Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Dark region observed in fluorescence under the condition of a quadrupole magnetic field

Quan Long, Shuyu Zhou, Shanyu Zhou, Yuzhu Wang

Published Jul 18, 2000• 3 citations
Publisher

Abstract

We report an experimental observation of a dark region, around the zero-field point of a spheric quadrupole magnetostatic field, in spatial fluorescence emitted by dilute vapor atoms, which were excited by a circularly polarized traveling-wave laser tuned to a $\stackrel{\ensuremath{\rightarrow}}{F}F+1$ transition of ${}^{87}\mathrm{Rb}.$ By ruling out some possible sources, we show that the fluorescence decrease is associated with the three-dimensional nature of the magnetic field; it is a consequence of a precession of magnetic dipole moments induced by the radial magnetic field, which significantly cancels the orientation caused by optical pumping near the point of level crossing in the presence of the axial magnetic field. In an alternative way, the phenomenon can be understood as resulting from a destructive quantum interference, which is related to a coherent double-quantum coupling of atomic levels with two fields; one is the laser field, the other is the magnetic field. Analytic expressions for the half-width and contrast of the dark region have been obtained with a simplified model in the limit of low laser power. A qualitative agreement between the theory and experiment is found. The relevance of our study to laser cooling and trapping in a widely used magneto-optical trap based on such a quadrupole magnetic field is discussed. Finally, some applications of the phenomenon are also presented.

DOI
10.1103/physreva.62.023406

Related papers

Dark region in fluorescence emitted by Rb atoms in a quadrupole magnetostatic field: observation and explanation

Q. Long, Shuyu Zhou, S.Y. Zhon +1 more

The quadrupole magnetostatic field (QMF), together with 3 pairs of laser beams, known as the magneto-optical trap, has been widely used for cooling and trapping atoms. This report concerns itself with some new phenomena observed in fluorescence emitted by Rb atoms in QMF under the circumstances of a single /spl sigma/ laser beam. A circularly polarized laser traveling-wave tuned to D/sub 2/-line is passed through a vacuum chamber along the central axis of two anti-Helmholtz coils. The fluorescence emitted by Rb atoms excited by the circularly polarized light in the direction at right angle to the direction of the incident laser beam is collected and imaged with all polarized directions taken into account. From the camera picture we can see that, around the zero-field point, there exists a dark region, the size of which is inversely proportional to the field gradient and is not sensitive to the detuning. The dark region corresponds to a dip in the profile of the fluorescence intensity versus the space. An attempt is made to explain the origin of this dark region.

Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)•Jan 20, 2003•0 citations

Polarization vs. magnetic field: competing eigenbases in laser-driven atoms

Nicolás A. Nuñez Barreto, Cecilia Cormick, Christian Tomás Schmiegelow

We present experimental results and a theoretical model that illustrate how competing eigenbases can determine the dynamics of a fluorescing atom. In the absence of a magnetic field, the atom can get trapped in a dark state, which inhibits fluorescence. In general, this will happen when the magnetic degeneracy of the ground state is greater than the one of the excited state. A canonical way to avoid optical pumping to dark states is to apply a magnetic field at an angle with respect to the polarization of the exciting light. This generates a competition of eigenbases which manifests as a crossover between two regimes dominated either by the laser or the magnetic field. We illustrate this crossover with fluorescence measurements on a single laser-cooled calcium ion in a Paul trap and find that it occurs at a critical laser intensity that is proportional to the external magnetic field. We contrast our results with numerical simulations of the atomic levels involved and also present a simple theoretical model that provides excellent agreement with experimental results and facilitates the understanding of the dynamics.

arXiv:2310.18525•Oct 27, 2023•1 citation

Conversion of bright magneto-optical resonances into dark resonances at fixed laser frequency for D2 excitation of atomic rubidium

