The Zeeman effect in the excited A 2Pi(3/2) state of CaF is measured and analyzed over a wide range of magnetic fields. It is found that the splitting of the Zeeman levels is largely determined by the coupling between different rotational states and there are no low-field seeking states in the J=3/2 manifold of Zeeman levels at high magnetic fields. A model of the Zeeman spectrum based on the ligand-field theory of CaF is shown to be accurate in the interval of magnetic fields 0-5 Tesla. This demonstrates that the magnetic moment of the CaF(A 2Pi(3/2)) molecule is effectively determined by the spin angular momentum of a single electron and the orbital motion of the valence electron around the Ca2+ core. An analysis of the Zeeman spectrum as a function of the molecular rotational constant indicates that 2Pi(3/2) molecules should have significant rotational constants (at least as large as twice the rotational constant of CaF) to be amenable to magnetic trapping in high fields.
The Zeeman effect in the excited A 2Pi(3/2) state of CaF is measured and analyzed over a wide range of magnetic fields. It is found that the splitting of the Zeeman levels is largely determined by the coupling between different rotational states and there are no low-field seeking states in the J=3/2 manifold of Zeeman levels at high magnetic fields. A model of the Zeeman spectrum based on the ligand-field theory of CaF is shown to be accurate in the interval of magnetic fields 0-5 Tesla. This demonstrates that the magnetic moment of the CaF(A 2Pi(3/2)) molecule is effectively determined by the spin angular momentum of a single electron and the orbital motion of the valence electron around the Ca2+ core. An analysis of the Zeeman spectrum as a function of the molecular rotational constant indicates that 2Pi(3/2) molecules should have significant rotational constants (at least as large as twice the rotational constant of CaF) to be amenable to magnetic trapping in high fields.
The collision-induced Zeeman relaxation rate for collisions of CaF ${X}^{2}\ensuremath{\Sigma}({v}^{\ensuremath{'}\ensuremath{'}}=0)$ with 3He is measured to be ${\ensuremath{\Gamma}}_{\mathrm{Z}}=(7.7+5.4/\ensuremath{-}2.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }{\mathrm{cm}}^{3}/\mathrm{s}$ at 2 K. This rate is a direct measurement of the influence of spin-rotation coupling on Zeeman relaxation in the first rotational level of CaF. The relationship of this rate to known molecular constants is consistent with recent theory of cold molecular collisions and outlines the $^{2}\ensuremath{\Sigma}$ molecules conducive to magnetic trapping.
In a recent experiment [Weinstein et al., Nature 395, 148 (1998)] we magnetically trapped 108 ground-state calcium monohydride molecules, CaH(X 2Σ,v″=0, J″=0). The molecules were prepared by laser ablation of a solid sample of CaH2 and loaded via thermalization with a cold (<1 K) He3 buffer gas. The magnetic trap was formed by superconducting coils arranged in the anti-Helmholtz configuration. The detection was done by laser fluorescence spectroscopy excited at 635 nm (in the B 2Σ,v′=0−X 2Σ,v″=0 band) and detected at 692 nm (within the B,v′=0−X,v″=1 band). Both a photomultiplier tube and a CCD camera were used. Due to the thermalization of molecular rotation, only a transition from the lowest rotational state could be detected at zero field, N′=1, J′=3/2←N″=0, J″=1/2. In the magnetic field this rotational transition splits into two features, one shifted towards lower and one towards higher frequencies. The measured shifts are linear in field strength and indicate a small difference (0.02 μB) in the magnetic moments between the ground and excited states. Here we present a theoretical analysis of the observed magnetic shifts. These are identified as arising from a rotational perturbation of the B 2Σ,v′=0 state by a close-lying A 2Π,v′=1 state that lends the B state some of its A character. We find that the Hamiltonian can be well approximated by a 3×3 matrix built out of elements that connect states from within the Σ-doublet and the Π3/22 manifolds. The interaction parameter describing the Σ−Π coupling in the Zeeman Hamiltonian is determined from the observed shifts and the field-free molecular parameters of CaH given by Berg and Klyning [Phys. Scr. 10, 331 (1974)] and by Martin [J. Mol. Spectrosc 108, 66 (1984)].
