An ion is located in a crystal at a site that is not a centre of inversion, with a Zeeman field directed at right angles to the crystal axis c. Periodic intensity variations in the optical spectrum that occur when the crystal is rotated about c are due to magnetic dipole transitions between levels of different type and to electric dipole transitions between levels having admixed opposite-parity parts of different type. Use of an antiunitary operator that commutes with the total Hamiltonian demonstrates that interference between electric and magnetic dipole radiation (or interference between any opposite-parity multipole radiation) does not occur for transitions appearing in the axial spectrum, but does occur for those appearing in the pi or sigma transverse spectrum. Depending on the site symmetry, two or four of the Zeeman components of a doublet-doublet transition have an additional periodicity as a result of this interference. Eigenstates are constructed that show the relationship between the M values of a Zeeman level, the crystal quantum number that labels it, and its type, and are used to calculate the angular dependence of certain doublet-doublet dipole transitions for ions at sites of point symmetries D 2d and C 3h . With explicit expressions for dipole matrix elements, it is discovered that two Zeeman components having the same angular dependence when interference is neglected exhibit dissimilar angular behaviour when the interference cross-term is included.
We have discovered an interference which results in the vanishing of some electric dipole transition amplitudes. A transition-matrix element
T between certain
S and
P sublevels with the same value of
MF vanishes when an applied magnetic field satisfies ${X}_{s}+{X}_{p}=\ensuremath{-}2{M}_{F}$, where $X={\ensuremath{\mu}}_{B}{g}_{J}\frac{B}{A}$, and
A is the hfs constant. There must be an avoided crossing between the two states of the same
MF which can only occur when one of the hyperfine manifolds has an inverted Zeeman effect. These conditions imply
MF<0 and
I>J. We observed the vanishing of
T in
23Na for one of the $\ensuremath{\Delta}{M}_{F}=0$ optical transitions of the $3{S}_{\frac{1}{2}}(F=1)\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}(F=1)$ manifold. Absorption of cw laser light was monitored by observing total fluorescence perpendicular to both the atomic and laser beams, and absorption vanished near an applied field of 155 G.
T vanishes for a large number of cases including rf and microwave frequencies and is a rather general consequence of angular momentum selection rules and perturbation theory. This phenomenon may have application in optical pumping, Lamb-shift measurements, and atomic weak neutral-current experiments.
The admixture effect of dipole and quadrupole type atomic transitions on the Stokes parameters characterizing the emitted radiation in the presence of an external magnetic field is studied. The transition from an upper level with angular momentum Ju = 3/2 to a lower level with angular momentum Jl = 1/2 is considered to take account of the admixture effect. The analytical expressions showing the emitted Stokes parameters for the case of upper and lower levels having same parities are derived. It is shown that the radiative transition probabilities of magnetic dipole (M1) and electric quadrupole transition (E2) are more intense than those of electric dipole transition (E1) and magnetic quadrupole transition (M2). The polarization components that are not usually seen in the Stokes I; Q and V profiles appear due to the admixture effect. The interference of the polarization components with opposite signs is responsible for the smaller strength of Stokes I; Q; V in admixture transition compared to those observed in pure transition. In pure dipole transition case, U Stokes profile is always zero for all emitted radiation directions. However, the Stokes U profile arises only due to the admixture effect.
The recently developed technique of Raman heterodyne detection has unveiled a new interference effect in the Zeeman spectrum of hyperfine transitions of impurity-ion solids. An earlier theory had been developed to explain the basic Raman heterodyne process which involves the resonant interaction of a three-level quantum system with coherent optical-frequency and radiofrequency fields. However, it was not realized that impurity-ion crystals can generate more than one type of Raman heterodyne signal and that these signals can interfere. This article describes two examples of interference where one originates from two or more inequivalent nuclear sites and the other from a single site that exhibits interference among Zeeman transitions. An analytical theory covering these two cases is presented and compared to observations for the impurity-ion crystals
Pr3+:
YAlO3 and
Pr3+:
LaF3, the interference behavior in the two being dramatically different.
Under the conditions of the total Paschen-Back effect the diamagnetic interaction determines the dependence of the intensity of the Zeeman components of atomic radiation lines on a magnetic field. The change in the matrix elements of the radiative transitions is due to the magnetically induced corrections to the wavefunctions of the initial and final states, whose contributions are of the same order of magnitude for the head lines of the optical series. For the high-frequency lines the positive corrections to the matrix element from the wavefunction of the upper level dominate. A magnetic field also induces dipole radiative transitions with selection rules for the orbital angular momentum | Δ l | ≥ 3. The matrix elements of such transitions increase rapidly with the energy of the upper level, making possible efficient single-photon population of the dipole-inaccessible Rydberg states in moderate magnetic fields.
When introduced as dopants into
Y2O3,
Er3+ ions replace
Y3+ ions at two crystallographic sites of
C2 and
C3i point symmetries. The
C3i site is particularly interesting, given that the inversion symmetry prohibits static electric-dipole moments and electric-dipole transitions, resulting in 1.5 \textmu{}m optical transitions characterized by purely magnetic-dipole properties. Employing $\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}\ensuremath{\leftrightarrow}^{4}I_{13/2}$ transitions, we examined the inherent
C3i site of
Er3+ in
Y2O3 for its potential in quantum information science and spectral hole burning applications. Our approach involved absorption and site-selective fluorescence spectroscopy to discern
Er3+ energy levels and revealed an excited-state lifetime of 14.6 ms. High-resolution laser spectroscopy at 3.7 K indicated an inhomogeneous linewidth of 1.3 GHz in our sample. Orientation-dependent Zeeman laser absorption spectroscopy facilitated the determination of the full
g tensors for both the ground and excited states, confirming the
C3i site assignment. Furthermore, it identified a suitable magnetic field direction for mitigating decoherence, a finding corroborated through two-pulse photon echo spectroscopy. Our study presents photon echo coherent transient measurements related to magnetic-dipole-allowed rare-earth ion transitions at the
C3i site. The observed decoherence, attributed to spectral diffusion arising from $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic-dipole interactions, underscores the complex spin dynamics at play in systems with multiple inequivalent dopant sites. Coupled with the practicality of telecom laser wavelengths, our investigation highlights the promise of magnetic-dipole transitions in advancing quantum information science and spectral hole burning applications.
We investigate the effects of spontaneously generated interference on the spectrum of quantum fluctuations in phase quadratures of resonant fluorescence emitted from the transition of j = 1/2 to j = 1/2 of a monochromatically driven four-level atom with antiparallel dipole moments. It is found that the spectrum exhibits obvious characteristics of quantum interference in both cases of weak and strong laser fields. For the Zeeman-degenerate system, strong radiation squeezing in weak atomic excitation can occur at the central frequency of the spectrum, which is quite different from the case without consideration of the interference. Moreover, when we apply an external magnetic field to the atom, we find that the quantum interference can lead to a narrowing spectrum with much stronger squeezing by adjusting the magnetic field strength. These results suggest that the phase-dependent fluorescence spectrum can serve as a probe of the quantum interference effects in a realistic system such as a trapped 198Hg+ ion or charged quantum dots.