Programme

I.7 -- Invited, VCTP-45

Date: Tuesday, 13 October 2020

Time: 15:00 - 15:30

Waveguide Arrays: from Discrete Optics to Quantum Field Theory

Tran Xuan Truong

Le Quy Don Technical University

The waveguide array (WA) is a perfect system to study many interesting discrete classic optical phenomena, such as discrete diffraction, discrete solitons [1], the generation of diffractive resonant radiation from discrete solitons [2], and supercontinuum generation in both the frequency and wave number [3]. In applications, logic functions such as AND and NOT, and time gating function can be realized in WAs. Amazingly, some fundamental nonrelativistic quantum mechanics effects rooted in the Schrödinger equation, such as Zener tunneling and Bloch oscillations [4], have been intensively investigated through their photonic analogs in WAs. More remarkably, the binary waveguide array (BWA) – a special class of WAs – is a wonderful system to simulate fundamental relativistic quantum mechanics effects rooted in the Dirac equation in quantum field theory, such as Zitterbewegung [5], Dirac solitons (DSs) [6–10], and the topological Jackiw–Rebbi (JR) states [11–14]. The JR states are well known for predicting the charge fractionalization phenomenon, which is basic in the fractional quantum Hall effect [15]. The JR state solutions are also well known for the topological nature and can be interpreted as a precursor to topological insulators, which have attracted a lot of interest recently. Another extraordinary fundamental relativistic quantum mechanics effect called Klein tunneling (KT) has also been simulated in BWAs [16]. The KT effect was predicted by Oscar Klein in 1929 with suggestion that relativistic fermions can tunnel through a repulsive potential step, whose height is greater than the particle energy, without the exponential damping conventionally ruled by the Schrödinger equation. In short, in this presentation I would like to show the achievements in exploiting this amazing platform of WAs from both classical and quantum points of view. References: [1] D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003). [2] Tr. X. Tran and F. Biancalana, Phys. Rev. Lett. 110, 113903 (2013). [3] Tr. X. Tran, D. C. Duong, and F. Biancalana, Phys. Rev. A 89, 013826 (2014). [4] T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999). [5] F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolt, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902 (2010). [6] Tr. X. Tran, S. Longhi, and F. Biancalana, Ann. Phys. 340, 179 (2014). [7] Tr. X. Tran and D. C. Duong, Ann. Phys. 361, 501 (2015). [8] Tr. X. Tran, X. N. Nguyen, and F. Biancalana, Phys. Rev. A 91, 023814 (2015). [9] Tr. X. Tran and D. C. Duong, Chaos 28, 013112 (2018). [10] Tr. X. Tran, J. Opt. Soc. Am. B 36, 2001 (2019). [11] Tr. X. Tran and F. Biancalana, Phys. Rev. A 96, 013831 (2017). [12] Tr. X. Tran, H. M. Nguyen, and D. C. Duong, Phys. Rev. A 100, 053849 (2019). [13] Tr. X. Tran, J. Opt. Soc. Am. B 36, 2559 (2019). [14] R. Jackiw and C. Rebbi, Phys. Rev. D 13, 3398 (1976). [15] R. B. Laughlin, “Nobel lecture: fractional quantization,” Rev. Mod. Phys. 71, 863 (1999). [16] Tr. X. Tran, J. Opt. Soc. Am. B 37, 1811 (2020).

Presenter: Tran Xuan Truong