| 研究課題/領域番号 |
20K14375
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| 研究種目 |
若手研究
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| 配分区分 | 基金 |
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| 審査区分 |
小区分13010:数理物理および物性基礎関連
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| 研究機関 | 東京大学 |
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研究代表者 |
Marra Pasquale 東京大学, 大学院数理科学研究科, 特任研究員 (20799861)
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| 研究期間 (年度) |
2020-04-01 – 2025-03-31
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| 研究課題ステータス |
交付 (2023年度)
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| 配分額 *注記 |
3,510千円 (直接経費: 2,700千円、間接経費: 810千円)
2022年度: 520千円 (直接経費: 400千円、間接経費: 120千円)
2021年度: 650千円 (直接経費: 500千円、間接経費: 150千円)
2020年度: 2,340千円 (直接経費: 1,800千円、間接経費: 540千円)
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| キーワード | topological matter / Majorana modes / Hofstadter model / quantum computation / quasiperiodic systems / low dimensional systems / superconductors / トポロジカル量子現象 / トポロジカル超伝導 / 準周期性 / 物質中のマヨラナ粒子 / 超対称性 / ナノワイヤ / 光格子中の冷却原子気体 / Thoulessポンプ / topological states / quasiperiodic structures / majorana fermions / ultracold atomic gases |
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| 研究開始時の研究の概要 |
Topological states of matter are of great interest for their fundamental theoretical aspects and applications in quantum computation, and can lead to a great advance in human society and in physics.
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| 研究実績の概要 |
In the last fiscal year, my research resulted in 1 publication and 2 papers submitted, currently under review.
The main scientific results are: 1) We established a scaling law for the lowest energy state in systems composed of arrays of several Majorana modes. This result is relevant for the realization of scalable quantum computers. 2) We proposed a novel platform for realizing Majorana modes in 2D topological superconductors with inhomogeneous order parameters. This may open new avenues for realizing Majorana-based quantum computers. 3) We derived an exact formula to parametrize the energy spectrum of the Hofstadter model. This result can be applied both to quasiperiodic systems in cold atomic gases trapped in optical lattices, and spatially periodic 2D systems in strong magnetic fields.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
The research outcome was more than originally planned:
1) Our work describing a new platform to realize Majorana modes in 2D topological superconductors with inhomogeneous order parameters was not originally planned. This platform, where Majorana modes localize at the ond of topologically nontrivial stripes, may be a versatile and realistic implementation of the Sachdev-Ye-Kitaev model (which can be regarded as a toy model to study the chaotic behavior of black holes). This model was not considered in the original research plan. 2) Our work on the Hofstadter model also has implications for the Toda lattice model studied in high-energy physics. This connection was not expected in the original research plan.
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| 今後の研究の推進方策 |
In the near future, I am planning to:
1) Generalize our novel platform to realize Majorana in 2D topological superconductors with inhomogeneous order parameters to similar systems with inhomogeneous fields.
2) Develop a framework to describe the adiabatic braiding of Majorana modes in these systems.
3) Study in more detail the connection between the Hofstadter model and the Toda lattice model.
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