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arXiv:1501.00608

Time-dependent resonant magneto-optical rotation

D. Dziczek

Published Jan 3, 2015• 0 citations

Abstract

Results of a fairly straightforward experiment on resonant magneto-optical rotation by rubidium-87 atoms revealed strong time-dependence of the polarization plane of light emerging from atomic vapors following a sudden irradiation with a laser beam. The rotation of the plane appears as a not direct consequence of the influence of the magnetic field on atoms. Reported measurements conducted using a vapor cell without any buffer gas or an anti-relaxation wall coating show that transmitted light has initially the same (linear) polarization as the incident one. Rotation of the polarization plane caused by an axial magnetic field develops in time scales similar to the pace of establishing the optical pumping/relaxation equilibrium in the atomic ensemble. The traditional passive Faraday rotation picture providing working description for the resonant magneto-optical effects in steady-state conditions does not explain the observed sequence of evolution of the polarization. The picture has to be augmented with analysis of time dependence in the spatial distribution of relevant quantum states within the atomic ensemble as well as longitudinal and transversal intensity profiles of the light beam. Isolation of external effects caused by the optical pumping and relaxation processes from consequences of internal atomic coherences should uncover more details of mechanisms of the latter in the presence of magnetic field. Plentitude of data available from time-dependent polarization measurements provides strong incentives for further development and tests of comprehensive models of coherent interactions of atomic ensembles with radiation and possibly a base for additional advance in understanding and applications of these phenomena.

DOI: 10.48550/arxiv.1501.00608

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Results of a fairly straightforward experiment on resonant magneto-optical rotation by rubidium-87 atoms revealed strong time-dependence of the polarization plane of light emerging from atomic vapors following a sudden irradiation with a laser beam. The rotation of the plane appears as a not direct consequence of the influence of the magnetic field on atoms. Reported measurements conducted using a vapor cell without any buffer gas or an anti-relaxation wall coating show that transmitted light has initially the same (linear) polarization as the incident one. Rotation of the polarization plane caused by an axial magnetic field develops in time scales similar to the pace of establishing the optical pumping/relaxation equilibrium in the atomic ensemble. The traditional passive Faraday rotation picture providing working description for the resonant magneto-optical effects in steady-state conditions does not explain the observed sequence of evolution of the polarization. The picture has to be augmented with analysis of time dependence in the spatial distribution of relevant quantum states within the atomic ensemble as well as longitudinal and transversal intensity profiles of the light beam. Isolation of external effects caused by the optical pumping and relaxation processes from consequences of internal atomic coherences should uncover more details of mechanisms of the latter in the presence of magnetic field. Plentitude of data available from time-dependent polarization measurements provides strong incentives for further development and tests of comprehensive models of coherent interactions of atomic ensembles with radiation and possibly a base for additional advance in understanding and applications of these phenomena.

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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.

When a gas of ultracold atoms is suddenly illuminated by light that is nearly resonant with an atomic transition, the atoms cannot respond instantaneously. This noninstantaneous response means the gas is initially more transparent to the applied light than in steady state. The timescale associated with the development of light absorption is set by the atomic excited-state lifetime. Similarly, the index of refraction in the gas also requires time to reach a steady-state value, but the development of the associated phase response is expected to be slower than absorption effects. Faraday rotation is one manifestation of differing indices of refraction for orthogonal circular light polarization components. We have performed experiments measuring the time-dependent development of polarization rotation in an ultracold gas subjected to a magnetic field. Our measurements match theoretical predictions based on solving optical Bloch equations. We are able to identify how parameters such as steady-state optical thickness and applied magnetic field strength influence the development of Faraday rotation.

A general solution of the Boltzmann kinetic equations for the atomic density matrix in a long cylindrical cell with an antirelaxation coating of the walls under conditions of laser pumping in a magnetic field is obtained. The theory involves only one relaxation parameter—the coefficient K refl of the diffusion reflection of polarized atoms from the cell walls. The solution consists of two terms. The first term is proportional to K refl and describes the contribution to the atomic polarization made by multiple passages of atoms through the pumping beam after their reflection from the walls with the antirelaxation coating. The second term does not depend on K refl and describes the polarization formed during a single passage of atoms through the pumping beam. This solution allows one to calculate the Stokes parameters for the pumping beam transmitted through the cell that are measured in experiments on magneto-optical rotation of the light polarization plane.

The dynamics of resonant light propagation in rubidium vapor in a cell with antirelaxation wall coating are investigated. We change the polarization of the input light and measure the time dependence of the polarization after the cell. The observed dynamics are shown to be analogous to those in electromagnetically induced transparency. Spectral dependence of light pulse delays is found to be similar to that of nonlinear magneto-optic rotation. Delays up to $\ensuremath{\approx}13\mathrm{ms}$ are observed, corresponding to a

8\mathrm{m}/\mathrm{s}

group velocity. Fields of a few microgauss are used to control the group velocity.