Instrument for determining the polarization state of reflected and transmitted light

An instrument is described which enables the state of polarization of a light beam to be found. It is discussed with reference to studies of optical rotation, circular dichroism and conventional ellipsometry. The main features are that it records automatically and allows the azimuth and ellipticity of an elliptically polarized beam to be measured simultaneously over a wide wavelength range. The performance is illustrated by spectra showing the optical rotation and circular dichroism of an octahedral cobalt lll species.     

Properties of a single vortex solution in a rotating Bose Einstein condensate

In this Note, we study the properties of the line energy for a vortex γ in a Bose Einstein condensate rotating at velocity $\text{Ω}$. The global minimizer is either the vortex free solution or U vortices which exist only for $\text{Ω}$ bigger than a critical value. For all values of $\text{Ω}$, we prove the existence of an S type vortex, which is a critical point of the line energy, observed in the experiments. We also prove uniqueness of the minimizer for almost every $\text{Ω}$ and a monotonicity property of the curve γ with respect to $\text{Ω}$. The proofs rely on a related isoperimetric problem. To cite this article: A. Aftalion, R.L. Jerrard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Non-existence of vortices in the small density region of a condensate

In this paper, we answer a question raised by Lev Pitaevskii and prove that the ground state of the Gross-Pitaevskii energy describing a Bose-Einstein condensate in a rotationally symmetric trap at low rotation does not have vortices in the low density region. Therefore, the first ground state with vortices has its vortices in the bulk. In fact we prove something stronger, which is that the ground state for the model at low and moderate rotations is equal to the ground state in a condensate with no rotation. This is obtained by proving that for small rotational velocities, the ground state is multiple of the ground state with zero rotation. We rely on sharp bounds of the decay of the wave function combined with weighted Jacobian estimates.