Physical Review A

Vanishing electric dipole transition moment

W.A. Davis, Harold J. Metcalf, William D. Phillips

Published Feb 1, 1979• 9 citations

Abstract

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 ${M}_{F}$ 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 ${M}_{F}$ which can only occur when one of the hyperfine manifolds has an inverted Zeeman effect. These conditions imply ${M}_{F}<0$ and $I>J$. We observed the vanishing of $T$ in $^{23}\mathrm{Na}$ 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.

DOI: 10.1103/physreva.19.700

Related papers

Dipole interference for optical transitions of ions in crystals in a transverse Zeeman field

Clinton DeW. Van Siclen

Journal of Physics C Solid State PhysicsNov 10, 19813 citations

Measurement of Dipole-Moment in Atomic Transitions under Strong External Magnetic Field

Koichi Nittoh, Akira Kuwako, Tadashi Ikehara +4 more

Journal of Nuclear Science and TechnologyJan 1, 19963 citations

Experimental Study of Zeeman Light Shifts in Weak Magnetic Fields

Claude N. Cohen-Tannoudji, J. Dupont-Roc

Physical Review AFeb 1, 1972265 citations

“Forbidden” transitions

P. van der Straten, Harold J. Metcalf

Cambridge University Press eBooksDec 31, 20150 citations

Observation of Level Crossing in H, n=2

R. T. Robiscoe

Physical ReviewApr 5, 196566 citations

Light with orbital angular momentum interacting with trapped ions

Christian Tomás Schmiegelow, Ferdinand Schmidt‐Kaler

arXiv:1112.3377Dec 14, 20113 citations

Physical Review A

Vanishing electric dipole transition moment

W.A. Davis, Harold J. Metcalf, William D. Phillips

Published Feb 1, 1979• 9 citations

Publisher

Abstract

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

{M}_{F}

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

{M}_{F}

which can only occur when one of the hyperfine manifolds has an inverted Zeeman effect. These conditions imply

{M}_{F}<0

and

I>J

. We observed the vanishing of

T

^{23}\mathrm{Na}

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.

DOI: 10.1103/physreva.19.700

Related papers

Dipole interference for optical transitions of ions in crystals in a transverse Zeeman field

Clinton DeW. Van Siclen

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.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.

Journal of Physics C Solid State PhysicsNov 10, 19813 citations

Measurement of Dipole-Moment in Atomic Transitions under Strong External Magnetic Field

Koichi Nittoh, Akira Kuwako, Tadashi Ikehara +4 more

Obtaining an accurate value of the electric dipole moment μ is essential in the fields of laser application technologies. A direct way of measuring the electric dipole moment μ is to observe the Rabi-oscillation which manifests itself in the coherent photo-excitation behavior of atoms. In the case of the elements which have large angular momenta, identifying the Rabi-oscillation in their excitation behavior becomes rather difficult. We proposed an accurate and straightforward method of determining the electric-dipole moment μ between multifold degenerate levels. The point is to remove the degeneracy by applying an external magnetic field with the aid of the Zeeman effect and, then, to realize a degeneration free coherent excitation. As a result, we can observe the Rabi-oscillations explicitly in the excitation vs. laser-fluence curves. The present method provides a reliable basis of experimental determination of μ. As an example, we applied the present method to a transition to 0–17,362 cm−1 level in uranium and obtained the value μ=0.86±0.06 (Debye).Obtaining an accurate value of the electric dipole moment μ is essential in the fields of laser application technologies. A direct way of measuring the electric dipole moment μ is to observe the Rabi-oscillation which manifests itself in the coherent photo-excitation behavior of atoms. In the case of the elements which have large angular momenta, identifying the Rabi-oscillation in their excitation behavior becomes rather difficult. We proposed an accurate and straightforward method of determining the electric-dipole moment μ between multifold degenerate levels. The point is to remove the degeneracy by applying an external magnetic field with the aid of the Zeeman effect and, then, to realize a degeneration free coherent excitation. As a result, we can observe the Rabi-oscillations explicitly in the excitation vs. laser-fluence curves. The present method provides a reliable basis of experimental determination of μ. As an example, we applied the present method to a transition to 0–17,362 cm−1 level in uranium and obtained the value μ=0.86±0.06 (Debye).

