List of Figures

1. 1. Figure 1.1 Schematic diagram (not to scale) of the hierarchical structure of the electronic, vibrational, and rotational energy levels for a typical molecule.
   2. Figure 1.2 Typical frequencies of electromagnetic field (in Hz) required to excite hyperfine, fine structure, rotational, vibrational, and electronic transitions in diatomic molecules.
   3. Figure 1.3 The electronic potentials of the molecule OH arising from the interaction of the oxygen atom in two lowest-energy electronic states labeled and with the hydrogen atom in the ground electronic state. The curves are labeled using standard spectroscopic notation [3]. In particular, the symbol X is the standard label for the lowest-energy (ground) electronic state of the molecule. These potential energies were calculated in Ref. [6].
   4. Figure 1.4 Couplings between different electronic states may affect the vibrational motion of molecules. These couplings become negligible when the electronic states are separated by a large amount of energy.
   5. Figure 1.5 The vibrational energy levels of the OH molecule in the ground electronic state . Only 10 lowest-energy levels are shown. The inset shows the vibrational wave functions for , , and .
2. 1. Figure 2.1 The molecular potential and the dipole moment function of the molecule LiCs in the ground electronic state .
   2. Figure 2.2 Shifts of the energy levels and in the presence of a perturbation that couples the states and .
   3. Figure 2.3 The Stark shifts of the rotational energy levels of a diatomic molecule in a electronic state with the permanent dipole moment and the rotational constant as functions of the electric field strength .
   4. Figure 2.4 The Stark shifts of the rotational energy levels of a diatomic molecule in a electronic state. The energy levels presented are for the molecule CaH, which has  cm ,  cm , and the dipole moment Debye. The different panels correspond to different values of in the limit of zero electric field. Bear in mind that is not a good quantum number because the electric-field-induced interaction (2.36) couples states with different .
   5. Figure 2.5 The Stark shifts of the rotational energy levels of a diatomic molecule in a electronic state. The energy levels presented are for the molecule OH, which has  cm ,  cm ,  cm ,  cm and the dipole moment Debye.
3. 1. Figure 3.1 A correlation diagram between the low- and high-field limits for states from within the ground electronic state and excited electronic state of the molecule CaH. The dashed lines show the perturbing states of the state coupled to the states by the operators. The states from within the and manifolds are labeled by the Hund's case (b) angular momentum quantum numbers in the low-field limit and their projections on the direction of the field axis in the high-field limit.
   2. Figure 3.2 Zeeman levels of a CaF molecule in the rotational state characterized by of the electronic state: Full curves-accurate calculations; dashed lines-the magnitudes of the diagonal matrix elements given by Eq. (3.47).
   3. Figure 3.3 Symbols - measured frequency shift for the (circles) and (triangles) transitions; curves - direction cosine calculations.
   4. Figure 3.4 Zeeman splitting of the hyperfine energy levels of Rb Cs( ) in the ground rotational state.
4. 1. Figure 4.1 A schematic diagram of the field-free molecular energy levels and shown by solid lines and the states and shown by dashed lines. The time-dependent operator couples with both and . The rotating wave approximation eliminates the coupling to .
   2. Figure 4.2 Stark shifts of the rotational energy levels of a molecule in an off-resonant microwave field.
5. 1. Figure 5.1 The rotational angular momentum of a linear molecule is perpendicular to the molecular axis. Here, we assume that , as is the case for a molecule in a electronic state. A molecule with the molecular axis oriented at an angle with respect to the -axis can be in a superposition of angular momentum states with and projections, representing an aligned angular momentum state.
   2. Figure 5.2 The expectation value of the orientation angle cosine of a rigid rotor in a DC electric field vs the dimensionless parameter for three lowest energy states with . The full lines show the results computed with Eq. (5.8) and the dotted lines with Eq. (5.9). Typical values of for simple diatomic molecules are in the range of 0-12. The values of are shown for higher values of to illustrate that the limit of is approached slowly, even for the lowest energy state.
   3. Figure 5.3 The eigenstates of a quantum pendulum (a) and a rigid rotor in a DC field (b). The vertical lines show the energies and the curves - the square of the corresponding wave functions plotted as functions of the orientation angle . The wave functions are not normalized and scaled for better visibility. The bound states of the rigid rotor are labeled by the quantum number . The bound states and wave functions are calculated for . The energy is in the units of for the planar pendulum and in the units of for the rigid rotor.
   4. Figure 5.4 Energy levels of a rigid rotor in an off-resonant laser field. The energy is in units of the rotational constant and the molecule-field interaction strength is in units of . The figure illustrates that the interaction with the laser field brings the molecular states of opposite parity together.
   5. Figure 5.5 The eigenstates of a rigid rotor in an AC electric field. The horizontal lines show the energies and the curves - the square of the corresponding wave functions plotted as functions of the orientation angle . The wave functions are not normalized and enhanced for better visibility. The bound states of the rigid rotor are labeled by the quantum number . The bound states and wave functions are calculated for . The energy is in the units of .
   6. Figure 5.6 An optical centrifuge for molecules. The spinning electric field is created by splitting a laser pulse at the center of its spectrum and applying an opposite frequency chirp to the two halves.
6. 1. Figure 6.1 The low-field-seeking and high-field-seeking states in the Stern-Gerlach experiment.
   2. Figure 6.2 Paths of molecules. The two solid curves indicate the paths of two molecules having different moments and velocities and whose moments are not changed during passage through the apparatus. This is indicated by the small gyroscopes drawn on one of these paths, in which the projection of the magnetic moment along the field remains fixed. The two dotted curves in the region of the magnet indicate the paths of two molecules the projection of whose nuclear magnetic moments along the field has been changed in the region of the magnet. This is indicated by means of the two gyroscopes drawn on the dotted curves, for one of which the projection of the magnetic moment along the field has been increased, and for the other of which the projection has been decreased.
   3. Figure 6.3 The electric field potential generated by a monopole (a), dipole (b), and quadrupole (c).
   4. Figure 6.4 An illustration of a device called "centrifuge decelerator" for the production of slow molecules. The molecules are injected into the space between four electrodes bent into a spiral shape. The spiral is then rotated to decelerate molecules moving toward the center by the inertial force. The electrodes are bent upward at the end of the spiral,...