| 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 – 2023-03-31
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| キーワード | continuum threshold / non-Markovian decay / exceptional point / optical vortex / PT-symmetry |
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| 研究実績の概要 |
I have published my work on the anomalous-order exceptional point (EP) occurring at the continuum threshold in 1-D continuum systems (or structured reservoirs). I showed in Ref. [1] that this EP involves the coalescence of a resonance, anti-resonance and a bound state and further 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 [1]. In a separate project, I recently published a work on the spectral properties of a parity-time (PT)-symmetric trimer coupled to two Su-Schrieffer-Heeger (SSH) chains with alternating couplings. The alternating couplings in the SSH chains gives an interesting chiral symmetry, which introduces topologically-protected edge states in the original SSH model. I showed how these edge states occur as modes with exactly zero energy in the PT-symmetric model and I showed that these can coalesce to form exceptional points with other eigenstates under certain circumstances. This again results in a characteristic non-Markovian dynamics, which we proposed to measure in a photonic lattice array experiment [2]. Finally, I also published a review article on my previous work on dynamics near EPs in open quantum systems [3].
[1] Phys. Rev. Research 3, 033029 (2021).
[2] Phys. Rev. A 104, 062215 (2021).
[3] J. Phys.: Conf. Ser. 2038, 012011 (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, I showed that the dynamics in the sector orthogonal to a Bound State in Continuum (BIC) should be non-Markovian under rather general conditions, which may open new opportunities for non-Markovian dynamical control in quantum systems. This result was published as a letter-style paper in Ref. [4]. More recently, I have completed several projects related to the optical vortex and more broadly to dynamical control in open quantum systems. In the first project, I demonstrated the existence of an anomalous-order exceptional point (EP) at the continuum threshold in certain 1-D systems under two general conditions, as well as the associated non-Markovian dynamics with a characteristic power law decay with fractional exponent [1]. In a separate work, 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 [5]. In the last few months, I have published two further papers related to the dynamics at the EPs [2,3] and I am thinking about extending the results from Ref. [2] in future work, which includes using zero-energy modes to control non-Markovian dynamics under a variety of circumstances as well as the possibility of a optical vortex laser.
[1] Phys. Rev. Research 3, 033029 (2021).
[2] Phys. Rev. A 104, 062215 (2021).
[3] J. Phys.: Conf. Ser. 2038, 012011 (2021).
[4] Phys. Rev. A 99, 010102(R) (2019).
[5] Phys. Rev. A 103, 043513 (2021).
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| 今後の研究の推進方策 |
In Ref. [2], I demonstrated that the chiral sub-lattice symmetry from the SSH model results in two topologically-protected zero-energy modes when one couples a parity-time (PT) symmetric trimer with two semi-infinite SSH chains. One of these zero-energy modes is localized while the other is anti-localized. I showed that under certain circumstances two or more of the ordinary eigenstates in the system can coalesce with the localized zero-energy mode to form an EP of order N. This results in a characteristic survival probability dynamics of the form t^{2N-2}.
In future work, I would like to extend this to better understand the influence of the anti-localized zero-energy mode on the dynamics. This is more subtle because the anti-localized state resides outside of the usual Hilbert space (it is not a usual normalized eigenstate). But my previous work has shown that anti-localized states can influence the dynamics when they appear close to the continuum threshold. Hence, I plan to investigate the dynamics in this situation. Further, since the zero-energy mode states are topologically protected, an intriguing possibility would be to introduce random disorder into the system and observe the influence on the dynamics. Due to the topological symmetry, one expects the non-Markovian dynamics could remain robust in the face of disorder, which could prove useful from the perceptive of quantum information processing.
[1] Phys. Rev. Research 3, 033029 (2021).
[2] Phys. Rev. A 104, 062215 (2021).
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| 次年度使用額が生じた理由 |
Because of the Covid pandemic, I have not been able to follow my scheduled travel plans.
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