Journal of Nuclear Science and TechnologyJan 1, 19963 citations

Experimental Study of Zeeman Light Shifts in Weak Magnetic Fields

Claude N. Cohen-Tannoudji, J. Dupont-Roc

According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian ${\mathcal{H}}_{e}$ which depends on the polarization and spectral profile of the incident light. In order to check the structure of ${\mathcal{H}}_{e}$ , we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to ${\mathcal{H}}_{e}$ . We have been able to obtain experimentally in the ground state of $^{199}\mathrm{Hg}$ , $^{201}\mathrm{Hg}$ , and $^{87}\mathrm{Rb}$ , Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of ${\mathcal{H}}_{e}$ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian ${\mathcal{H}}_{e}$ which depends on the polarization and spectral profile of the incident light. In order to check the structure of ${\mathcal{H}}_{e}$, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to ${\mathcal{H}}_{e}$. We have been able to obtain experimentally in the ground state of $^{199}\mathrm{Hg}$, $^{201}\mathrm{Hg}$, and $^{87}\mathrm{Rb}$, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of ${\mathcal{H}}_{e}$ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.

Physical Review AFeb 1, 1972265 citations

“Forbidden” transitions

P. van der Straten, Harold J. Metcalf

Introduction The selection rules discussed in Sec. 3.5 forbid many kinds of transitions that are frequently observed or exploited. It must be remembered that these “rules” are based on the approximations of Sec. 3.2, but of course, those can be extended. Such expansions to higher orders of approximation may seem to be little more than a tedious exercise, but this chapter will show that the results are extremely important, because they cause qualitatively different kinds of transitions. Since they involve both the electric and magnetic components of the light, their atomic dipole moments will be identified with the superscript E and B for the remainder of this chapter. The magnetic dipole transitions, called M1, discussed in Sec. 4.2.1 that arise from extension of the electric dipole approximation encompass all of magnetic resonance, including atomic clocks, forced evaporative cooling in Bose–Einstein Condensation (BEC), MRI, and astrophysical processes such as generation of the all-important 21 cm radio frequency line. The electric quadrupole transitions, called E2, discussed in Sec. 4.2.2 describe myriad stellar spectral features as well as the vast majority of nuclear γ-ray transitions. Even with these extensions there are many cases where the relaxation of the electric dipole (E1) selection rules to include M1 and E2 transitions as in Sec. 4.2 still do not account for observed processes. Thus other approximations have to be extended so that their limitations can be relaxed as well. Extension of the perturbation approximation (see Sec. 4.3.1) provides an analytical description of most of non-linear optics, including second harmonic generation, four wave mixing, Raman spectroscopy, and the fabled decay of the hydrogen 2S state. A semi-classical description of the interaction between radiation and atoms can begin with a multipole expansion of the Hamiltonian. The lowest-order term is just from the point charges α located at, and vanishes for neutral atoms. The next-order term is the electric dipole interaction that arises from the non-isotropic distribution of charges induced by the electric field of the light. This term produces the electric dipole transitions (E1) that have been described in some detail in Chap. 3.Introduction The selection rules discussed in Sec. 3.5 forbid many kinds of transitions that are frequently observed or exploited. It must be remembered that these “rules” are based on the approximations of Sec. 3.2, but of course, those can be extended. Such expansions to higher orders of approximation may seem to be little more than a tedious exercise, but this chapter will show that the results are extremely important, because they cause qualitatively different kinds of transitions. Since they involve both the electric and magnetic components of the light, their atomic dipole moments will be identified with the superscript E and B for the remainder of this chapter. The magnetic dipole transitions, called M1, discussed in Sec. 4.2.1 that arise from extension of the electric dipole approximation encompass all of magnetic resonance, including atomic clocks, forced evaporative cooling in Bose–Einstein Condensation (BEC), MRI, and astrophysical processes such as generation of the all-important 21 cm radio frequency line. The electric quadrupole transitions, called E2, discussed in Sec. 4.2.2 describe myriad stellar spectral features as well as the vast majority of nuclear γ-ray transitions. Even with these extensions there are many cases where the relaxation of the electric dipole (E1) selection rules to include M1 and E2 transitions as in Sec. 4.2 still do not account for observed processes. Thus other approximations have to be extended so that their limitations can be relaxed as well. Extension of the perturbation approximation (see Sec. 4.3.1) provides an analytical description of most of non-linear optics, including second harmonic generation, four wave mixing, Raman spectroscopy, and the fabled decay of the hydrogen 2S state. A semi-classical description of the interaction between radiation and atoms can begin with a multipole expansion of the Hamiltonian. The lowest-order term is just from the point charges α located at, and vanishes for neutral atoms. The next-order term is the electric dipole interaction that arises from the non-isotropic distribution of charges induced by the electric field of the light. This term produces the electric dipole transitions (E1) that have been described in some detail in Chap. 3.

