Physical Review

Observations of Transitions Between Stationary States in a Rotating Magnetic Field

W. Happer

Published Oct 5, 1964• 14 citations

Abstract

The stationary states of an atom in a combined static and rotating magnetic field have been investigated by using two frequency transitions in an atomic-beam machine. Very accurate measurements of a strong rf magnetic field may be made by inducing transitions between the stationary states with a small "tickling" rf field. The relaxation of the selection rules associated with the $z$ component of angular momentum makes normally forbidden hyperfine transitions visible.

DOI: 10.1103/physrev.136.a35

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Physical Review

Observations of Transitions Between Stationary States in a Rotating Magnetic Field

W. Happer

Published Oct 5, 1964• 14 citations

Publisher

Abstract

z

component of angular momentum makes normally forbidden hyperfine transitions visible.

DOI: 10.1103/physrev.136.a35

Related papers

Frequency Shifts in Atomic Beam Experiments

L. Evans

In certain triple-loop atomic beam experiments reported in the literature, a shift in the resonance frequency was observed on reversing the direction of the $C$ field. This shift is explained by assuming that the rf field changes in direction along the transition region, which causes the moving atom to experience a frequency different from that of the basic oscillatory frequency. All the observed properties of the shift can be accounted for by the explanation given.In certain triple-loop atomic beam experiments reported in the literature, a shift in the resonance frequency was observed on reversing the direction of the $C$ field. This shift is explained by assuming that the rf field changes in direction along the transition region, which causes the moving atom to experience a frequency different from that of the basic oscillatory frequency. All the observed properties of the shift can be accounted for by the explanation given.

Physical ReviewFeb 5, 19690 citations

Symmetry-suppressed two-photon transitions induced by hyperfine interactions and magnetic fields

M. G. Kozlov, D. English, Dmitry Budker

Two-photon transitions between atomic states of total electronic angular-momentum ${J}_{a}=0$ and ${J}_{b}=1$ are forbidden when the photons are of the same energy. This selection rule is analogous to the Landau-Yang theorem in particle physics that forbids decays of vector particle into two photons. It arises because it is impossible to construct a total angular-momentum ${J}_{2\ensuremath{\gamma}}=1$ quantum-mechanical state of two photons that is permutation symmetric, as required by Bose-Einstein statistics. In atoms with nonzero nuclear spin, the selection rule can be violated due to hyperfine interactions. Two distinct mechanisms responsible for the hyperfine-induced two-photon transitions are identified, and the hyperfine structure of the induced transitions is evaluated. The selection rule is also relaxed, even for zero-nuclear-spin atoms, by application of an external magnetic field. Once again, there are two similar mechanisms at play: Zeeman splitting of the intermediate-state sublevels, and off-diagonal mixing of states with different total electronic angular momentum in the final state. The present theoretical treatment is relevant to the ongoing experimental search for a possible Bose-Einstein-statistics violation using two-photon transitions in barium, where the hyperfine-induced transitions have been recently observed, and the magnetic-field-induced transitions are being considered both as a possible systematic effect, and as a way to calibrate the measurement.Two-photon transitions between atomic states of total electronic angular-momentum ${J}_{a}=0$ and ${J}_{b}=1$ are forbidden when the photons are of the same energy. This selection rule is analogous to the Landau-Yang theorem in particle physics that forbids decays of vector particle into two photons. It arises because it is impossible to construct a total angular-momentum ${J}_{2\ensuremath{\gamma}}=1$ quantum-mechanical state of two photons that is permutation symmetric, as required by Bose-Einstein statistics. In atoms with nonzero nuclear spin, the selection rule can be violated due to hyperfine interactions. Two distinct mechanisms responsible for the hyperfine-induced two-photon transitions are identified, and the hyperfine structure of the induced transitions is evaluated. The selection rule is also relaxed, even for zero-nuclear-spin atoms, by application of an external magnetic field. Once again, there are two similar mechanisms at play: Zeeman splitting of the intermediate-state sublevels, and off-diagonal mixing of states with different total electronic angular momentum in the final state. The present theoretical treatment is relevant to the ongoing experimental search for a possible Bose-Einstein-statistics violation using two-photon transitions in barium, where the hyperfine-induced transitions have been recently observed, and the magnetic-field-induced transitions are being considered both as a possible systematic effect, and as a way to calibrate the measurement.

