability of the RFS. This is a pulsed population transfer scheme. The microwave interrogation takes place in the absence of strong pumping light. This has the potential for eliminating the light shift and thereby improving the long-term frequency stability of a an RFS.>
Coherent-population-trapping resonance in vapor cell is a quantum interference effect that appears in the two-photon transitions between the ground-state hyperfine levels of alkali-metal atoms and is often utilized in miniature and centimeter-scale clock devices. To quantitatively understand and predict the performance of this phenomenon, it is necessary to consider the transitions and relaxations between all hyperfine Zeeman sublevels involved in the different excitation processes of the atom. In this paper, we constructed a computational multilevel atomic model of the Liouville density-matrix equation for 32 Zeeman sublevels involved in the D1{D}_{1}D1​ line of 133Cs^{133}\mathrm{Cs}133Cs irradiated by two frequencies with circularly polarized components and then simulated the amplitude and shape of the resonance spectrum of the transmitted light through centimeter-scale Cs-vapor cells. We show that the numerical solutions of the equation and analytical investigations adequately explain a variety of the characteristics observed in the experiment.