| 研究課題/領域番号 |
18K03466
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| 研究機関 | 大阪府立大学 |
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研究代表者 |
ガーモン サバンナスターリング 大阪府立大学, 理学(系)研究科(研究院), 助教 (30733860)
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| 研究期間 (年度) |
2018-04-01 – 2022-03-31
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| キーワード | continuum threshold / non-Markovian decay / exceptional point / bound state in continuum / optical vortex / exceptional manifold |
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| 研究実績の概要 |
I have studied the occurrence of an exceptional point (EP) occurring at the continuum threshold quite generally in 1-D continuum systems, which has unusual dynamical and mathematical properties. I have shown this EP involves the coalescence of three eigenstates: a resonance, anti-resonance and a bound state. Further, a subtle reorganization of the spectrum occurs at the threshold, which shows this EP is fundamentally more general than those occurring in purely discrete systems. I further showed that the dynamics near the EP are fully non-Markovian, exhibiting an unusual power-law decay. The systems in which such an exceptional point could be realized include a quantum emitter traveling in an electromagnetic waveguide, which could be applied to the problem of optical vortex production when a charged particle experiences cyclotron motion in a waveguide. These results have recently been released as a preprint and have been submitted for publication [1].
In a separate project with my student, I have recently studied the occurrence of higher-dimensional exceptional manifolds in a polyacetylene molecule with a magnetically-sensitive donor impurity. I demonstrated the presence of an exceptional ring and exceptional surface in the parameter space of an applied magnetic field and showed that the giant response in the electron spin resonance spectrum near the EP ring could give rise to a single-spin detector. These results have recently been published in Ref. [2].
[1] S. Garmon, et al, arXiv:2104.06929
[2] Phys. Rev. A 103, 043513 (2021).
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
3: やや遅れている
理由
In the the first year of the project, I showed that the dynamics in the sector orthogonal to a Bound State in Continuum (BIC) should be non-Markovian under fairly general conditions. This may open new opportunities for non-Markovian dynamical control in quantum systems. This result was published as a letter-style paper in Ref. [3].
In the second and third years I have completed two projects. In the first project, I demonstrated that the existence of an anomalous-order exceptional point (EP) at the continuum threshold in certain 1-D systems. I showed two general conditions are required for such an EP to appear in a given system and I showed that the dynamics near the EP are generally non-Markovian, described by an unusual power-law decay with fractional exponent. These results will be published soon in an open-access journal similar to Physical Review Research [1]. In the second project, I have shown the existence of an exceptional ring and exceptional surface in the parameter space of a local magnetic field applied to a donor impurity in a 1-D polyacetylene molecule. These results have been published in Ref. [2].
[1] S. Garmon, et al, arXiv:2104.06929
[2] Phys. Rev. A 103, 043513 (2021).
[3] Phys. Rev. A 99, 010102(R) (2019).
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| 今後の研究の推進方策 |
I will finally publish the results appearing in [1] (on the anomalous-order exceptional point in 1-D systems) in a peer-reviewed journal such as Physical Review Research. While the previous two projects on non-Markovian decay apply quite generally in open quantum systems, in future work I will consider their application more specifically to the problem of optical vortex production in a waveguide.
I am also planning future works building on the results published in Ref. [2]. In future work, I will show that the model of a magnetically sensitive impurity embedded in a polyacetylene molecule exhibits a spectral feature known as a bound state in continuum, which can be used to test the modifications of the usual quantum adiabatic principles when encircling an exceptional point. This model should also exhibit interesting non-Markovian dynamical features. Such work will be the subject of future publications in Physical Review and similar journals. I am also planning to give seminars in future virtual conferences, including next year’s American Physical Society March Meeting (March 2022).
[1] S. Garmon, et al, arXiv:2104.06929
[2] Phys. Rev. A 103, 043513 (2021).
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| 次年度使用額が生じた理由 |
My travel plans to promote my research were cancelled due to the Covid-19 crisis.
In the next year, funds will be applied towards travel to promote my research and for publishing charges in high-quality, peer-reviewed journals.
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