Physical Review A

Quantitative investigation of the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium 52S1/2→52D5/2 two-photon transition

Masashi Abe, Ryohei Itoyama, Yuta Komiyama, Takuma Ito, Taro Mashimo, 賢東條

Published May 28, 2019• 4 citations

Abstract

We precisely investigate the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium $5{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ two-photon transition. Owing to the high sensitivity of the $D$ state of atoms to a magnetic field, the splittings of the spectra of the $D$ state are sufficiently large in a weak magnetic field of $<10$ G. We experimentally observe how in the hyperfine coupling in the $5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ state is disrupted even in weak magnetic fields around 10 G and the energy levels are arranged according to their total angular momentum $J$ and nuclear spin $I$. The transient of the spectra known as the Paschen-Back effect is observed even in a weak magnetic field with an order of magnitude of several tens of gauss. The results of theoretical calculations for energy shifts and transition intensities under a magnetic field are in quantitative agreement with the experimental results.

DOI: 10.1103/physreva.99.053420

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Hyperfine Paschen–Back regime in alkali metal atoms: consistency of two theoretical considerations and experiment

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

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Physical Review A

Quantitative investigation of the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium 52S1/2→52D5/2 two-photon transition

Masashi Abe, Ryohei Itoyama, Yuta Komiyama, Takuma Ito, Taro Mashimo, 賢東條

Published May 28, 2019• 4 citations

Publisher

Abstract

We precisely investigate the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium

5{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}

two-photon transition. Owing to the high sensitivity of the

D

state of atoms to a magnetic field, the splittings of the spectra of the

D

state are sufficiently large in a weak magnetic field of

<10

G. We experimentally observe how in the hyperfine coupling in the

5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}

state is disrupted even in weak magnetic fields around 10 G and the energy levels are arranged according to their total angular momentum

J

and nuclear spin

I

. The transient of the spectra known as the Paschen-Back effect is observed even in a weak magnetic field with an order of magnitude of several tens of gauss. The results of theoretical calculations for energy shifts and transition intensities under a magnetic field are in quantitative agreement with the experimental results.

DOI: 10.1103/physreva.99.053420

Related papers

Hyperfine Paschen–Back regime in alkali metal atoms: consistency of two theoretical considerations and experiment

Armen D. Sargsyan, G. Hakhumyan, Claude Leroy +4 more

Simple and efficient λ-method and λ/2-method (λ is the resonant wavelength of laser radiation) based on a nanometric-thickness cell filled with rubidium (Rb) are implemented to study the splitting of hyperfine transitions of an Rb85 and Rb87D1 line in an external magnetic field in the range of B=0.5–0.7 T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in Rb85 (Rb87) spectra in the case of σ+ polarized laser radiation, only 6 (4) remain at B>0.5 T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen–Back regime). The expressions derived in the frame of completely uncoupled basis (J,mJ;I,mI) describe the experimental results extremely well for Rb85 transitions at B>0.6 T (that is a manifestation of hyperfine Paschen–Back regime). A remarkable result is that the calculations based on the eigenstates of the coupled (F,mF) basis, which adequately describe the system for a low magnetic field, also predict reduction of the number of transition components from 20 to 6 for Rb85 and from 12 to 4 for Rb87 spectrum at B>0.5 T. Also, the Zeeman transition frequency shifts, frequency intervals between the components and their slope versus B, are in agreement with the experiment.Simple and efficient λ-method and λ/2-method (λ is the resonant wavelength of laser radiation) based on a nanometric-thickness cell filled with rubidium (Rb) are implemented to study the splitting of hyperfine transitions of an Rb85 and Rb87D1 line in an external magnetic field in the range of B=0.5–0.7 T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in Rb85 (Rb87) spectra in the case of σ+ polarized laser radiation, only 6 (4) remain at B>0.5 T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen–Back regime). The expressions derived in the frame of completely uncoupled basis (J,mJ;I,mI) describe the experimental results extremely well for Rb85 transitions at B>0.6 T (that is a manifestation of hyperfine Paschen–Back regime). A remarkable result is that the calculations based on the eigenstates of the coupled (F,mF) basis, which adequately describe the system for a low magnetic field, also predict reduction of the number of transition components from 20 to 6 for Rb85 and from 12 to 4 for Rb87 spectrum at B>0.5 T. Also, the Zeeman transition frequency shifts, frequency intervals between the components and their slope versus B, are in agreement with the experiment.

arXiv:1309.5775Journal of the Optical Society of America BApr 8, 201443 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.

