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arXiv:1711.06028 · Physical Review A

Transient dynamics of a nonlinear magneto-optical rotation

Raghwinder Singh Grewal, Szymon Pustelny, Andrzej Rybak, Marek Florkowski

Published Apr 16, 2018• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.97.043832

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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.
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.
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 study resonant nonlinear magneto-optic rotation (NMOR) in a paraffin-coated Rb vapor cell as the magnetic field is swept. At low sweep rates, the nonlinear rotation appears as a narrow resonance signal with a linewidth of about ``300300300 $\ensuremath{\mu}$G'' ($2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}420$ Hz). At high sweep rates, the signal shows transient response with an oscillatory decay. The decay time constant is of order 100100100 ms. The behavior is different for transitions starting from the lower or the upper hyperfine level of the ground state because of optical pumping effects.
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.
We observe the transient evolution of the laser pumped magnetic resonance in a paraffin-coated rubidium vapor cell and analyze the phenomena numerically by using the four-level density matrix. With the increased radio frequency (RF) sweep rate, the traditional Lorentz signal turns to an asymmetric shape at low sweep rate and starts to oscillate at a high sweep rate. The transient oscillation's features, including frequency and the decay time, are studied by suddenly turning on the RF field to the resonance Larmor precession frequency under the different RF field and light field parameters. The experimental result reveals the transient signals' strong dependence on the RF field power and light power. Especially, the transient oscillation frequency primarily depends on the RF field's power and whatever power the laser light is. When the laser power is lower, the transient oscillation frequency is proportional to the RF field's amplitude. These transient evolution signals are also confirmed with the numerical calculations based on the density-matrix equation of motion.
We study numerically the nonlinear magneto-optical rotation of polarization (NMOR) of the laser pulse during its propagation through a cold Rb cloud with induced Zeeman coherences and electromagnetically induced transparency. Evolution of NMOR is calculated by solving the Maxwell–Bloch equations. We consider a linearly polarized Gaussian pulse with different pulse peak amplitudes and widths. For an intensity peak of 5 mW cm−2 and full-width at half-maximum of 10 μs, transient behaviour of NMOR does not follow the pulse intensity variation: NMOR begins to decrease as the pulse's intensity nears its peak value. When the pulse has a smaller peak intensity, NMOR behaves qualitatively differently: the angle of rotation constantly increases during the pulse propagation. Observed differences are explained by the optical pumping into the dark state and the behaviour of the ground-state coherences subjected to coherent population trapping. The same pulse intensity, from different sides of the pulse, during rising and falling sides, produces qualitatively different NMOR shapes, its amplitudes and widths which result can be explained by the successive excitation of atoms during the pulse propagation. It was shown that increasing the relaxation rates of the ground-state coherences, shifts the maximum of the NMOR to higher magnetic field, while the atomic density strongly influences the magnitude of the NMOR.