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Optics Express

Transient evolution of optical magnetic resonance in rubidium vapor

Ge Jin, Yunfei Xu, Zhaoying Wang

Published Feb 25, 2019• 11 citations
Publisher

Abstract

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.

DOI
10.1364/oe.27.007087

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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 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 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.
The time evolution of the polarization of a rubidium atom spin ensemble driven by a resonant radio-frequency (RF) magnetic field is analyzed based on the rate equation. A simple optical pumping experimental system is constructed and the time response of the rubidium atomic ensemble is demonstrated by recording the transmitted intensity of pumping light. In the steady-state response, the polarization difference between the optical pumping steady state and the magnetic resonance steady state depends on the optical pumping power and RF magnetic intensity. We can obtain the optimal power value corresponding to the maximum polarization difference. In terms of transient response, where the intensity of RF magnetic field is too weak to observe Rabi oscillations, two decay processes between magnetic resonance and optical pumping steady states are monitored. The decay time from magnetic resonance steady state to optical pumping steady state depends on the optical pumping rate and the spin relaxation rate. The decay time from optical pumping steady state to magnetic resonance steady state depends on the optical pumping rate, the RF driving rate, and the spin relaxation rate. The scale factor of pumping rate to pumping power is obtained, in addition to that of RF driving rate to the RF magnetic field. It can provide an intuitive understanding of the spin dynamic evolution of the polarized atomic ensemble.
The temporal evolution of coherent population trapping (CPT) was observed in rubidium atomic vapor when sudden changes were made to the detuning of a weak Raman field. The subsequent creation and destruction of CPT are caused by the temporal oscillations of optically induced Raman coherence, with their period depending on the Raman detuning. The oscillating signal was observed over a time of order of tens of milliseconds, and the dependence of the relaxation time on the cell temperature and laser power were investigated. The main features of the experimental observations were well explained by the time-dependent density-matrix equations.
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.