Marcis P. Auzinsh, Andris Bērziņš, R. Ferber +4 more

Nonlinear magneto-optical resonances on the hyperfine transitions belonging to the ${D}_{2}$ line of rubidium were changed from bright to dark resonances by changing the laser power density of the single exciting laser field or by changing the vapor temperature in the cell. In one set of experiments atoms were excited by linearly polarized light from an extended cavity diode laser with polarization vector perpendicular to the light's propagation direction and magnetic field, and laser-induced fluorescence was observed along the direction of the magnetic field, which was scanned. A low-contrast bright resonance was observed at low laser power densities when the laser was tuned to the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of ${}^{87}$Rb and near to the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of ${}^{85}$Rb. The bright resonance became dark as the laser power density was increased above 0.6 mW/cm${}^{2}$ or 0.8 mW/cm${}^{2}$, respectively. When the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of ${}^{87}$Rb was excited with circularly polarized light in a second set of experiments, a bright resonance was observed, which became dark when the temperature was increased to around 50${}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\circ}}$C. The experimental observations at room temperature could be reproduced with good agreement by calculations based on a theoretical model, although the theoretical model was not able to describe measurements at elevated temperatures, where reabsorption was thought to play a decisive role. The model was derived from the optical Bloch equations and included all nearby hyperfine components, averaging over the Doppler profile, mixing of magnetic sublevels in the external magnetic field, and a treatment of the coherence properties of the exciting radiation field.

arXiv:1111.6432•Physical Review A•Mar 16, 2012•22 citations

Polarization-dependent sensitivity of level-crossing, coherent-population-trapping resonances to stray magnetic fields

Arno Huss, Roland Lammegger, Laurentius Windholz +5 more

Coherent-population-trapping resonances within the degenerate two-level system of the F=2-->F′=1 transition of the 87Rb D1 line were investigated in an uncoated Rb vapor cell by means of level-crossing-type experiments. Tuning over the two-photon resonance is achieved sweeping a magnetic field around zero value. The influence of transverse magnetic fields on the amplitude and the width of the resonances, recorded in fluorescence and absorption, were investigated in the cases of excitation with linear, circular, and elliptical laser light polarization. A theoretical analysis was performed for the case of linearly polarized excitation, the results of which are in good agreement with the experiment.

Journal of the Optical Society of America B•Aug 31, 2006•41 citations

Magneto-optical resonance of the polarized fluorescence in a paraffin-coated87Rb vacuum cell

Elena T. Taskova, Emilia A. Alipieva, G. Todorov

In this work we investigate the magneto-optical resonance on 87Rb D1 line. In two-level degenerated system this resonance is due to the interference between the Zeeman sub-levels, created by interaction of resonance linear polarized laser beam with the atoms. The observed signal is detected by sweeping magnetic field B around its zero value. This phenomenon is also known as a Coherent Population Trapping (CPT) in Hanle-configuration. In a coated vacuum cell the fluorescence signal has a complex form, because the anti-relaxation coating preserves the created coherence, having different relaxation rates. The ground state coherence is transmitted by the laser field to the upper level; thereby polarization moments with different rank contribute to the fluorescence. The manifestation of the different polarization moments in the observed signal depends on the geometry of the experiment – direction of observation, plane of the laser polarization, polarization of the registered light. The resonances obtained in the fluorescence having different polarization are compared in order to clear up what are the contributions to the fluorescent signal from the polarization moments with different rank. The experiment is performed on the D1 87Rb line, F=2→ F=1 transition in a paraffin-coated cell. The magneto-optical resonances, detected in two orthogonal polarizations are measured. Numerical calculations with parameters, close to the experimental ones are performed by using a program, which is based on the irreducible tensor operator formalism. The results of the modelling are compared with the measured ones at different experimental conditions.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 8, 2015•0 citations