Laser cooling and trapping in a magneto-optical trap (MOT) have been essential to the success of cold atom physics in the last decades. Recently, the application of the same techniques to molecules has begun. The complexity of even a simple diatomic molecule makes laser cooling difficult, but promises new applications in many areas of research. In this thesis I describe the development of the first three-dimensional MOT of calcium fluoride (CaF) molecules. First, a cryogenic buffer gas source was set up, producing a pulsed beam of 9.3*10^10 molecules per steradian per pulse with forward velocities around 170 m/s. A similar source for very large molecules was set up during a 5 month internship at the University of Vienna. Next, the molecular pulse was slowed down to the capture velocity of a MOT using chirped laser slowing, resulting in about 7*10^5 CaF molecules passing through the typical MOT volume of 1 cm^3 at velocities of 15+-5 m/s. A new deceleration method, called Zeeman-Sisyphus deceleration, was also investigated. In this method molecules move through a spatially varying magnetic field and are optically pumped between low- and high-field seeking states in such as a way that they are always losing kinetic energy. The method promises to deliver more slow molecules because the molecules are guided transversely as they are decelerated. A small prototype was built and the optical pumping step was tested successfully. Finally, 7.6*10^3 CaF molecules were trapped in a MOT and cooled to a temperature of 8.5 mK. The radial trap frequency is 2 pi*130 Hz and the damping constant is beta=9.5*10^2 s^-1. The lifetime is about 100 ms and depends strongly on the scattering rate. This MOT is an an ideal starting point for a wide range of new experiments with ultracold molecules.
This chapter discusses the prime cause of the magnetic moment within an individual atom. In the classical model, the angular momentum of the electrons can be used to determine the magnetic moments of the electrons by invoking the concept of electrical charge in motion. There are two contributions to the electronic magnetic moment: an orbital magnetic moment due to orbital angular momentum and a spin magnetic moment due to electron spin. The component of orbital angular momentum along the axis of a magnetic field is restricted to discrete values by quantum mechanics. Electrons have spin angular momentum, which can be represented by the spin quantum number. As the magnetic field is increased and the field splitting becomes greater than the multiple splitting, the anomalous Zeeman effect changes over to a normal Zeeman effect. The chapter looks at experimental evidence confirming the quantization of magnetic moments, specifically the Zeeman effect and the Stern-Gerlach experiment.
We investigate the helium dimer in strong magnetic fields, focusing on the spectrum of low-lying electronic states and their dissociation curves, at the full configuration-interaction level of theory. To address the loss of cylindrical symmetry and angular momentum as a good quantum number for nontrivial angles between the bond axis and magnetic field, we introduce the almost quantized angular momentum (AQAM) and show that it provides useful information about states in arbitrary orientations. In general, strong magnetic fields dramatically rearrange the spectrum, with the orbital Zeeman effect bringing down states of higher angular momentum below the states with pure σ character as the field strength increases. In addition, the spin Zeeman effect pushes triplet states below the lowest singlet; in particular, a field of one atomic unit is strong enough to push a quintet state below the triplets. In general, the angle between the bond axis and the magnetic field also continuously modulates the degree of σ, π, and δ character of bonds and the previously identified perpendicular paramagnetic bonding mechanism is found to be common among excited states. Electronic states with preferred skew field orientations are identified and rationalized in terms of permanent and induced electronic currents.
The theory of how excited-state hyperfine structure can be determined using a magnetic field to decouple the nuclear and electronic angular momentum is presented. The initial excited state is assumed to have an anisotropic Zeeman sublevel population distribution, which can be conveniently created by a laser-induced multiphoton excitation of an unpolarized atom. The Zeeman sublevel populations are subsequently mixed by the hyperfine interaction. The degree of mixing is controlled by a magnetic field applied along the quantization axis. The relative Zeeman sublevel populations can be monitored by detecting the polarization of fluorescence emitted when the excited state radiatively decays. It is convenient to take the ratio of two time-integrated fluorescent signals measured for orthogonal linear polarizations, since this is independent of the excited-state number density. The plot of this ratio versus magnetic field is very well approximated by a Lorentzian curve whose half-width is proportional to the magnetic dipole hyperfine coupling constant. This method was used to determine the magnitude of the magnetic dipole constant of the cesium 8D3/2 state to be 3.92\ifmmode\pm\else\textpm\fi{}0.10 MHz, which is in excellent agreement with previous results.