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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.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.

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Hyperfine transition induced by atomic motion above a paraffin-coated magnetic film

Naota Sekiguchi, Hiroaki Usui, A. Hatakeyama

Abstract We measured transitions between the hyperfine levels of the electronic ground state of potassium-39 atoms (transition frequency: 460 MHz) as the atoms moved through a periodic magneto-static field produced above the magnetic-stripe domains of a magnetic film. The period length of the magnetic field was 3.8 µm. The atoms were incident to the field as an impinging beam with the most probable velocity of 550 m s−1 and experienced a peak oscillating field of 20 mT. Unwanted spin relaxation caused by the collisions of the atoms with the film surface was suppressed by the paraffin coating on the film. We observed increasing hyperfine transition probabilities as the frequency of the field oscillations experienced by the atoms increased from 0 to 140 MHz for the atomic velocity of 550 m s−1, by changing the incident angle of the atomic beam with respect to the stripe domains. Numerical calculation of the time evolution of the hyperfine states revealed that the oscillating magnetic field experienced by the atoms induced the hyperfine transitions, and the main process was not a single-quantum transition but rather multi-quanta transitions.Abstract We measured transitions between the hyperfine levels of the electronic ground state of potassium-39 atoms (transition frequency: 460 MHz) as the atoms moved through a periodic magneto-static field produced above the magnetic-stripe domains of a magnetic film. The period length of the magnetic field was 3.8 µm. The atoms were incident to the field as an impinging beam with the most probable velocity of 550 m s−1 and experienced a peak oscillating field of 20 mT. Unwanted spin relaxation caused by the collisions of the atoms with the film surface was suppressed by the paraffin coating on the film. We observed increasing hyperfine transition probabilities as the frequency of the field oscillations experienced by the atoms increased from 0 to 140 MHz for the atomic velocity of 550 m s−1, by changing the incident angle of the atomic beam with respect to the stripe domains. Numerical calculation of the time evolution of the hyperfine states revealed that the oscillating magnetic field experienced by the atoms induced the hyperfine transitions, and the main process was not a single-quantum transition but rather multi-quanta transitions.

arXiv:2308.00888Journal of Physics B Atomic Molecular and Optical PhysicsSep 27, 20232 citations

z

component of angular momentum makes normally forbidden hyperfine transitions visible.

In certain triple-loop atomic beam experiments reported in the literature, a shift in the resonance frequency was observed on reversing the direction of the

C

field. This shift is explained by assuming that the rf field changes in direction along the transition region, which causes the moving atom to experience a frequency different from that of the basic oscillatory frequency. All the observed properties of the shift can be accounted for by the explanation given.

Two-photon transitions between atomic states of total electronic angular-momentum

{J}_{a}=0

and

{J}_{b}=1

are forbidden when the photons are of the same energy. This selection rule is analogous to the Landau-Yang theorem in particle physics that forbids decays of vector particle into two photons. It arises because it is impossible to construct a total angular-momentum ${J}_{2\ensuremath{\gamma}}=1$ quantum-mechanical state of two photons that is permutation symmetric, as required by Bose-Einstein statistics. In atoms with nonzero nuclear spin, the selection rule can be violated due to hyperfine interactions. Two distinct mechanisms responsible for the hyperfine-induced two-photon transitions are identified, and the hyperfine structure of the induced transitions is evaluated. The selection rule is also relaxed, even for zero-nuclear-spin atoms, by application of an external magnetic field. Once again, there are two similar mechanisms at play: Zeeman splitting of the intermediate-state sublevels, and off-diagonal mixing of states with different total electronic angular momentum in the final state. The present theoretical treatment is relevant to the ongoing experimental search for a possible Bose-Einstein-statistics violation using two-photon transitions in barium, where the hyperfine-induced transitions have been recently observed, and the magnetic-field-induced transitions are being considered both as a possible systematic effect, and as a way to calibrate the measurement.

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.