arXiv:0907.3727Physical Review AOct 9, 200910 citations

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We report on rubidium vapor-cell Rydberg electromagnetically induced transparency (EIT) in a 0.7~T magnetic field where all involved levels are in the hyperfine Paschen-Back regime, and the Rydberg state exhibits a strong diamagnetic interaction with the magnetic field. Signals from both $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ are present in the EIT spectra. This feature of isotope-mixed Rb cells allows us to measure the field strength to within a $\pm 0.12$ \% relative uncertainty. The measured spectra are in excellent agreement with the results of a Monte Carlo calculation and indicate unexpectedly large Rydberg-level dephasing rates. Line shifts and broadenings due to small inhomogeneities of the magnetic field are included in the model.We report on rubidium vapor-cell Rydberg electromagnetically induced transparency (EIT) in a 0.7~T magnetic field where all involved levels are in the hyperfine Paschen-Back regime, and the Rydberg state exhibits a strong diamagnetic interaction with the magnetic field. Signals from both $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ are present in the EIT spectra. This feature of isotope-mixed Rb cells allows us to measure the field strength to within a $\pm 0.12$\% relative uncertainty. The measured spectra are in excellent agreement with the results of a Monte Carlo calculation and indicate unexpectedly large Rydberg-level dephasing rates. Line shifts and broadenings due to small inhomogeneities of the magnetic field are included in the model.

arXiv:1702.05556Feb 18, 201724 citations

Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime

Lee Weller, Kathrin S Kleinbach, Mark A. Zentile +3 more

Here we report on measurements of the absolute absorption and dispersion properties of an isotopically pure 87 Rb vapour for magnetic fields up to and including 0.6 T. We discuss the various regimes that arise when the hyperfine and Zeeman interactions have different magnitudes, and show that we enter the hyperfine Paschen–Back regime for fields greater than 0.33 T on the Rb D 2 line. The experiment uses a compact 1 mm 3 microfabricated vapour cell that makes it easy to maintain a uniform and large magnetic field with a small and inexpensive magnet. We find excellent agreement between the experimental results and numerical calculations of the weak probe susceptibility where the line positions and strengths are calculated by matrix diagonalization.Here we report on measurements of the absolute absorption and dispersion properties of an isotopically pure 87 Rb vapour for magnetic fields up to and including 0.6 T. We discuss the various regimes that arise when the hyperfine and Zeeman interactions have different magnitudes, and show that we enter the hyperfine Paschen–Back regime for fields greater than 0.33 T on the Rb D 2 line. The experiment uses a compact 1 mm 3 microfabricated vapour cell that makes it easy to maintain a uniform and large magnetic field with a small and inexpensive magnet. We find excellent agreement between the experimental results and numerical calculations of the weak probe susceptibility where the line positions and strengths are calculated by matrix diagonalization.

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Theoretical Investigation of $^{41}$ K States Behavior under Strong Magnetic Field and $π$ Polarized Laser FieldTheoretical Investigation of $^{41}$K States Behavior under Strong Magnetic Field and $π$ Polarized Laser Field

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Theoretically research of the behavior of $^{41}$ K $D_1$ and $D_2$ lines for $π$ polarized resonant light is conducted in the presence of strong magnetic field when the total electronic angular momentum $J$ and nuclear spin $I$ are decoupled. We show that in the case of linear polarization and for D1 line there are two transitions, so called guiding transitions (GT) that maintain their probabilities and frequency slopes. In Hyperfine Paschen-Back (HPB) regime other transitions are coming together to those GTs, making 2 groups (4 in each). Each transition in the group has the same frequency slope and probability as the GT in their group. It is demonstrated that from 12 ( $D_1$ ) and 20 ( $D_2$ ) initially allowed Zeeman transitions (taking into account the selection rules) at low B-field, only 8 transitions in each $D$ line remain in absorption spectra at $B > 200$ G. A complete HPB regime for relatively low magnetic fields $B \sim 200$ G has been observed. This value is the smallest for all alkali metals.Theoretically research of the behavior of $^{41}$K $D_1$ and $D_2$ lines for $π$ polarized resonant light is conducted in the presence of strong magnetic field when the total electronic angular momentum $J$ and nuclear spin $I$ are decoupled. We show that in the case of linear polarization and for D1 line there are two transitions, so called guiding transitions (GT) that maintain their probabilities and frequency slopes. In Hyperfine Paschen-Back (HPB) regime other transitions are coming together to those GTs, making 2 groups (4 in each). Each transition in the group has the same frequency slope and probability as the GT in their group. It is demonstrated that from 12 ($D_1$) and 20 ($D_2$) initially allowed Zeeman transitions (taking into account the selection rules) at low B-field, only 8 transitions in each $D$ line remain in absorption spectra at $B > 200$ G. A complete HPB regime for relatively low magnetic fields $B \sim 200$ G has been observed. This value is the smallest for all alkali metals.

arXiv:1707.04468Jul 14, 20170 citations

Four-level N -scheme crossover resonances in Rb saturation spectroscopy in magnetic fields