Cambridge University Press eBooksDec 31, 20150 citations

Observation of Level Crossing in H, n=2

R. T. Robiscoe

We have observed the crossing of the atomic hydrogen levels ${\ensuremath{\beta}}_{B}(2{S}_{\frac{1}{2}}, {m}_{J}=\ensuremath{-}\frac{1}{2}, {m}_{I}=\ensuremath{-}\frac{1}{2})$ and ${e}_{B}(2{P}_{\frac{1}{2}}, {m}_{J}=+\frac{1}{2}, {m}_{I}=\ensuremath{-}\frac{1}{2})$ near 605 G. A new atomic-beam method is used. H atoms are excited to the metastable $2S$ state by electron bombardment. The $2S({m}_{J}=\ensuremath{-}\frac{1}{2})$ state is quenched in the bombardment region. The $2S({m}_{J}=+\frac{1}{2})$ beam passes through a zero-field region where $\frac{1}{3}$ of it is converted to the single hyperfine level ${\ensuremath{\beta}}_{B}$. The ${\ensuremath{\beta}}_{B}$ atoms enter a uniform magnetic field parallel to the beam. With no externally applied electric field, 92% of them reach the detector. When we apply an electrostatic field of about 0.7 V/cm perpendicular to the beam, the ${\ensuremath{\beta}}_{B}$ atoms are strongly quenched near the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing point. Observed quenching agrees with the Bethe-Lamb theory of the $2S$ lifetime in external fields. We measure magnetic field by the nuclear magnetic resonance frequency of protons in water. Natural asymmetry and minor experimental corrections reduce the observed center of the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ quenching resonance by 1 part in ${10}^{4}$ . The corrected ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing occurs at 2577.57\ifmmode\pm\else\textpm\fi{}0.25 kc/sec, proton nmr in water. From this, we calculate the Lamb shift $\mathcal{S}$ in H, $n=2$ . With a diamagnetic shielding correction, and the accurately known $2S$ hyperfine interval, we get $\mathcal{S}=1058.07\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec. This disagrees with $\mathcal{S}=1057.77\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec from the Lamb experiments.We have observed the crossing of the atomic hydrogen levels ${\ensuremath{\beta}}_{B}(2{S}_{\frac{1}{2}}, {m}_{J}=\ensuremath{-}\frac{1}{2}, {m}_{I}=\ensuremath{-}\frac{1}{2})$ and ${e}_{B}(2{P}_{\frac{1}{2}}, {m}_{J}=+\frac{1}{2}, {m}_{I}=\ensuremath{-}\frac{1}{2})$ near 605 G. A new atomic-beam method is used. H atoms are excited to the metastable $2S$ state by electron bombardment. The $2S({m}_{J}=\ensuremath{-}\frac{1}{2})$ state is quenched in the bombardment region. The $2S({m}_{J}=+\frac{1}{2})$ beam passes through a zero-field region where $\frac{1}{3}$ of it is converted to the single hyperfine level ${\ensuremath{\beta}}_{B}$. The ${\ensuremath{\beta}}_{B}$ atoms enter a uniform magnetic field parallel to the beam. With no externally applied electric field, 92% of them reach the detector. When we apply an electrostatic field of about 0.7 V/cm perpendicular to the beam, the ${\ensuremath{\beta}}_{B}$ atoms are strongly quenched near the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing point. Observed quenching agrees with the Bethe-Lamb theory of the $2S$ lifetime in external fields. We measure magnetic field by the nuclear magnetic resonance frequency of protons in water. Natural asymmetry and minor experimental corrections reduce the observed center of the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ quenching resonance by 1 part in ${10}^{4}$. The corrected ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing occurs at 2577.57\ifmmode\pm\else\textpm\fi{}0.25 kc/sec, proton nmr in water. From this, we calculate the Lamb shift $\mathcal{S}$ in H, $n=2$. With a diamagnetic shielding correction, and the accurately known $2S$ hyperfine interval, we get $\mathcal{S}=1058.07\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec. This disagrees with $\mathcal{S}=1057.77\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec from the Lamb experiments.

