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Journal of the Optical Society of America B

Experimental observation of the rotation properties of atomic multipoles

Dieter Suter, Thomas Marty

Published Jan 1, 1994• 7 citations
Publisher

Abstract

The resonant interaction of optical radiation with atomic vapors can excite the atoms into anisotropic states with long lifetimes. The conventional description of these states uses an expansion in a basis of multipole moments, which are represented by irreducible tensor operators. We demonstrate an experimental method that permits the excitation of these atomic multipole moments in specific, experimentally controllable spatial orientations. Complementary optical methods permit the observation of multipole moments of arbitrary order and a direct measurement of their spatial orientation. We demonstrate these procedures in the ground state of atomic sodium, using optical pumping to polarize the angular-momentum substates. We show how the experimental results can be used to separate signal contributions that originate from different multipole moments.

DOI
10.1364/josab.11.000242

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The resonant interaction of optical radiation with atomic vapors can excite the atoms into anisotropic states with long lifetimes. The conventional description of these states uses an expansion in a basis of multipole moments, which are represented by irreducible tensor operators. We demonstrate an experimental method that permits the excitation of these atomic multipole moments in specific, experimentally controllable spatial orientations. Complementary optical methods permit the observation of multipole moments of arbitrary order and a direct measurement of their spatial orientation. We demonstrate these procedures in the ground state of atomic sodium, using optical pumping to polarize the angular-momentum substates. We show how the experimental results can be used to separate signal contributions that originate from different multipole moments.
We theoretically investigate the magneto-optical rotation (MOR) effect in cesium atoms in the Voigt geometry, in which an off-resonance linearly polarized laser beam serves as both pump and probe. By calculating the detailed evolution of atomic multipole moments truncated to second-rank, alignment-to-orientation conversion (AOC) effects are observed in two hyperfine ground states. The mechanisms responsible for this effect are demonstrated. The tensor AC-Stark shift produced by the optical pumping generates a nonlinear effect, resulting in atomic alignment directly coupled to orientation, which enables spin orientation to be obtained. Simultaneously, spin-exchange collisions lead to atomic alignment and orientation transfer between two ground-state manifolds. Additionally, we present the analytical expression of atomic spin polarization described by atomic multipole moments, and the contributions of the AOC effect to the optical-rotation signals are discussed in different light power regimes. Our results can be helpful for guiding MOR experiments by refining and optimizing the parameters.
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A variation of the usual method of atomic orientation of alkali metal vapors by optical pumping is proposed. This variation consists of employing a single circularly polarized D1{D}_{1}D1​ line as pumping radiation, instead of a mixture of the two DDD lines. Under these conditions, one magnetic substate of the ground state is transparent to the pumping radiation. It is shown that for a sufficiently intense light source and relatively weak relaxation, the entire population of the vapor will tend to be pumped into this single state, resulting in nearly one-hundred percent atomic orientation. The pumping process is analyzed in detail for sodium vapor illuminated with $3{P}_{\frac{1}{2}}\ensuremath{-}3{S}_{\frac{1}{2}}$ radiation, and the time dependence of the populations of the eight magnetic sublevels of the ground state is computed. It is shown that in the steady state, the light absorption by the vapor is linear rather than exponential with distance. A simple method of measuring relaxation times based on this observation is suggested. The conditions under which the imprisonment of resonance radiation limits the size of the oriented sample are discussed, and it is suggested that the proposed technique will allow the alignment of larger samples than is possible by the usual method of optical pumping.
We describe a method of selective generation and study of polarization moments of up to the highest-rank kappa=2F possible for a quantum state with total angular momentum F. The technique is based on nonlinear magneto-optical rotation with frequency-modulated light. Various polarization moments are distinguished by the periodicity of light-polarization rotation induced by the atoms during Larmor precession and exhibit distinct light-intensity and frequency dependences. We apply the method to study polarization moments of 87Rb atoms contained in a vapor cell with antirelaxation coating. Distinct ultranarrow (1-Hz wide) resonances, corresponding to different multipoles, appear in the magnetic-field dependence of the optical rotation. The use of the highest-multipole resonances supported by a given system has important applications in quantum and nonlinear optics and in magnetometry.
For a quantum system, the density matrix contains all the statistical information that can be obtained from measurements. For excited atomic states, the coefficients in a spherical basis expansion of the density matrix, up to rank two, are proportional to Alignment and Orientation Parameters given by Fano and Macek and are called the state multipoles or multipole moments. They can be experimentally determined from the measurements of the Stokes parameters of the emitted photon. To obtain maximum possible information, one needs to break the axial symmetry of the experiment by specifying a reflection plane determined through a coincidence measurement. For LS coupled atomic states, if one can spectroscopically resolve J-multiplets, and if the process is spin dependent, information about the contributions to the state multipoles due to orbital and spin angular momenta can be extracted. In the process, it is also possible to determine the octupole moments of the excited state due to orbital and spin angular momenta. An illustrative example from transfer-excitation reactions in He+-Ar collisions at low keV energies will be presented. For coupling schemes other than LS coupling, using a similar decoupling one can determine the contributions due to appropriate angular momenta. The method is general enough that one can apply it to ion, atom, electron or photon projectiles incident on atomic targets.