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Physical Review A

Biaxial spatial orientation of atomic angular momentum

Valery Milner, Yehiam Prior

Published Mar 1, 1999• 10 citations
Publisher

Abstract

We experimentally create and theoretically explain a different type of highly anisotropic atomic angular-momentum distribution with two preferential axes. Such a biaxial spatial orientation is created by optical pumping with elliptically polarized light, and measured by the observation of coherent population trapping in a weak external magnetic field. We probe the angular-momentum distribution by the Hanle configuration, and observe two dark resonances at nonzero magnetic fields---the expected signature of the biaxial spatial geometry. A direct method for preparing arbitrarily oriented atomic ensembles is discussed.

DOI
10.1103/physreva.59.r1738

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The interaction of laser light of arbitrary polarization with systems of high angular momentum is considered. We show that elliptically polarized light creates an anisotropic spatial distribution of atomic and molecular angular momentum which is qualitatively different from the alignment and orientation induced by light of circular or linear polarization. Multilevel coherent population trapping within a manifold of ground-state magnetic sublevels results in a nonclassical behavior of a high-$J$ molecular rotor. The classical approximation for the angular momentum distribution is compared with the exact quantum calculations, and is shown to fail in cases of long interaction times and high intensities of the exciting light. In these limits, the quantum uncertainty defines the spatial width of the angular distribution. The applicability of the classical treatment is analyzed and found to be different in the cases of $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ and $\stackrel{\ensuremath{\rightarrow}}{J}J$ transitions. A biaxial spatial orientation with two preferential axes of rotation is experimentally created in sodium atoms via coherent population trapping by elliptically polarized light. A method for producing an arbitrary orientation of atomic angular momentum by magnetic field assisted coherent population trapping is proposed.

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We experimentally create and theoretically explain a different type of highly anisotropic atomic angular-momentum distribution with two preferential axes. Such a biaxial spatial orientation is created by optical pumping with elliptically polarized light, and measured by the observation of coherent population trapping in a weak external magnetic field. We probe the angular-momentum distribution by the Hanle configuration, and observe two dark resonances at nonzero magnetic fields---the expected signature of the biaxial spatial geometry. A direct method for preparing arbitrarily oriented atomic ensembles is discussed.
The interaction of laser light of arbitrary polarization with systems of high angular momentum is considered. We show that elliptically polarized light creates an anisotropic spatial distribution of atomic and molecular angular momentum which is qualitatively different from the alignment and orientation induced by light of circular or linear polarization. Multilevel coherent population trapping within a manifold of ground-state magnetic sublevels results in a nonclassical behavior of a high-JJJ molecular rotor. The classical approximation for the angular momentum distribution is compared with the exact quantum calculations, and is shown to fail in cases of long interaction times and high intensities of the exciting light. In these limits, the quantum uncertainty defines the spatial width of the angular distribution. The applicability of the classical treatment is analyzed and found to be different in the cases of $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ and $\stackrel{\ensuremath{\rightarrow}}{J}J$ transitions. A biaxial spatial orientation with two preferential axes of rotation is experimentally created in sodium atoms via coherent population trapping by elliptically polarized light. A method for producing an arbitrary orientation of atomic angular momentum by magnetic field assisted coherent population trapping is proposed.
The Wigner representation of angular-momentum orientation in the classical limit on $J\ensuremath{\gg}1$ has been used to derive an equation of angular-momentum motion in the case of a closed two-level system interacting with an arbitrary polarized radiation. This equation enables us to carry out a theoretical analysis of angular-momentum motion and consider final states of the quantum system for all types of dipole transitions. We have found that in the case of a zero magnetic field in the final state of the system with $\stackrel{\ensuremath{\rightarrow}}{J}J$ or $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ optical transition, the angular momentum is directed along or opposite to the wave vector of the radiation depending on the sign of the polarization ellipsity, while for a linear polarization the angular momentum is isotropically distributed on the plane orthogonal to the polarization vector. For the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition two directions of angular momentum are possible in the final state. These directions are determined by the ellipsity of polarization. The spatial size of the final distribution of the angular momentum has been defined by the quantum uncertainty, 1/J,1/\sqrt{J},1/J​, of the angular-momentum orientation. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ or $\stackrel{\ensuremath{\rightarrow}}{J}J,$ transition particles come into ``dark'' states while for the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition they occupy the ``brightest'' state. In the presence of a nonzero magnetic field, particles with $\stackrel{\ensuremath{\rightarrow}}{J}J$ transition have in the final state only one angular-momentum orientation, i.e., along or opposite to the direction of the magnetic field depending on the polarization ellipsity sign. For the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition both directions are possible, i.e., along and opposite to the magnetic field. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition the directions of the angular momentum form a cone around the magnetic field.
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.
Anisotropy of angular momenta: ideas and methods The fundamental idea forming the basis of early quantum theory was the quantization of the angular momentum of the atom, which, at a later stage, assumed the form of the Bohr–Sommerfeld quantization rule [360], namely ∲ pdq = n ℏ where p and q are the generalized momentum and coordinate. This concept has retained its physical meaning in modern-day quantum mechanics [371, 372]. In the course of the further development of quantum mechanical concepts it became increasingly clear that in the theory of atoms and molecules the angular momentum is a ‘dominant’ notion, the fundamental significance of which is in no small degree connected with its dimension of action, which coincides with that of Planck's constant ℏ. In the interaction between particles and a directed beam of photons the angular momentum of the system is conserved, thus forming the basis for the optical method of producing spatial anisotropy of the distribution of the angular momenta of the ensemble of particles, i.e. its optical polarization . In terms of quantum concepts, spatial anisotropy means that in an ensemble of particles a non-equilibrium population of magnetic sublevels m j of angular momenta is created. We make a distinction between the alignment of momenta, for instance in the absorption of linear polarized light, when there is no difference between the population of ± m j -sublevels, and orientation , when such a difference exists. Anisotropic distribution of angular momenta in an excited state, as produced in absorption, manifests itself directly in the polarization of fluorescence. It is rather likely that understanding of the anisotropic distribution of the angular momenta of atoms was enhanced by Hanle's [184] discovery in 1924.
Optically pumped magnetometers usually rely on optical pumping using circularly or linearly polarized light. We study here zero-field magnetometers pumped with elliptically polarized light, preparing both atomic orientation and alignment with complementary geometries. We start by extending the three-step approach for elliptically polarized pumping. This allows us to study the Hanle effect in elliptical polarization by comparing the analytical absorption signals with experiments made on 4He^{4}\mathrm{He}4He metastable state. We then study parametric resonance magnetometers based on elliptical polarization by using the dressed-atom formalism with one and two radio-frequency fields. The results show good agreement with the experimental measurements and interesting perspectives for magnetometry where symmetry breaking by pumping light is mitigated.
We report the experimental observation of alignment to orientation conversion in the 7D3/2 and 9D3/2 states of Cs in the presence of an external dc electric field and without the influence of magnetic fields or atomic collisions. Initial alignment of angular momentum states was created by two-step excitation with linearly polarized laser radiation. The appearance of transverse orientation of angular momentum was confirmed by the observation of circularly polarized light. We present experimentally measured signals and compare them with the results of a detailed theoretical model based on the optical Bloch equations. The effect is odd under time reversal and should be taken into account in ever more sensitive searches for an electron electric dipole moment.