If an ensemble of atoms or molecules is excited by linearly polarized light, then usually one expects linearly polarized fluorescence form the ensemble. This reflects a symmetry of the excitation process, namely the fact that the electric field in a light wave and consequently the angular momentum distribution of atoms or molecules in an excited state can be characterized by a double headed arrow . An ensemble of particles in an excited state possesses a net alignment. In this paper some processes that for molecules'in an external field can break this symmetry are reviewed. As a result of symmetry breaking the ensemble of molecules acquires a net orientation of angular momentum, that can be characterized by a single headed arrow , and one can expect a circularly polarized fluorescence from this ensemble.
If an ensemble of atoms or molecules is excited by linearly polarized light, then usually one expects linearly polarized fluorescence form the ensemble. This reflects a symmetry of the excitation process, namely the fact that the electric field in a light wave and consequently the angular momentum distribution of atoms or molecules in an excited state can be characterized by a double headed arrow . An ensemble of particles in an excited state possesses a net alignment. In this paper some processes that for molecules'in an external field can break this symmetry are reviewed. As a result of symmetry breaking the ensemble of molecules acquires a net orientation of angular momentum, that can be characterized by a single headed arrow , and one can expect a circularly polarized fluorescence from this ensemble.
We know now how alignment and orientation of angular momenta arise in the excited state as a result of optical excitation from the primarily isotropic distribution of the ensemble of angular momenta. This phenomenon reflects, in essence, the anisotropy of absorption probability G (θ,ϕ). Since spatial structures of the type shown in Fig. 2.2 appear in the excited state the same structure must be ‘eaten out’ from the angular momentum distribution in the ground (initial) state. If the gap created is not closed quickly enough, the ensemble of the remaining angular momenta of the absorbing molecules in the ground state must necessarily also be polarized. If, from another point of view, fluorescent decay leads to a considerable population of the ground state level c, (see, e.g., Fig. 1.2), then molecules on this level may exhibit angular momenta polarization, being particularly noticeable for thermally unpopulated, high lying levels. In the present chapter we intend to discuss the conditions necessary for the creation of ground state angular momenta polarization, the possibilities of its experimental observation, and to develop the theoretical description of broad line radiation interaction with molecules further. Angular momenta polarization via depopulation For many years there existed the widespread opinion that in molecules we obtain an anisotropic distribution of angular momenta only in the excited state in the absorption process, whilst in the ground state isotropy is conserved [124]. This conjecture is based essentially on the assumption of the existence of a so-called ‘weak’ excitation. At first sight it may appear, for instance, from Eq. (2.20) that, as is usual in non-linear spectroscopy, such an admission is correct if condition Γ p /Γ ≫ 1 is valid.
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.
When a diatomic molecule is photodissociated on a singlet molecular potential energy surface to give two singlet atoms, one of which is electronically excited, the atoms are left in pure angular momentum states referred to the molecular quantization axis. Transformation of such pure states to a laboratory frame of reference gives atomic wave functions that are described as coherent superpositions of states. Application of an external magnetic field to an ensemble of excited atoms causes quantum beats, or, alternately, a Hanle effect to appear in the fluorescence emitted by the atoms. Calculations show that the interference effects are observed only for certain geometrical arrangements of the electric vector of the photodissociating radiation, the external field, and the polarization direction accepted by the fluorescence detector. The expressions for the fluorescence intensity show that the phase and modulation depth of the quantum beat can be used to determine the asymmetry parameter for recoil of the photofragments.
We present a detailed theoretical model and experimentally measured signals of alignment to orientation conversion (AOC) in the 7D3/2 and 9D3/2 states of cesium atoms in the presence of an external dc electric field [1]. Alignment produced by linearly polarized light can be converted into orientation by the quadratic Stark effect in an electric field if the angle between the electric field and the polarization vector of the exciting radiation is neither 0 or 90 degrees and if there are magnetic sublevels with Δm = ±1 that cross as the electric field is scanned. The appearance of orientation is verified by the appearance of a net circular polarization in the laser induced fluorescence. The theoretical model is based on the optical Bloch equation and extends models previously developed to solve the rate equations for Zeeman coherences in single-step [2] and double step laser excitation [3] of atoms. The agreement between the simulated and measured signals is excellent.
Excited-state angular-momentum alignment--orientation conversion for atoms with hyperfine structure in the presence of an external magnetic field is investigated. Transversal orientation in these conditions is reported. This phenomenon occurs under Paschen Back conditions at intermediate magnetic-field strength. Weak radiation from a linearly polarized diode laser is used to excite Rb atoms in a cell. The laser beam is polarized at an angle of $\ensuremath{\pi}/4$ with respect to the external magnetic-field direction. Ground-state hyperfine levels of the 5S1/2 state are resolved using laser-induced fluorescence spectroscopy under conditions for which all excited 5P3/2 state hyperfine components are excited simultaneously. Circularly polarized fluorescence is observed to be emitted in the direction perpendicular to both to the direction of the magnetic field B and direction of the light polarization E. The obtained circularity is shown to be in quantitative agreement with theoretical predictions.
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.