Stefano Scotto, D. Ciampini, Carlo Rizzo +1 more

We perform saturated absorption spectroscopy on the ${D}_{2}$ line for room temperature rubidium atoms immersed in magnetic fields within the 0.05--0.13 T range. At those medium-high field values the hyperfine structure in the excited state is broken by the Zeeman effect, while in the ground-state hyperfine structure and Zeeman shifts are comparable. The observed spectra are composed by a large number of absorption lines. We identify them as saturated absorptions on two-level systems, on three-level systems in a $\mathsf{V}$ configuration, and on four-level systems in an $\mathsf{N}$ or double- $\mathsf{N}$ configuration where two optical transitions not sharing a common level are coupled by spontaneous emission decays. We analyze the intensity of all those transitions within a unified simple theoretical model. We concentrate our attention on the double- $\mathsf{N}$ crossovers signals whose intensity is very large because of the symmetry in the branching ratios of the four levels. We point out that these structures, present in all alkali-metal atoms at medium-high magnetic fields, have interesting properties for electromagnetically induced transparency and slow light applications.We perform saturated absorption spectroscopy on the ${D}_{2}$ line for room temperature rubidium atoms immersed in magnetic fields within the 0.05--0.13 T range. At those medium-high field values the hyperfine structure in the excited state is broken by the Zeeman effect, while in the ground-state hyperfine structure and Zeeman shifts are comparable. The observed spectra are composed by a large number of absorption lines. We identify them as saturated absorptions on two-level systems, on three-level systems in a $\mathsf{V}$ configuration, and on four-level systems in an $\mathsf{N}$ or double-$\mathsf{N}$ configuration where two optical transitions not sharing a common level are coupled by spontaneous emission decays. We analyze the intensity of all those transitions within a unified simple theoretical model. We concentrate our attention on the double-$\mathsf{N}$ crossovers signals whose intensity is very large because of the symmetry in the branching ratios of the four levels. We point out that these structures, present in all alkali-metal atoms at medium-high magnetic fields, have interesting properties for electromagnetically induced transparency and slow light applications.

arXiv:1509.06978Physical Review ADec 7, 201534 citations

We precisely investigate the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium

5{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}

two-photon transition. Owing to the high sensitivity of the

D

state of atoms to a magnetic field, the splittings of the spectra of the

D

state are sufficiently large in a weak magnetic field of

<10

G. We experimentally observe how in the hyperfine coupling in the

5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}

state is disrupted even in weak magnetic fields around 10 G and the energy levels are arranged according to their total angular momentum

J

and nuclear spin

I

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.

^{85}\mathrm{Rb}

and

^{87}\mathrm{Rb}

are present in the EIT spectra. This feature of isotope-mixed Rb cells allows us to measure the field strength to within a

\pm 0.12

\% relative uncertainty. The measured spectra are in excellent agreement with the results of a Monte Carlo calculation and indicate unexpectedly large Rydberg-level dephasing rates. Line shifts and broadenings due to small inhomogeneities of the magnetic field are included in the model.

Theoretical Investigation of

^{41}

K States Behavior under Strong Magnetic Field and

π

Polarized Laser Field

Theoretically research of the behavior of

^{41}

D_1

and

D_2

lines for

π

polarized resonant light is conducted in the presence of strong magnetic field when the total electronic angular momentum

J

and nuclear spin

I

are decoupled. We show that in the case of linear polarization and for D1 line there are two transitions, so called guiding transitions (GT) that maintain their probabilities and frequency slopes. In Hyperfine Paschen-Back (HPB) regime other transitions are coming together to those GTs, making 2 groups (4 in each). Each transition in the group has the same frequency slope and probability as the GT in their group. It is demonstrated that from 12 (

D_1

) and 20 (

D_2

) initially allowed Zeeman transitions (taking into account the selection rules) at low B-field, only 8 transitions in each

D

line remain in absorption spectra at

B > 200

G. A complete HPB regime for relatively low magnetic fields

B \sim 200

G has been observed. This value is the smallest for all alkali metals.

We perform saturated absorption spectroscopy on the

{D}_{2}

line for room temperature rubidium atoms immersed in magnetic fields within the 0.05--0.13 T range. At those medium-high field values the hyperfine structure in the excited state is broken by the Zeeman effect, while in the ground-state hyperfine structure and Zeeman shifts are comparable. The observed spectra are composed by a large number of absorption lines. We identify them as saturated absorptions on two-level systems, on three-level systems in a

\mathsf{V}

configuration, and on four-level systems in an

\mathsf{N}

or double-

\mathsf{N}

configuration where two optical transitions not sharing a common level are coupled by spontaneous emission decays. We analyze the intensity of all those transitions within a unified simple theoretical model. We concentrate our attention on the double-

\mathsf{N}

crossovers signals whose intensity is very large because of the symmetry in the branching ratios of the four levels. We point out that these structures, present in all alkali-metal atoms at medium-high magnetic fields, have interesting properties for electromagnetically induced transparency and slow light applications.