Multilevel dark states in an inhomogeneously broadened open atomic system

Yifu Zhu, Shijun Wang, Neil Mulchan

We report an experimental observation of coherent population trapping in multilevel dark states prepared in the ground hyperfine states of ${}^{87}\mathrm{Rb}$ atoms confined in a room-temperature vapor cell. The dark states are created by a linearly polarized coupling laser that is tuned to the ${}^{87}\mathrm{Rb}$ ${D}_{1}$ $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=1$ or 2 transition and establishes \ensuremath{\Lambda}-type transition chains. The Doppler shift for the \ensuremath{\Lambda}-type transition chains is compensated by the left and right circularly polarized components of the coupling laser. The multilevel dark states that consist of three or two magnetic sublevels among the five degenerate magnetic sublevels in the $F=2$ ground hyperfine state are probed by a weak probe laser scanned across the same ${D}_{1}$ transition and their existence is manifested by a strong dependence of the probe excitation on the probe polarization. Our experiment demonstrates the importance of coherent population trapping in a laser coupled degenerate multilevel open atomic system, which may play an important role in diverse physical phenomena such as atom cooling and trapping, optical pumping, and multiple laser excitation and ionization of atoms and molecules.

Physical Review A•May 1, 1999•16 citations
We report an experimental observation of a dark region, around the zero-field point of a spheric quadrupole magnetostatic field, in spatial fluorescence emitted by dilute vapor atoms, which were excited by a circularly polarized traveling-wave laser tuned to a F\ensuremath→F+1\stackrel{\ensuremath{\rightarrow}}{F}F+1F\ensuremath→​F+1 transition of 87Rb.{}^{87}\mathrm{Rb}.87Rb. By ruling out some possible sources, we show that the fluorescence decrease is associated with the three-dimensional nature of the magnetic field; it is a consequence of a precession of magnetic dipole moments induced by the radial magnetic field, which significantly cancels the orientation caused by optical pumping near the point of level crossing in the presence of the axial magnetic field. In an alternative way, the phenomenon can be understood as resulting from a destructive quantum interference, which is related to a coherent double-quantum coupling of atomic levels with two fields; one is the laser field, the other is the magnetic field. Analytic expressions for the half-width and contrast of the dark region have been obtained with a simplified model in the limit of low laser power. A qualitative agreement between the theory and experiment is found. The relevance of our study to laser cooling and trapping in a widely used magneto-optical trap based on such a quadrupole magnetic field is discussed. Finally, some applications of the phenomenon are also presented.
The quadrupole magnetostatic field (QMF), together with 3 pairs of laser beams, known as the magneto-optical trap, has been widely used for cooling and trapping atoms. This report concerns itself with some new phenomena observed in fluorescence emitted by Rb atoms in QMF under the circumstances of a single /spl sigma/ laser beam. A circularly polarized laser traveling-wave tuned to D/sub 2/-line is passed through a vacuum chamber along the central axis of two anti-Helmholtz coils. The fluorescence emitted by Rb atoms excited by the circularly polarized light in the direction at right angle to the direction of the incident laser beam is collected and imaged with all polarized directions taken into account. From the camera picture we can see that, around the zero-field point, there exists a dark region, the size of which is inversely proportional to the field gradient and is not sensitive to the detuning. The dark region corresponds to a dip in the profile of the fluorescence intensity versus the space. An attempt is made to explain the origin of this dark region.
We present experimental results and a theoretical model that illustrate how competing eigenbases can determine the dynamics of a fluorescing atom. In the absence of a magnetic field, the atom can get trapped in a dark state, which inhibits fluorescence. In general, this will happen when the magnetic degeneracy of the ground state is greater than the one of the excited state. A canonical way to avoid optical pumping to dark states is to apply a magnetic field at an angle with respect to the polarization of the exciting light. This generates a competition of eigenbases which manifests as a crossover between two regimes dominated either by the laser or the magnetic field. We illustrate this crossover with fluorescence measurements on a single laser-cooled calcium ion in a Paul trap and find that it occurs at a critical laser intensity that is proportional to the external magnetic field. We contrast our results with numerical simulations of the atomic levels involved and also present a simple theoretical model that provides excellent agreement with experimental results and facilitates the understanding of the dynamics.
