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arXiv:1912.07553 · Physical Review A

Nanosecond-timescale development of Faraday rotation in an ultracold gas

Jonathan R. Gilbert, Mark A. Watkins, Jacob Roberts

Published May 20, 2020• 0 citations
arXivHTMLPDF

Abstract

When a gas of ultracold atoms is suddenly illuminated by light that is nearly resonant with an atomic transition, the atoms cannot respond instantaneously. This noninstantaneous response means the gas is initially more transparent to the applied light than in steady state. The timescale associated with the development of light absorption is set by the atomic excited-state lifetime. Similarly, the index of refraction in the gas also requires time to reach a steady-state value, but the development of the associated phase response is expected to be slower than absorption effects. Faraday rotation is one manifestation of differing indices of refraction for orthogonal circular light polarization components. We have performed experiments measuring the time-dependent development of polarization rotation in an ultracold gas subjected to a magnetic field. Our measurements match theoretical predictions based on solving optical Bloch equations. We are able to identify how parameters such as steady-state optical thickness and applied magnetic field strength influence the development of Faraday rotation.

DOI
10.1103/physreva.101.053848

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When a gas of ultracold atoms is suddenly illuminated by light that is nearly resonant with an atomic transition, the atoms cannot respond instantaneously. This noninstantaneous response means the gas is initially more transparent to the applied light than in steady state. The timescale associated with the development of light absorption is set by the atomic excited-state lifetime. Similarly, the index of refraction in the gas also requires time to reach a steady-state value, but the development of the associated phase response is expected to be slower than absorption effects. Faraday rotation is one manifestation of differing indices of refraction for orthogonal circular light polarization components. We have performed experiments measuring the time-dependent development of polarization rotation in an ultracold gas subjected to a magnetic field. Our measurements match theoretical predictions based on solving optical Bloch equations. We are able to identify how parameters such as steady-state optical thickness and applied magnetic field strength influence the development of Faraday rotation.
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Nonlinear in laser power, near-resonant light-atom interaction leads to a number of spectacular modifications of a well-known effect -polarization plane rotation in a magnetic field applied along the direction of light propagation.In particular, the rotation can be enhanced by up to nine orders of magnitude compared to the linear case.Faraday effect [ 1 ] is the rotation of the plane of linear light polarization by a medium in a magnetic field applied in the direction of light propagation.In 1898, Macaluso and Corbino eJ, studying absorption spectra of the alkali atoms in the presence of magnetic fields, discovered that the Faraday effect in the vicinity of resonance absorption lines also had a distinct resonant character.The essence of the Macaluso-Corbino effect can be illustrated by considering a simple case of a F= 1 ~ F'=O transition (Fig. 1 ).Linearly polarized light incident on the sample can be resolved into two counter-rotating circular components ( cr~.In the absence of a magnetic field, the M=±l sublevels are degenerate and the optical resonance
We report on a combined experimental and theoretical study of polarization self-rotation in an ultracold atomic sample. In the experiments, a probe laser is tuned in the spectral vicinity of the D1{D}_{1}D1​ line to observe polarization self-rotation in a sample of ultracold 87Rb^{87}\mathrm{Rb}87Rb prepared in a magneto-optical trap (MOT). Systematic measurements of the rotation angle of the light-polarization ellipse as a function of laser intensity, initial ellipticity, and detuning are made. The observations, in good agreement with theoretical simulations, are indicative of the presence of a residual static magnetic field, resulting in measured asymmetries in the rotation angle for right and left ellipticities. In this paper we present our detailed experimental results and analysis of the combined influences of polarization self-rotation and the Faraday effect.
A collection of ultracold atoms has an index of refraction that varies depending on the spatial density distribution of the gas. For many confined gases commonly found in ultracold atom experiments, there can be a substantial gradient in the spatial density distribution and hence the index of refraction. In addition, these gases can have a smaller spatial extent than that of the cross section of a laser beam that illuminates them. With a sufficient gradient in density under these conditions, the resulting index variation leads to frequency-dependent focusing or defocusing of incident near-resonant light as demonstrated by the calculations in this work. Nonintuitive intensity pattern formations result within the gas from the combination of refraction and diffraction of the incident light, including focusing effects that substantially increase the intensity of the light as compared to its incident value despite the nominally absorptive nature of the gas.
Electromagnetism and light-matter interaction in rotating systems is a rich area of ongoing research. We study the interaction of light with a gas of non-interacting two-level atoms confined to a rotating disk. We numerically solve the optical Bloch equations to investigate the how relativistic rotation affects the atoms' polarisation and inversion. The results are used to predict the steady-state stimulated emission seen by an observer at rest with the optical source in the laboratory frame. Competing physical effects due to time dilation and motion-induced detuning strongly modify solutions to the Bloch equations when the gas's velocity becomes relativistic. We account for the non-inertial motion by including acceleration-dependent excitation and emission rates, arising from a generalised Unruh effect. The effective thermal vacuum resulting from large accelerations de-polarises the gas while driving it towards population inversion, negating coherent driving due to the external light source. The results illustrate the intuitive, special-relativistic approach of assigning instantaneously comoving frames to understand non-inertial motion's influence when only local fields are physically significant.