{'fraction_non_alphanumeric': 0.03268876611418048, 'fraction_numerical': 0.01289134438305709, 'mean_word_length': 5.467261904761905, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Direct, non-destructive imaging of magnetization in a spin-1 bose gas

Polarization-dependent phase-contrast imaging is used to spatially resolve the magnetization of an optically trapped degenerate and nondegenerate spin-1 Rb gases. Transverse magnetization of the Bose-Einstein condensate persists for the condensate lifetime, while the noncondensed gas decoheres rapidly. Quantum fluids with a spin degree of freedom have been of longstanding interest, stimulated both by the complex phenomenology of superfluid [1] and by p-wave superconductivity [2]. Advances in ultracold atomic physics have now led to the creation of novel multicomponent quantum fluids including pseudospin-1/2 Bose-Einstein condensates (BECs) [3] and spin-1 and -2 condensates of Na [4,5] and Rb [6-8]. The internal state of a multi-component system is characterized by the populations in each of the components and the coherences among them. However, in all previous studies of the spin-1 or spin-2 spinor condensates, while the populations in each magnetic sublevel were measured, no information was obtained regarding the coherence between overlapping populations [4,6-10]. Moreover, although spatial patterns of longitudinal magnetization have been reconstructed from images of freely expanding spinor gases, the expansion process severely limits the resolution obtainable [9,11,12]. In this work, we exploit atomic birefringence to image the magnetization of an ultracold spin-1 Bose gas non-destructively with high spatial resolution. By varying the orientation of an applied magnetic field with respect to our imaging axis, we measure either longitudinal magnetization, which derives from the static populations in each of the magnetic sublevels, or transverse magnetization, which derives from time-varying ∆m=1 coherences. This probe is used to observe Larmor precession in both degenerate and non-degenerate spinor Bose gases. In particular, optical characterization of Larmor precession in a BEC provides a novel probe of the relative phases between condensates in different internal states with excellent temporal and spatial resolution (see Refs.[13] for other recent measurements of