Nonlinear magneto-optical resonances on the hyperfine transitions belonging to the D2{D}_{2}D2​ line of rubidium were changed from bright to dark resonances by changing the laser power density of the single exciting laser field or by changing the vapor temperature in the cell. In one set of experiments atoms were excited by linearly polarized light from an extended cavity diode laser with polarization vector perpendicular to the light's propagation direction and magnetic field, and laser-induced fluorescence was observed along the direction of the magnetic field, which was scanned. A low-contrast bright resonance was observed at low laser power densities when the laser was tuned to the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 87{}^{87}87Rb and near to the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of 85{}^{85}85Rb. The bright resonance became dark as the laser power density was increased above 0.6 mW/cm2{}^{2}2 or 0.8 mW/cm2{}^{2}2, respectively. When the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 87{}^{87}87Rb was excited with circularly polarized light in a second set of experiments, a bright resonance was observed, which became dark when the temperature was increased to around 50${}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\circ}}$C. The experimental observations at room temperature could be reproduced with good agreement by calculations based on a theoretical model, although the theoretical model was not able to describe measurements at elevated temperatures, where reabsorption was thought to play a decisive role. The model was derived from the optical Bloch equations and included all nearby hyperfine components, averaging over the Doppler profile, mixing of magnetic sublevels in the external magnetic field, and a treatment of the coherence properties of the exciting radiation field.
Coherent-population-trapping resonances within the degenerate two-level system of the F=2-->F′=1 transition of the 87Rb D1 line were investigated in an uncoated Rb vapor cell by means of level-crossing-type experiments. Tuning over the two-photon resonance is achieved sweeping a magnetic field around zero value. The influence of transverse magnetic fields on the amplitude and the width of the resonances, recorded in fluorescence and absorption, were investigated in the cases of excitation with linear, circular, and elliptical laser light polarization. A theoretical analysis was performed for the case of linearly polarized excitation, the results of which are in good agreement with the experiment.
In this work we investigate the magneto-optical resonance on 87Rb D1 line. In two-level degenerated system this resonance is due to the interference between the Zeeman sub-levels, created by interaction of resonance linear polarized laser beam with the atoms. The observed signal is detected by sweeping magnetic field B around its zero value. This phenomenon is also known as a Coherent Population Trapping (CPT) in Hanle-configuration. In a coated vacuum cell the fluorescence signal has a complex form, because the anti-relaxation coating preserves the created coherence, having different relaxation rates. The ground state coherence is transmitted by the laser field to the upper level; thereby polarization moments with different rank contribute to the fluorescence. The manifestation of the different polarization moments in the observed signal depends on the geometry of the experiment – direction of observation, plane of the laser polarization, polarization of the registered light. The resonances obtained in the fluorescence having different polarization are compared in order to clear up what are the contributions to the fluorescent signal from the polarization moments with different rank. The experiment is performed on the D1 87Rb line, F=2→ F=1 transition in a paraffin-coated cell. The magneto-optical resonances, detected in two orthogonal polarizations are measured. Numerical calculations with parameters, close to the experimental ones are performed by using a program, which is based on the irreducible tensor operator formalism. The results of the modelling are compared with the measured ones at different experimental conditions.
We report an experimental observation of coherent population trapping in multilevel dark states prepared in the ground hyperfine states of 87Rb{}^{87}\mathrm{Rb}87Rb atoms confined in a room-temperature vapor cell. The dark states are created by a linearly polarized coupling laser that is tuned to the 87Rb{}^{87}\mathrm{Rb}87Rb D1{D}_{1}D1​ $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=1$ or 2 transition and establishes \ensuremath{\Lambda}-type transition chains. The Doppler shift for the \ensuremath{\Lambda}-type transition chains is compensated by the left and right circularly polarized components of the coupling laser. The multilevel dark states that consist of three or two magnetic sublevels among the five degenerate magnetic sublevels in the F=2F=2F=2 ground hyperfine state are probed by a weak probe laser scanned across the same D1{D}_{1}D1​ transition and their existence is manifested by a strong dependence of the probe excitation on the probe polarization. Our experiment demonstrates the importance of coherent population trapping in a laser coupled degenerate multilevel open atomic system, which may play an important role in diverse physical phenomena such as atom cooling and trapping, optical pumping, and multiple laser excitation and ionization of atoms and molecules.