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Chinese Physics B

Spin dynamics of magnetic resonance with parametric modulation in a potassium vapor cell

Rui Zhang, Zhiguo Wang, Xiang Peng, Wenhao Li, Song-Jian Li, Hong Mei Guo

Published Mar 1, 2017• 9 citations
Publisher

Abstract

A typical magnetic-resonance scheme employs a static bias magnetic field and an orthogonal driving magnetic field oscillating at the Larmor frequency, at which the atomic polarization precesses around the static magnetic field. Here we demonstrate both theoretically and experimentally the variations of the resonance condition and the spin precession dynamics resulting from the parametric modulation of the bias field. We show that the driving magnetic field with the frequency detuned by different harmonics of the parametric modulation frequency can lead to resonance as well. Also, a series of frequency sidebands centered at the driving frequency and spaced by the parametric modulation frequency can be observed in the precession of the atomic polarization. We further show that the resonant amplitudes of the sidebands can be controlled by varying the ratio between the amplitude and the frequency of the parametric modulation. These effects could be used in different atomic magnetometry applications.

DOI
10.1088/1674-1056/26/3/030701

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A typical magnetic-resonance scheme employs a static bias magnetic field and an orthogonal driving magnetic field oscillating at the Larmor frequency, at which the atomic polarization precesses around the static magnetic field. Here we demonstrate both theoretically and experimentally the variations of the resonance condition and the spin precession dynamics resulting from the parametric modulation of the bias field. We show that the driving magnetic field with the frequency detuned by different harmonics of the parametric modulation frequency can lead to resonance as well. Also, a series of frequency sidebands centered at the driving frequency and spaced by the parametric modulation frequency can be observed in the precession of the atomic polarization. We further show that the resonant amplitudes of the sidebands can be controlled by varying the ratio between the amplitude and the frequency of the parametric modulation. These effects could be used in different atomic magnetometry applications.
We present a combined theoretical and experimental study of magnetic resonance transitions induced by polarization-modulated light in cesium vapor exposed to a transverse magnetic field. Signals are obtained by phase-sensitive analysis of the light power traversing the vapor cell at six harmonics of the polarization modulation frequency. Resonances appear whenever the Larmor frequency matches an integer multiple of the modulation frequency. We have further investigated the modifications of the spectra when varying the modulation duty cycle. The resonance amplitudes of both in-phase and quadrature components are well described in terms of the Fourier coefficients of the modulation function. The background-free signals generated by the polarization modulation scheme have a high application potential in atomic magnetometry.
Introduction Soon after the development of optical magnetometers based on the radio-optical double resonance method (see Chapter 4), it was realized by Bell and Bloom [1] that an alternative method for optical magnetometry was to modulate the light used for optical pumping at a frequency resonant with the Larmor precession of atomic spins. In a Bell-Bloom optical magnetometer, circularly polarized light resonant with an atomic transition propagates through an atomic vapor along a direction transverse to a magnetic field B . Atomic spins immersed in B precess at the Larmor frequency Ω L , and when the light intensity is modulated at Ω m = Ω L , a resonance in the transmitted light intensity is observed. The essential ideas of the Bell–Bloom optical magnetometer are reviewed in Chapter 1 (Section 1.2), and can be summarized in terms of what Bell and Bloom termed optically driven spin precession: in analogy with a driven harmonic oscillator, in a magnetic field B atomic spins precess at a natural frequency equal to Ω L and the light acts as a driving force oscillating at the modulation frequency Ω m . From another point of view, the Bell-Bloom optical magnetometer can be described in terms of synchronous optical pumping: when Ω m = Ω L , there is a “stroboscopic” resonance in which atoms are optically pumped into a spin state stationary in the frame rotating with Ω L . Depending on the details of the atomic structure, the spin state stationary in the rotating frame can be either a dark state that does not interact with the modulated light or a bright state for which the strength of the light–atom interaction is increased.
We experimentally demonstrate resonant symmetry lifting in a parametrically modulated magneto-optical trap of cold 85Rb^{85}\mathrm{Rb}85Rb atoms. This is achieved by applying a weak additional modulation at half the frequency of the strong parametric modulation, which acts as an effective static bias field to the system. We measure the system response by varying the amplitude of the additional fictitious bias as well as the relative phase between the bias and the parametric drive, and the results are in good agreement with theory. The additional modulation provides an additional degree of freedom to control the system, which is useful for investigating system properties such as susceptibility, dynamic response, and related critical phenomena. We also have measured the amplitude of the response to higher harmonics of the additional modulation frequency, which allows more precise understanding of the system dynamics.
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.
Abstract We theoretically describe the phenomenon of non-adiabatic spin dynamics, which occurs in a gas cell filled by alkali vapor in the presence of a strong alternating magnetic field and pump light. Steep increase of the spin polarization occurs if the frequency of the magnetic field is equal to the certain value. The observable effect relies on the periodic field that consists of two perpendicular components defined by harmonics with the same amplitudes and different frequencies. The considered effect of the coherent spin motion cannot be explained by a resonance, because the Larmor precession is absent without a constant component of magnetic field. Moreover, there are some clearly visible peaks in the excitation spectrum of spin polarization, which are narrow in comparison to the relaxation rate. Detailed analysis according to proposed quantum model results in the reasoning of the effect via qualitative properties of non-adiabatic dynamics of atomic spin.
We theoretically describe the phenomenon of non-adiabatic spin dynamics, which occurs in a gas cell filled by alkali vapor in presence of a strong alternating magnetic field and pump light. Steep increase of the spin polarization occurs if frequency of the magnetic field is equal to the certain value. Although, the observable effect relies on the periodic field that consists of two perpendicular components defined by harmonics with the same amplitudes and different frequencies. Considered spin effect cannot be explained by a resonance, because the own Larmor frequency of spin precession is absent without a constant component of magnetic field. Moreover, there are some clearly visible peaks in the excitation spectrum of spin polarization, and they are super narrow in comparison to relaxation rate. Detailed analysis according to proposed quantum model results in the reasoning of the effect via qualitative properties of non-adiabatic dynamics of atomic spin.