The Rabi frequency (coupling strength) of an electric-dipole transition is an important experimental parameter in laser-cooling and other atomic physics experiments. Though the relationship between Rabi frequency and atomic wavefunctions and/or atomic lifetimes is discussed in many references, there is a need for a concise, self-contained, accessible introduction to such calculations suitable for use by the typical student of laser cooling (experimental or theoretical). In this paper, I outline calculations of the Rabi frequencies for atoms with sub-structure due to orbital, spin and nuclear angular momentum. I emphasize the physical meaning of the calculations.
The Rabi frequency (coupling strength) of an electric-dipole transition is an important experimental parameter in laser-cooling and other atomic physics experiments. Though the relationship between Rabi frequency and atomic wavefunctions and/or atomic lifetimes is discussed in many references, there is a need for a concise, self-contained, accessible introduction to such calculations suitable for use by the typical student of laser cooling (experimental or theoretical). In this paper, I outline calculations of the Rabi frequencies for atoms with sub-structure due to orbital, spin and nuclear angular momentum. I emphasize the physical meaning of the calculations.
The electronic structure, including the spin–orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω(±) and 2s+1Ʌ(+/-) representation. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energies De agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ -Π, Π - ∑+ and Δ - Φ transitions among specific Ω(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission Aν′ν, and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character fionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.
A simple way to calculate Rabi frequencies is outlined for interactions of atomic or nuclear multipole moments with laser fields that focuses on their relative geometry. The resulting expression takes the form of a dot product between the laser polarization and a vector spherical harmonic, thereby naturally connecting to the multipole's far-field spontaneous-emission pattern and providing a way to visualize the interaction. Since the vector spherical harmonics are not yet a standard tool in quantum science, their relevant properties are reviewed. This approach is illustrated in the calculation of a variety of beam effects, yielding both perturbative corrections and some nontrivial cases with non-vanishing coupling.
When optical frequency fields are used to couple a ground state to a Rydberg state, the resonant dipole coupling is to a low angular momentum state. Higher angular momentum states are typically thought not to play a role in the excitation. The extremely large dipole matrix elements coupling Rydberg states of the same n but differing l, however, allow optical fields of modest strengths to produce Rabi frequencies larger than optical frequencies. We demonstrate that these optical fields can therefore readily excite the higher angular momentum states, and we examine the consequences of this coupling.
This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics. Beginning with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the author goes on to discuss the Clebsch-Gordan coefficients for a two-component system. After developing the necessary mathematics, specifically spherical tensors and tensor operators, the author then investigates the 3- j , 6- j , and 9- j symbols. Throughout, the author provides practical applications to atomic, molecular, and nuclear physics. These include partial-wave expansions, the emission and absorption of particles, the proton and electron quadrupole moment, matrix element calculation in practice, and the properties of the symmetrical top molecule.
This concise and accessible book provides a detailed introduction to the fundamental principles of atomic physics at an undergraduate level. Concepts are explained in an intuitive way and the book assumes only a basic knowledge of quantum mechanics and electromagnetism. With a compact format specifically designed for students, the first part of the book covers the key principles of the subject, including the quantum theory of the hydrogen atom, radiative transitions, the shell model of multi-electron atoms, spin-orbit coupling, and the effects of external fields. The second part provides an introduction to the four key applications of atomic physics: lasers, cold atoms, solid-state spectroscopy and astrophysics. This highly pedagogical text includes worked examples and end of chapter problems to allow students to test their knowledge, as well as numerous diagrams of key concepts, making it perfect for undergraduate students looking for a succinct primer on the concepts and applications of atomic physics.
We present the ab initio study of spin-orbit coupling effects on laser cooling of BeI and MgI molecules. Potential energy curves for the X(2)Σ(+)(1/2), A(2)Π(1/2,3/2), and 2(2)Π(3/2,1/2) states are calculated using multi-reference configuration interaction method plus Davidson corrections. Spectroscopic parameters of BeI and MgI are in excellent agreement with available experimental and theoretical values. The A(2)Π(3/2) state of MgI is a repulsive state. It is an unsuitable scheme for the A(2)Π(3/2)(υ')← X(2)Σ(+)(1/2) (υ″) transition for laser cooling of MgI. Highly diagonally distributed Franck-Condon factors f00 for the A(2)Π(1/2,3/2) (υ' = 0) ← X(2)Σ(+)(1/2) (υ″ = 0) transitions and suitable radiative lifetimes τ for the A(2)Π(1/2,3/2) (υ' = 0) of BeI and MgI are obtained. Three laser wavelength drives are required for the A(2)Π(1/2,3/2)(υ')←X(2)Σ(+)(1/2) (υ″) transitions of BeI and MgI. The proposed cooling wavelengths of BeI and MgI are both in the violet region. The results imply the feasibility of laser cooling of BeI and MgI, and that laser cooling of BeI is more possible.