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Physical Review A

Nonlinear magneto-optical rotation narrowing in vacuum gas cells due to interference between atomic dark states of two spatially separated laser beams

Marina M. Mijailović, Z. D. Grujić, Milan Radonjić, D. Arsenović, B. M. Jelenkovic

Published Nov 12, 2009• 1 citation
Publisher

Abstract

We present, experimentally and theoretically, nonlinear magneto-optical rotation (NMOR) using two spatially separated laser beams, the pump laser beam for creation and the probe laser beam for detection of the coherence between ground Zeeman sublevels. Both pump and probe lasers are tuned to ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=1$ transition in $^{87}\text{R}\text{b}$. With the specially designed spatial configuration of the pump and the probe beams we were able to obtain dispersively shaped probe laser NMOR resonances in the Rb vacuum gas cell. The theory indicates that the obtained line shapes are due to the interference between prepared atomic states and the probe laser field. The interference nature of the resonances is supported by narrowing of NMOR resonances with increased separation between laser beams, and by the shift of the central fringe from the zero magnetic field with increased angle between initial orientation of electric vectors of linearly polarized pump and probe beams.

DOI
10.1103/physreva.80.053819

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Письма в Журнал экспериментальной и теоретической физики•Apr 15, 2023•1 citation
We present, experimentally and theoretically, nonlinear magneto-optical rotation (NMOR) using two spatially separated laser beams, the pump laser beam for creation and the probe laser beam for detection of the coherence between ground Zeeman sublevels. Both pump and probe lasers are tuned to Fg=2\ensuremath→Fe=1{F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=1Fg​=2\ensuremath→Fe​=1 transition in 87Rb^{87}\text{R}\text{b}87Rb. With the specially designed spatial configuration of the pump and the probe beams we were able to obtain dispersively shaped probe laser NMOR resonances in the Rb vacuum gas cell. The theory indicates that the obtained line shapes are due to the interference between prepared atomic states and the probe laser field. The interference nature of the resonances is supported by narrowing of NMOR resonances with increased separation between laser beams, and by the shift of the central fringe from the zero magnetic field with increased angle between initial orientation of electric vectors of linearly polarized pump and probe beams.
Nonlinear magneto-optical rotation (NMOR) of linearly polarized light, resonant to the Fg = 2 → Fe = 1 atomic transition of D1 line of 87Rb is investigated experimentally, by applying spatially separated laser fields in the Rb vacuum cell. In our experiment, the probe laser beam propagates through the center of the pump laser beam, which has the shape of a hollow cylinder. We have measured the rotation of the probe laser beam polarization with respect to the incident polarization, as a function of the external magnetic field, parallel to the laser beam propagation. We show substantial narrowing of the resonance if the pump beam, with the same linear polarization, is present. The opposite direction of the probe rotation was obtained when the pump laser beam polarization is orthogonal to the probe laser beam polarization.
Experimental and theoretical investigations show the strong effect of the pump beam, spatially separated from the probe beam, on the probe's electromagnetically induced absorption (EIA) and nonlinear magneto-optical rotation (NMOR). Linearly polarized pump and probe laser beams are locked to the Fg = 2 → Fe = 3 transition of the 87Rb D2 line and pass a vacuum Rb gas cell coaxially. We show that the observed narrowing of EIA and NMOR resonances is due to the Ramsey effect. Linewidths of the resonances decrease when the size of the dark region between pump and probe lasers increases. Variation of the angle between pump and probe linear polarizations strongly influences the phases of atomic coherences generated by the pump beam and consequently the line-shapes of the probe EIA and NMOR resonances. Complete change of the resonance sign is possible if the phases of the ground state coherences, Δmg = 2, are altered by π. The central EIA fringe becomes less pronounced if the probe intensity increases, due to the larger probe contribution to atomic evolution. Ramsey-like interference is a manifestation of the evolution of ground state Zeeman coherences, required for EIA, in the dark region in the presence of a small magnetic field.
Specific types of atomic coherences between Zeeman sublevels can be generated and detected using a method based on nonlinear magneto-optical rotation with frequency-modulated light. Linearly polarized, frequency-modulated light is employed to selectively generate ground-state coherences between Zeeman sublevels for which $\mathrm{\ensuremath{\Delta}}m=2$ and $\mathrm{\ensuremath{\Delta}}m=4$ in 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb atoms, and additionally $\mathrm{\ensuremath{\Delta}}m=6$ in 85Rb^{85}\mathrm{Rb}85Rb. The atomic coherences are detected with a separate, unmodulated probe light beam. Separation of the pump and probe beams enables independent investigation of the processes of creation and detection of the atomic coherences. With the present technique the transfer of the Zeeman coherences, including high-order coherences, from excited to ground state by spontaneous emission has been observed.
We compare the nonlinear magneto-optical rotation (NMOR) effect in a single-beam probe scheme and a two-beam Raman-coherence-assisted scheme using cold rubidium atoms produced with an integrating sphere apparatus. In both schemes, NMOR arising from D1 and D2 excitation combinations was studied. We show that adding a Raman-coherence manipulation laser can substantially increase the NMOR, and the largest NMOR enhancement occurs when both probe and Raman-coherence lasers couple the same D2 transitions with different detunings. For far-off resonance excitation with a weak probe laser, we show that the Raman-coherence-assisted NMOR enhancement can be about 6 times larger than the single probe scheme operated under the same conditions. The Raman-coherence-enhanced NMOR is also shown to be substantially larger than that from an optically pumped magnetometer using a single strong circularly polarized probe.
Larmor precession of laser-polarized atoms contained in antirelaxation-coated cells, detected via nonlinear magneto-optical rotation (NMOR), is a promising technique for a new generation of ultrasensitive atomic magnetometers. For magnetic fields directed along the light propagation direction, resonances in NMOR appear when linearly polarized light is frequency or amplitude modulated at twice the Larmor frequency. Because the frequency of these resonances depends on the magnitude but not the direction of the field, they are useful for scalar magnetometry. Additional NMOR resonances at the Larmor frequency appear when the magnetic field is tilted away from the light propagation direction in the plane defined by the light propagation and polarization vectors. These resonances, studied both experimentally and with a density matrix calculation in the present work, offer a convenient method of achieving additional information about a direction of the magnetic field.
Nonlinear resonances in alkali metal vapor, which are detected by the magneto-optical rotation of the linear polarization of light, are actively used in quantum magnetometry to fabricate atomic magnetometers. The magneto-optical rotation in most such sensors is due to magnetic birefringence, and rotation angles usually do not exceed tens of milliradians. In this work, an experiment where magneto-optical resonances of linear polarization rotation of a probe wave are due to strong dichroism induced in a medium by a counterpropagating pump wave has been proposed. Both waves are in resonance with the Fg = 2 → Fe = 1 optical transition in the 87Rb D1 line (λ ≈ 795 nm). Experiments have been carried out with a 2-cm-long cylindrical cell filled with a buffer gas, and the maximum rotation angle is ≈390 mrad (22°) at a width of resonance of about 300 nT. The results show that the configuration proposed for the observation of magneto-optical rotation is promising for the fabrication of compact high-sensitivity atomic magnetometers.