qmnh2018

基底状態のボーズ粒子系を準位反転させる断熱サイクル：新奇な量子ホロノミーの一例として

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1. جఈঢ়ଶͷϘʔζཻࢠܥΛ४Ґ൓సͤ͞Δஅ೤αΠΫϧɿ ৽حͳྔࢠϗϩϊϛʔͷҰྫͱͯ͠ ాதಞ࢘ʢट౎େཧ޻ʣ ྔࢠϗϩϊϛʔͱ͸ʁ ௨ৗͷྔࢠϗϩϊϛʔʢ͍ΘΏΔϕϦʔҐ૬ʣ ɹ அ೤αΠΫϧ͸ྔࢠঢ়ଶʹඇࣗ໌ͳҐ૬มԽΛ΋ͨΒ͢͜ͱ͕͋Δ [Berry 1984]. ৽حͳྔࢠϗϩϊϛʔ ɹ அ೤αΠΫϧ͸ҟͳΔఆৗঢ়ଶΛ݁ͼ͚ͭΔ͜ͱ͕͋Δ [ాதɺશɺ೔ຊ෺ཧֶձࢽ 2017೥4݄߸]. ৽حͳྔࢠϗϩϊϛʔ͸ࣗ༝౓ͷখ͞ͳܥ΍ՄղͳଟମܥͰͷྫ͕஌Β Ε͍ͯΔ͕ɺ͜͜Ͱ͸ɺ“೤ྗֶత”ͳঢ়گԼͷଟମܥͰͷྫΛࣔ͢ɻ ཁࢫɿ૬ޓ࡞༻͢ΔϘʔζཻࢠܥ͸ɺஅ೤αΠΫϧʹΑͬͯجఈঢ়ଶ͔Β ४Ґ൓సঢ়ଶʹҠ͢͜ͱ͕Ͱ͖Δ |Ψ(X) X Ψ(0) : ground Ψ(2π) : inverted ४Ґ൓సঢ়ଶ ▶ ྭىঢ়ଶ͕جఈঢ়ଶΑΓ΋ଟ͘઎༗͞ ΕΔඇฏߧঢ়ଶ ▶ ϨʔβʔͰར༻͞ΕΔ ▶ ௨ৗ͸ϙϯϐϯάͰ࡞Δ Ұ࣍ݩͷശʹೖͬͨ N ཻࢠܥͷஅ೤αΠΫϧ C (= C1 + C2 + C3 ) |ψ0 શܥΛఆৗঢ়ଶʹ४උ͢Δ C1 X1 அ೤తʹนΛૠೖʢน͸ δؔ਺Ͱهड़ʣ C2 X1 X2 அ೤తʹนΛҠಈ C3 X2 அ೤తʹนΛআڈ |? ϋϛϧτχΞϯ͸࠷ॳʹ໭Δ͕ɺঢ়ଶ͸ |?⟩ N = 1Ͱͷྔࢠϗϩϊϛʔʢஅ೤αΠΫϧ C ͸ҟͳΔఆৗঢ়ଶΛ݁Ϳʣ ਤɿC ʹԊͬͨݻ༗ΤωϧΪʔ C ͸४ҐަࠩΛ؏͘ʢ¯ k ∝ √ E/Nʣ ਤɿݻ༗ؔ਺ͷஅ೤มԽ S. Kasumie, M. Miyamoto and AT, PRA 93, 042105 (2016). ઁಈతͳٞ࿦ (N = 2)ɿC1,3 Ͱͷ४Ґ൓ൃ͕४Ґ൓సΛ๦͛Δ ྖҬ C1,3 ʹ͋Δ४Ґަࠩ͸ཻࢠؒ૬ޓ࡞༻ V Ͱյ͞ΕΔͨΊɺஅ೤४Ґ ͷͭͳ͕Γํ͸ɺV = 0 ͷ৔߹͔ΒมԽ͢Δɻ ରͯ͠ɺྖҬ C2 ʹަ͕ࠩ͋ͬͯ΋ཻࢠؒ૬ޓ࡞༻ͷӨڹ͸ऑ͍ɻ ઁಈతͳٞ࿦ (N > 2)ɿબ୒ଇ͕४Ґ൓సΛอޢ͢Δ બ୒ଇɿೋମͷཻࢠؒ૬ޓ࡞༻ V ͷ |2⊗N⟩ ͱඇθϩͷߦྻཁૉΛ࣋ͭ૬ ख͸ |2⊗N−2n1 n2⟩ ͷΈɻ N = 3 N = 4 ྫɿ|111⟩ C → |222⟩ Ͱ͸ C3 Ͱ |222⟩ ͱ |113⟩ ͕ަࠩ͢Δ͕ɺબ୒ଇ͔Β ⟨113|V |222⟩ = 0 ͱͳΓঢ়ଶͷ݁ͼ͖ͭ͸มԽ͠ͳ͍ɻ AT and T. Cheon, New J. Phys. 18, 045023 (2016). ฏۉ৔ۙࣅͰͷղੳ αΠΫϧ C ʹԊͬͯे෼Ώͬ͘ΓนΛมԽͤ͞Δաఔʹ͍ͭͯɺ࣌ؒґ ଘ͢Δ Gross-Pitaevskii ํఔࣜͷ਺஋ܭࢉ͔Β࣍ͷ͜ͱΛ֬ೝͨ͠ɿ ʢ̍ʣཻࢠؒ૬ޓ࡞༻ʢڧ౓ gʣ͕े෼ऑ͍৔߹ɺجఈঢ়ଶ͔Βग़ൃ͢Δ ͱ४Ґ൓స͕࣮ݱ͢Δʀ ʢ̎ʣେ͖ͳ |g| Ͱ͸४Ґ൓స͠ͳ͍ɻ 3 2 1 0 1 2 3 4 g 0.0 0.2 0.4 0.6 0.8 1.0 prob. p1 p2 ਤɿஅ೤αΠΫϧऴྃޙͷ֬཰෼෍ͷ g ґଘੑ Cf. ։͍ͨಁ೤աఔΛ࢖ͬͨμʔΫιϦτϯͷੜ੒๏ͷఏҊ [Karkuszewski, Sacha and Zakrzewski 2001] AT, T. Nakamura and T. Cheon (work in progress). ల๬ ▶ ඇஅ೤ޮՌͷղੳ ▶ ޫ૿෯΍Ϩʔβʔ΁ͷԠ༻ʢՙిཻࢠܥ΁ͷ֦ு͕ඞཁʣ cf. TC and Shigehara, Fermion-Boson Duality of One-Dimensional Quantum Particles with Generalized Contact Interactions, PRL 82, 2536 (1999). ▶ அ೤աఔͷՃ଎ (Masuda and Nakamura 2009౳)ͷద༻ cf. Mart´ ınez-Garaot, Palmero, Muga and Gu´ ery-Odelin, Fast driving between arbitrary states of a quantum particle by trap deformation, PRA 94, 063418 (2016). ऑ஋ɾऑଌఆɺΤϯλϯάϧϝϯτɺྔࢠίώʔϨϯεͷ৽஍ฏʢQMNH2018ʣ@ KEK