We present the first experimental realization and characterization of two-dimensional Skyrmions and half-Skyrmions in a spin-2 Bose-Einstein condensate. The continuous rotation of the local spin of the Skyrmion through an angle of pi (and half-Skyrmion through an angle of pi/2) across the cloud is confirmed by the spatial distribution of the three spin states as parametrized by the bending angle of the l vector. The winding number w = (0,1,2) of the internal spin states comprising the Skyrmions is confirmed through matter-wave interference.
SignificanceCancer alters both the morphological and the biochemical properties of multiple cell types in a tissue. Generally, the morphology of epithelial cells is practical for routine disease diagnoses. Here, infrared spectroscopic imaging biochemically characterizes breast cancer, both epithelial cells and the tumor-associated microenvironment. Unfortunately, conventional spectral analyses are slow. Hence, we designed and built a laser confocal microscope that demonstrates a high signal-to-noise ratio for confident diagnoses. The instrument cuts down imaging time from days to minutes, making the technology feasible for research and clinical translation. Finally, automated human breast cancer biopsy imaging is reported in ∼1 hour, paving the way for routine research into the total tumor (epithelial plus microenvironment) properties and rapid, label-free diagnoses.
We report an error in the representation of the local spin, or ' vector, [Eq. (2)] of both the Skyrmion and half-Skyrmion in our Letter. We made the assumption that the three-component spin texture created in the F ¼ 2 manifold of 87 Rb and described by Eq. (1),was an effective spin-1 system composed of states: j2; 2i, j2; 0i, j2; À2i. It was further assumed that this pseudo-spin-1 system was equivalent to one consisting of spin states: j2; 1i, j2; 0i, j2; À1i.We presented the following ' vector for our spin textures:'ðrÞ ¼ẑ cosðrÞ þ sinðrÞðx cos' þŷ sin'Þ;where nðrÞ is the density of the cloud, (r, ') are polar coordinates, and ðrÞ is the bending angle. For the spin textures we created, Eq. (2) is only valid if both of the above assumptions hold. A full calculation of the expectation value of the local spin, h^Fi ¼', using the spin-2 order parameter of Eq. (1) and the spin-2 angular momentum spin matrices does not produce the ' vector of Eq. (2). As a result, the plots of the local spin, Figs. 1(e) and 2(e), are incorrect. All other representations of the data are based on the wave function, Eq. (1), and are still valid. In light of this error, it is not clear whether the classification of these spin textures as a Skyrmion and half-Skyrmion is still appropriate.
PRL
We use Raman-detuned laser pulses to achieve spatially varying control of the amplitude and phase of the spinor order parameter of a Bose-Einstein condensate. We present experimental results confirming precise radial and azimuthal control of amplitude and phase during the creation of vortex-antivortex superposition states.
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