Study on spontaneous symmetry breaking in ultracold atomic gases

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In this study, we have studied various types of symmetry breaking in ultracold atomic gases. Special focus is made on Bose-Einstein condensates (BECs) with spin degrees of freedom, systems subject to spin-orbit interactions, and fast-rotating Bose systems subject to synthetic gauge fields. As for the first topic, we have succeeded in developing spinor Beliaev theory which is the next-order theory beyond Bongoliubov theory, and used it to successfully explain the phase transition in spin-2 BECs. As for the second topic, we have found various types of quantized vortices and vortex lattices which arises from spin-orbit interactions. As for the last topic, we have found the quantum Hall effect of bosons.