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arXiv:1904.08753 · Physical Review A

Transient dynamics of nonlinear magneto-optical rotation in the presence of a transverse magnetic field

Raghwinder Singh Grewal, Szymon Pustelny

Published Mar 16, 2020• 9 citations
arXivHTMLPDF

Abstract

Nonlinear magneto-optical rotation is studied under nonequilibrium conditions. The polarization rotation of linearly polarized light, traversing a room-temperature rubidium vapor, is observed versus the time-dependent (swept) longitudinal magnetic field in the presence of static transverse magnetic fields. Presence of the transverse fields modifies the character of the observed signals. In particular, for the weaker fields, the longitudinal-field sweep leads to a two-frequency oscillation of the polarization rotation while crossing zero. Unlike the steady state, this was observed independent of the transverse-field direction. For the stronger transverse fields, the oscillations deteriorate eventually reaching a situation when a nonoscillating dynamic signal, with a distinct minimum close to the zero longitudinal field, is observed. The presented experimental results are supported with theoretical analysis based on the density-matrix formalism. The analysis confirms all the features of experimental results while providing an intuitive explanation of the observed behavior based on angular-momentum probability surfaces used for density-matrix visualization.

DOI
10.1103/physreva.101.033825

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Nonlinear magneto-optical rotation is studied under nonequilibrium conditions. The polarization rotation of linearly polarized light, traversing a room-temperature rubidium vapor, is observed versus the time-dependent (swept) longitudinal magnetic field in the presence of static transverse magnetic fields. Presence of the transverse fields modifies the character of the observed signals. In particular, for the weaker fields, the longitudinal-field sweep leads to a two-frequency oscillation of the polarization rotation while crossing zero. Unlike the steady state, this was observed independent of the transverse-field direction. For the stronger transverse fields, the oscillations deteriorate eventually reaching a situation when a nonoscillating dynamic signal, with a distinct minimum close to the zero longitudinal field, is observed. The presented experimental results are supported with theoretical analysis based on the density-matrix formalism. The analysis confirms all the features of experimental results while providing an intuitive explanation of the observed behavior based on angular-momentum probability surfaces used for density-matrix visualization.
We analyze nonlinear magneto-optical rotation (NMOR) in rubidium vapor subjected to a continuously scanned magnetic field. By varying the magnetic-field sweep rate, a transition from traditionally observed dispersivelike NMOR signals (low sweep rate) to oscillating signals (higher sweep rates) is demonstrated. The transient oscillatory behavior is studied versus light and magnetic-field parameters, revealing a strong dependence of the signals on magnetic sweep rate and light intensity. The experimental results are supported with density-matrix calculations, which enable quantitative analysis of the effect. Fitting of the signals simulated versus different parameters with a theoretically motivated curve reveals the presence of oscillatory and static components in the signals. The components depend differently on the system parameters, which suggests their distinct nature. The investigations provide insight into the dynamics of ground-state coherence generation and enable application of NMOR in detection of transient spin couplings.
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.
We report on investigations of nonlinear magneto-optical rotation (NMOR) in rubidium vapor subjected to a modulated magnetic field and continuous-wave (cw) laser-light illumination. By superimposing modulation and a static (dc) magnetic field, we demonstrate the appearance of resonances at both small and large (compared to the ground-state relaxation rate) values of the static field. Since in conventional NMOR there is no rotation at high fields, this suggests an existence of an alternative mechanism generating anisotropy in the considered case, which we identify as parametric resonance. The experiments are performed using light of small ellipticity, and rotation signals are significantly enhanced by combining atom-induced polarization rotation with a passive rotation induced with a wave plate. All the observations are supported with theoretical simulations. The density-matrix formalism and angular-momentum probability surfaces are used to provide an intuitive explanation of the observed signals.
In this paper, we analyze the transient behavior of nonlinear magneto-optical rotation in a 87Rb vapor cell. Our focus is on optimizing the optical rotation signal by identifying influential factors. We investigate the impact of cell temperature on alkali atom density and consider characteristics of the light field, such as polarization direction, frequency, intensity, and beam diameter. Low scanning magnetic field rates produce the usual absorption signal, whereas high rates show an asymmetric transient response with oscillatory decay. To further investigate this phenomenon, we evaluate signal amplitude and resonant peaks along the x-, y-, and z-axis directions. Notably, we establish a one-dimensional quadratic equation that describes the relationship between magnetic field scan rate and signal amplitude/peak value. Our findings facilitate the quick evaluation of cell performance, provide insights into the dynamics of ground-state coherence generation, and have potential applications in detecting transient spin coupling or monitoring magnetic fields.
We observe a narrow secondary dispersive feature nested within conventional nonlinear magneto-optical rotation (NMOR) signals obtained with a laser-cooled rubidium vapor. A similar feature has been previously named a "twist" by Budker et. al., in the context of warm vapor optical magnetometry [Phys. Rev. A. 81, 5788-5791 (1998)], and was ascribed to simultaneous optical pumping through multiple nearby hyperfine levels. In this work the twist is observed in a cold atom vapor, where the hyperfine levels are individually addressable, and thus is due to a different mechanism. We experimentally and numerically characterize this twist in terms of magnetic field strength, polarization, and optical intensity and find good agreement between our data and numerical models. We find that the twist width is proportional to the magnetic field in the transverse direction, and therefore two independent directions of the magnetic field can be measured simultaneously. This technique is useful as a simple and rapid in-situ method for nulling background magnetic fields.