Physical ReviewApr 5, 196566 citations

Light with orbital angular momentum interacting with trapped ions

Christian Tomás Schmiegelow, Ferdinand Schmidt‐Kaler

We study the interaction of a light beams carrying angular momentum with a single, trapped and well localized ion. We provide a detailed calculation of selection rules and excitation probabilities for quadrupole transitions. The results show the dependencies on the angular momentum and polarization of the laser beam as well as the direction of the quantization magnetic field. In order to observe optimally the specific effects, focusing the angular momentum beam close to the diffraction limit is required. We discuss a protocol for examining experimentally the effects on the S $_{1/2}$ to D $_{5/2}$ transition using a $^{40}$ Ca $^+$ ion. Various applications and advantages are expected when using light carrying angular momentum: In quantum information processing, where qubit states of ion crystals are controlled, parasitic light shifts could be avoided as the ion is excited in the dark zone of the beam at zero electric field amplitude. Such interactions also open the door to high dimensional entanglement between light and matter. In spectroscopy one might access transitions which have escaped excitation so far due to vanishing transition dipole moments.We study the interaction of a light beams carrying angular momentum with a single, trapped and well localized ion. We provide a detailed calculation of selection rules and excitation probabilities for quadrupole transitions. The results show the dependencies on the angular momentum and polarization of the laser beam as well as the direction of the quantization magnetic field. In order to observe optimally the specific effects, focusing the angular momentum beam close to the diffraction limit is required. We discuss a protocol for examining experimentally the effects on the S$_{1/2}$ to D$_{5/2}$ transition using a $^{40}$Ca$^+$ ion. Various applications and advantages are expected when using light carrying angular momentum: In quantum information processing, where qubit states of ion crystals are controlled, parasitic light shifts could be avoided as the ion is excited in the dark zone of the beam at zero electric field amplitude. Such interactions also open the door to high dimensional entanglement between light and matter. In spectroscopy one might access transitions which have escaped excitation so far due to vanishing transition dipole moments.

arXiv:1112.3377Dec 14, 20113 citations

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

{M}_{F}

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

{M}_{F}

which can only occur when one of the hyperfine manifolds has an inverted Zeeman effect. These conditions imply

{M}_{F}<0

and

I>J

. We observed the vanishing of

T

^{23}\mathrm{Na}

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

{\mathcal{H}}_{e}

which depends on the polarization and spectral profile of the incident light. In order to check the structure of

{\mathcal{H}}_{e}

, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to

{\mathcal{H}}_{e}

. We have been able to obtain experimentally in the ground state of

^{199}\mathrm{Hg}

^{201}\mathrm{Hg}

, and

^{87}\mathrm{Rb}

, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of

{\mathcal{H}}_{e}

can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.

2S

state by electron bombardment. The $2S({m}_{J}=\ensuremath{-}\frac{1}{2})$ state is quenched in the bombardment region. The

2S({m}_{J}=+\frac{1}{2})

beam passes through a zero-field region where

\frac{1}{3}

of it is converted to the single hyperfine level ${\ensuremath{\beta}}_{B}$. The ${\ensuremath{\beta}}_{B}$ atoms enter a uniform magnetic field parallel to the beam. With no externally applied electric field, 92% of them reach the detector. When we apply an electrostatic field of about 0.7 V/cm perpendicular to the beam, the ${\ensuremath{\beta}}_{B}$ atoms are strongly quenched near the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing point. Observed quenching agrees with the Bethe-Lamb theory of the

2S

lifetime in external fields. We measure magnetic field by the nuclear magnetic resonance frequency of protons in water. Natural asymmetry and minor experimental corrections reduce the observed center of the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ quenching resonance by 1 part in

{10}^{4}

. The corrected ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing occurs at 2577.57\ifmmode\pm\else\textpm\fi{}0.25 kc/sec, proton nmr in water. From this, we calculate the Lamb shift

\mathcal{S}

in H,

n=2

. With a diamagnetic shielding correction, and the accurately known

2S

hyperfine interval, we get $\mathcal{S}=1058.07\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec. This disagrees with $\mathcal{S}=1057.77\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec from the Lamb experiments.

_{1/2}

to D

_{5/2}

transition using a

^{40}

^+

ion. Various applications and advantages are expected when using light carrying angular momentum: In quantum information processing, where qubit states of ion crystals are controlled, parasitic light shifts could be avoided as the ion is excited in the dark zone of the beam at zero electric field amplitude. Such interactions also open the door to high dimensional entanglement between light and matter. In spectroscopy one might access transitions which have escaped excitation so far due to vanishing transition dipole moments.