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arXiv:physics/0608109 · Physical Review A

Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances

Szymon Pustelny, Derek F. Jackson Kimball, Simon Rochester, Valeriy V. Yashchuk, Dmitry Budker

Published Dec 12, 2006• 74 citations
arXivHTMLPDF

Abstract

In this work, a sensitivity of the rate of relaxation of ground-state atomic coherences to magnetic-field inhomogeneities is studied. Such coherences give rise to many interesting phenomena in light-atom interactions, and their lifetimes are a limiting factor for achieving better sensitivity, resolution, or contrast in many applications. For atoms contained in a vapor cell, some of the coherence-relaxation mechanisms are related to magnetic-field inhomogeneities. We present a simple model describing relaxation due to such inhomogeneities in a buffer-gas-free antirelaxation-coated cell. A relation is given between relaxation rate and magnetic-field inhomogeneities including the dependence on cell size and atomic species. Experimental results, which confirm predictions of the model, are presented. Different regimes, in which the relaxation rate is equally sensitive to the gradients in any direction and in which it is insensitive to gradients transverse to the bias magnetic field, are predicted and demonstrated experimentally.

DOI
10.1103/physreva.74.063406

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Field-inhomogeneity-induced relaxation of atomic spins confined in vapor cells with depolarizing walls is studied. In contrast to nuclear spins, such as noble-gas spins, which experience minimal polarization loss at cell walls, atomic spins in uncoated cells undergo randomization at the boundaries. This distinct boundary condition results in a varied dependence of the relaxation rate on the field gradient. By solving the Bloch-Torrey equation under fully depolarizing boundary conditions, we illustrate that the relaxation rate induced by field inhomogeneity is more pronounced for spins with a smaller original relaxation rate (in the absence of the inhomogeneous field). We establish an upper limit for the relaxation rate through calculations in the perturbation regime. Moreover, we connect it to the spin-exchange-relaxation-free magnetometers, demonstrating that its linewidth is most sensitive to inhomogeneous fields along the magnetometer's sensitive axis. Our theoretical result agrees with the experimental data for cells subjected to small pump power. A deviation in high input-power scenarios arises from pump field attenuation, resulting in a nonuniformly distributed light shift that behaves like an inhomogeneous magnetic field.
In this work, we experimentally measure the broadened linewidth of magneto-optical resonance signal due to magnetic-field gradient with an alkali buffer-gas-free anti-relaxation-coated cell. We also study how the temperature of the atomic vapor cell affects the magneto-optical resonance signal linewidth under different magnetic-field gradients. Theoretical calculations show that the relaxation caused by magnetic-field gradient could be suppressed with increased temperature, which could be useful to optimize the working parameters for unshielded atomic magnetometer based on anti-relaxation-coated cells.
Reducing the transverse relaxation rate of alkali atoms is crucial to improve the sensitivity of the magnetometers. In a perturbative treatment of the effects of the magnetic-field gradients, the transverse relaxation rates of alkali atoms are predicted to be proportional to the square of the longitudinal magnetic-field gradient. The theoretical predictions are confirmed in our experiments. The magnetic-field gradients in the vapor cell are measured by experiments. The magnetic-field gradient in the cell is suppressed drastically through compensating it with the compensation coils. Experimental results show that suppressing the magnetic-field gradient can reduce the transverse relaxation rate of alkali atoms significantly. This study contributes to the development of ultra-high sensitivity alkali atomic magnetometers.
Several dispersionlike features in the magnetic field dependence of the nonlinear magneto-optic effect were observed in an experiment performed on rubidium atoms contained in a vapor cell with antirelaxation coating. The narrowest feature has effective resonance width $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}g\ensuremath{\mu}\ensuremath{\Delta}{B}_{z}\ensuremath{\approx}2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}1.3\mathrm{Hz}$, where $\ensuremath{\Delta}{B}_{z}\ensuremath{\approx}2.8\ensuremath{\mu}\mathrm{G}$ is the peak-to-peak separation. The observed nontrivial dependence of the magneto-optic effect on transverse magnetic fields is discussed. The results of this work may be applied to low-field magnetometry, to parity and time reversal invariance violation experiments, etc.
In this work, the influence of the operating magnetic field gradient on the frequency of the 0-0-transition of a lamp-pumped rubidium atomic clock was investigated. As a gas cell, we used a cell with an antirelaxation coating of the walls and containing Rb87 atoms. Experimental dependences of the atomic clock model resonance frequency on the applied magnetic field gradient in the range of 0.003 Oe / cm - 0.012 Oe / cm and in the magnetic fields range of 0.0135 Oe - 0.027 Oe were obtained. The orientation 0-0-resonance frequency shift having value more than value of the frequency shift due to the quadratic magnetic dependence of the 0-0-resonance frequency was measured.
Magnetic-field-gradient-induced spin polarization transverse relaxation is re-examined in an alkali-metal atomic cell with antirelaxation coating. The experimentally observed motional-narrowing effect in a paraffin-coated vapor cell, a phenomenon for depicting the suppression of spin polarization transverse relaxation caused by the magnetic-field gradient, is more than an order of magnitude weaker than theoretical predictions. Such a discrepancy is due to the existence of background gas. By taking the background gas into consideration, Redfield theory combined with the Langevin approach is proposed to depict the magnetic-field-gradient-induced spin relaxation in a coated cell, and the model is verified to be consistent with the previous results derived under two limits in which the mean free path is either much smaller (diffusion regime) or much larger than (ballistic regime) the cell size. Our work provides a potentially feasible method to evaluate the background gas pressure inside the coated cell, and it can help to foster better comprehension of the performance of an antirelaxation coated cell.