In mesoscopic transport phenomena through small constrictions, quantum mechanical effects are known to be directly reflected in transport coefficients. One of the best known is the Landauer formula in which the two-terminal conductance of normal metals is quantized.In addition, states of matter in reservoirs play an important role in mesoscopic transport. The prototype example is a superconducting point contact where reservoirs consist of superconductors. In this case, it is known that the direct current does not obey Ohm’s law. The key ingredient there is multiple Andreev reflections where quasiparticles repeat Andreev reflections at the boundaries between superconductor and contact. As a result, the current-bias characteristics become highly nonlinear.In contrast, each constituent particle in detail is expected to be irrelevant in mesoscopic transport. This type of universality can nowadays be confirmed with ultracold atomic gases. Indeed, a two-terminal transport setup with a quantum point contact has been realized in experiments of ultracold Fermi gases that observed the conductance quantization and nonlinear current-bias characteristics.It must be noted that the presence or absence of charge may cause a difference in transport between electron and atomic systems. Especially, this difference may qualitatively be important for systems with Bose- Einstein condensation of Cooper pairs where Nambu-Goldstone (NG) modes emerge due to spontaneous symmetry breaking. In the case of electrons, the NG modes become gapped ones due to the Coulomb interaction. In the case of neutral atoms, however, these NG modes remain gapless, and the NG modes may play an important role in low-energy transport. At the same time, as the NG modes are a non-superfluid component, there is a view that the effects of such modes are negligible at low temperature. Since the NG mode in mesoscopic transport have yet to be incorporated in an explicit manner, it is not clear whether it is reasonable to neglect the effect of the gapless mode in experiments of ultracold atomic gases.By using the effective theory and tunneling Hamiltonian, we have discussed DC transport of the NG modes in the fermionic superfluid point contact. We have focused on the BCS regime and revealed the anomalous contribution in mass transport, which is the conversion process between the condensate and NG mode. We also discussed that the anomalous contribution is not present in heat transport, which gives rise to breakdown of the Wiedemann-Franz law and the absence of the bunching effect in current noise.

本研究では、２端子量子ポイントコンタクト系におけるボース原子気体超流動体の量子輸送現象を理論的に解析した。トンネル・ハミルトニアン、Bogoliubov理論、Keldysh形式を組み合わせることで、２端子間に化学ポテンシャル勾配や温度勾配がある場合のACおよびDCカレントの表式を明らかにし、数値解析も行なった。そして、超伝導ポイントコンタクト系とは全く異なる輸送メカニズム、低バイアス領域におけるオーム則、Wiedemann-Franz則の破れ、冷却原子気体の実験で観測される２端子間の粒子数差の緩和ダイナミクスを明らかにした。<!-- /* Font Definitions */ @font-face {font-family:"Cambria Math"; panose-1:2 4 5 3 5 4 6 3 2 4; mso-font-charset:0; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face {font-family:游明朝; panose-1:2 2 4 0 0 0 0 0 0 0; mso-font-charset:128; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-2147482905 717749503 18 0 131231 0;}@font-face {font-family:"\@游明朝"; mso-font-charset:128; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-2147482905 717749503 18 0 131231 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:""; margin:0mm; margin-bottom:.0001pt; text-align:justify; text-justify:inter-ideograph; mso-pagination:none; font-size:10.5pt; mso-bidi-font-size:12.0pt; font-family:"游明朝",serif; mso-ascii-font-family:游明朝; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:游明朝; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:游明朝; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-font-kerning:1.0pt;}.MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; font-family:"游明朝",serif; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}size:612.0pt 792.0pt; margin:99.25pt 30.0mm 30.0mm 30.0mm; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;}div.WordSection1 {page:WordSection1;}

本課題では非平衡下での量子多体系の性質を理論的に解明すべく、冷却原子気体に焦点を当てた研究を行なった。具体的には、冷却原子気体を用いて、ポーラロンや量子輸送、そしてスピン自由度を持ったボース・アインシュタイン凝縮の研究を行なった。ポーラロン問題では、有限温度のスペクトル関数の非自明な性質を明らかにした。量子輸送問題では、ボース超流動系のメゾスコピック伝導を記述する基礎理論の構築に取り組んだ。スピン自由度を持ったボース・アインシュタイン凝縮の研究では、フロケ・エンジニアリングを考えることで、系に非自明な性質が出現することを明らかにした。@font-face { font-family: "Cambria Math";}@font-face { font-family: 游明朝;}@font-face { font-family: "@游明朝";}p.MsoNormal, li.MsoNormal, div.MsoNormal { margin: 0mm 0mm 0.0001pt; text-align: justify; font-size: 10.5pt; font-family: "游明朝", serif; }.MsoChpDefault { font-family: "游明朝", serif; }div.WordSection1 { }