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Journal of Physics B Atomic and Molecular Physics

Radiofrequency multiple-quantum transitions in the presence of an optical pumping cycle

E. Arimondo, G. Moruzzi

Published Apr 1, 1976• 10 citations

Abstract

The theoretical behaviour of radiofrequency transitions with Delta m>or=1 in an atomic vapour under the simultaneous action of a longitudinal optical pumping, a static field introducing small decoupling between I and J and a relaxation mechanism is investigated. It is shown that the information contained in the eigenvalues and eigenvectors of the Hamiltonian of the atom 'dressed' by the RF field can be used to simplify significantly the equations of the time evolution of the atomic density matrix. Although an analytical solution is obtained only in a few simple cases a numerical solution is possible for any RF polarization. Several previous treatments are shown to be limiting cases of the general equations presented here. From the analysis of the recent experimental results of Arimondo and Corbalan (1974) on the ground state of 87 Rb, it turns out that the observable quantities are strongly dependent on all the parameters describing the simultaneous action of the pumping cycle, relaxation and the RF interaction. Thus accurate descriptions of the pumping cycle and the relaxation mechanism are required for any comparison with theory of experimental results for the widths and shifts of multiple-quantum transitions.

DOI: 10.1088/0022-3700/9/5/015

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The theoretical behaviour of radiofrequency transitions with Delta m>or=1 in an atomic vapour under the simultaneous action of a longitudinal optical pumping, a static field introducing small decoupling between I and J and a relaxation mechanism is investigated. It is shown that the information contained in the eigenvalues and eigenvectors of the Hamiltonian of the atom 'dressed' by the RF field can be used to simplify significantly the equations of the time evolution of the atomic density matrix. Although an analytical solution is obtained only in a few simple cases a numerical solution is possible for any RF polarization. Several previous treatments are shown to be limiting cases of the general equations presented here. From the analysis of the recent experimental results of Arimondo and Corbalan (1974) on the ground state of 87 Rb, it turns out that the observable quantities are strongly dependent on all the parameters describing the simultaneous action of the pumping cycle, relaxation and the RF interaction. Thus accurate descriptions of the pumping cycle and the relaxation mechanism are required for any comparison with theory of experimental results for the widths and shifts of multiple-quantum transitions.

Abstract We dress atoms with multiple-radiofrequency (RF) fields and investigate the spectrum of transitions driven by an additional probe field. A complete theoretical description of this rich spectrum is presented, in which we find allowed transitions and determine their amplitudes using the resolvent formalism. Experimentally, we observe transitions up to sixth order in the probe field using RF spectroscopy of Bose–Einstein condensates trapped in single- and multiple-RF-dressed potentials. We find excellent agreement between theory and experiment, including the prediction and verification of previously unobserved transitions, even in the single-RF case.

A theory is presented of induced Raman emission in a three-level system whose parameters are appropriate for microwave to optical frequencies. Solutions of the time-dependent Schrödinger equation are obtained for arbitrary intensity of the pump and signal radiations, which are assumed to be not too many line-widths off resonance. It is shown how the quantum-mechanical aspects of the problem may be separated from the statistical-mechanical aspects, in contrast to the density matrix techniques. The frequency dependence of the Raman emission on the frequency and intensity of the pumping radiation obtained by this method is presented and compared with the results we have obtained by other methods. The intensity and line shape of the Raman emission when the pump frequency is far off resonance are also obtained. The case of three interacting fields is also considered.

A set of operators, which act on the eigenstates of the atomic Hamiltonian in the presence of a partial I-J decoupling in a way analogous to the way the usual irreducible tensor operators act on the eigenstates of the total angular momentum, is introduced. Starting from these operators a set of operators, analogous to Haroche's pseudotensor operators, is obtained for the dressed-atom Hilbert space. They are thus particularly suitable to the theoretical treatment of the Delta m F >1 multiple quantum transitions within the Zeeman levels of a hyperfine state of an alkali atom. As an example, this treatment is applied to a system having a 'fictitious' spin F=1, and it is shown that the contribution of the single and multiple quantum transitions to the multipole components of the dressed-atom density matrix is separated.

Cs) atoms by applying circularly polarized light at an optimal frequency for electronic transitions from ground to excited states. To enhance control over sublevel populations following optical pumping, we incorporate a radiofrequency (RF) field. This integrated approach enables us to achieve a tailored distribution of atomic sublevel populations with high efficiency. Utilizing the Lindblad master equation, we provide a comprehensive framework for analyzing these dynamics, examining relaxation rates, repopulation processes, and the evolution of cesium Zeeman sublevels. Our findings underscore the effectiveness of the Lindblad master equation in accounting for external field effects and environmental interactions, significantly improving the accuracy and generalizability of optical pumping models. This method holds substantial promise for various applications in optical experiments, including magnetometry and quantum computing, paving the way for future advancements in these fields.

Relaxation experiments performed on alkali atoms polarized in their ground state by optical pumping in the presence of a rare gas have been previously reported and interpreted. It was shown that the relaxation governed by the spin-orbit interaction is strongly affected by the formation of chemically unstable Rb-Kr molecules bound by van der Waals forces. The previous theoretical analysis, restricted to the longitudinal relaxation, is extended here to relaxation processes involving the transverse components of the electronic polarization and hyperfine "coherences" (elements of the density matrix between different hyperfine states). The effects resulting from the action of a rf field are also examined. The main results of this work, among others, are (a) the prediction of a Zeeman transition-line pressure shift, in some circumstances larger by several orders of magnitude than the one calculated by Herman, and having a very peculiar variation with the rare-gas pressure; (b) a quantitative explanation of the anomalous pressure dependence of the hyperfine transition linewidth discovered by Bender and Cohen; (c) a proposal of a method of detection of rf transitions between states of the alkali---rare-gas molecules by their effect on the relaxation process.