Atomic excitation delocalization at the clean to disordered interface in a chirally-coupled atomic array

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Atomic excitation delocalization at the clean to disordered interface in a chirally-coupled atomic array

C.-C. Wu, K.-T. Lin, I. G. N. Y. Handayana, C.-H. Chien, S. Goswami, G.-D. Lin, Y.-C. Chen, and H. H. Jen

Phys. Rev. Research 6, 013159 – Published 12 February 2024

Abstract

In one-dimensional quantum emitter systems, the dynamics of atomic excitations are influenced by the collective coupling between emitters through photon-mediated dipole-dipole interactions. By introducing positional disorders in a portion of the atomic array, we investigate the delocalization phenomena at the interface between the disordered and clean zones. The excitation is initialized as symmetric Dicke states in the disordered zone, and several measures are used to quantify the excitation localization. We first use population imbalance and half-chain entropy to investigate the excitation dynamics under time evolutions, and further investigate the crossover of excitation localization to delocalization via the gap ratio from the eigenspectrum in the reciprocal coupling case. In particular, we study the participation ratio of the whole chain and the photon loss ratio between both ends of the atomic chain, which can be used to quantify the delocalization crossover in the nonreciprocal coupling cases. Furthermore, by increasing the overall size or the ratio of the disordered zone under a fixed number of the whole chain, we observe that excitation localization occurs at a smaller disorder strength in the former case, while in the latter, facilitation of the delocalization appears when a significant ratio of the clean zone to disordered zone is applied. Our results can reveal the competition between the clean zone and the disordered zone sizes on localization phenomenon, give insights to nonequilibrium dynamics in the emitter-waveguide interface, and provide potential applications in quantum information processing.

Received 25 September 2023
Accepted 12 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.013159

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Localization

Collective dynamics Disordered systems

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

C.-C. Wu ^1,*, K.-T. Lin ², I. G. N. Y. Handayana ^1,3,4, C.-H. Chien ^1,2, S. Goswami ¹, G.-D. Lin^2,5,6, Y.-C. Chen¹, and H. H. Jen ^1,5,†

¹Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
²Department of Physics and Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan
³Molecular Science and Technology Program, Taiwan International Graduate Program, Academia Sinica, Taipei 115201, Taiwan
⁴Department of Physics, National Central University, Taoyuan City 320317, Taiwan
⁵Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
⁶Trapped-Ion Quantum Computing Laboratory, Hon Hai Research Institute, Taipei 11492, Taiwan

^*freddywu0811@gmail.com
^†sappyjen@gmail.com

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Issue

Vol. 6, Iss. 1 — February - April 2024

Subject Areas

Quantum Physics

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Images

Figure 1
Schematic plot for an emitter-waveguide interface with chiral couplings ( $γ_{L}$ and $γ_{R}$ ), where the right half-chain is under disorders. The time evolution of (a) imbalance, (b) the excitation population in the right half-chain, and (c) half-chain entropy in logarithmic time scale for $N = 100, ξ / π = 0.25, D = 0.2,$ and $\bar{w} / π = 0.5, 0.2, 0.1, 0.05, 0$ (blue, red, black, green, and cyan line) in the clean-disordered (fully disordered) system as solid (dash) line. (d) The excitation distribution at $ξ / π = 0.25, D = 0.2, γ t = 10^{4}$ for $\bar{w} / π = 0.5, 0.1, 0.05$ (blue, red, and black). The inset figure is the excitation distribution near the interface.
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Figure 2
The mean gap ratio and the intrasample variance with $N = 100$ and $D = 0$ for different disorder strength $\bar{w}$ . (a) At $ξ / π = 0.5$ , we plot the mean gap ratio (blue line) and intrasample variance (red line) of the fully disordered system (dash line), clean-disordered system (dash-dot line), and the clean-disordered system composed of eigenvalues with more excitation in disordered zone (solid line). (b) The mean gap ratio (blue line) and intrasample variance (red line) of clean-disordered system at $ξ / π = 0.125$ (dot), $0.25$ (dash), and $0.5$ (solid).
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Figure 3
Participation ratio for $N = 100$ with equal sizes of clean zone and disordered zone. (a) Time evolution of PR for $ξ = 0.5 π, D = 0.2$ under different disorder strength $\bar{w}$ . (b) The excitation distribution for localization with $\bar{w} = 0.5, 0.08$ , and $0.02$ . The PR (c) for $D = 0.2$ at $ξ / π = 0.125, 0.25, 0.5, 1$ and (d) with $ξ = 0.5 π$ at $D = 0, \pm 0.2, \pm 0.333$ at $γ t = 10000$ .
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Figure 4
Directional photon loss ratio for $N = 100$ with equal sizes of clean zone and disordered zone. (a) Time-evolved DPLR and (b) the probability distribution when $\bar{w} = 0.5$ (blue line), $0.2$ (red line), $0.15$ (black line), $0.1$ (green line), $0.02$ (cyan line) with $ξ = 0.25 π, D = 0.2$ . (c) DPLR with $D = 0.2$ for $ξ / π = 0.125$ (red line), $0.25$ (blue line), $0.5$ (black line), and 1 (green line) at $γ t = 4000$ . (d) DPLR with $ξ = 0.25 π$ for $D = - 0.2$ (red line), 0 (black line), $0.2$ (blue line), and $0.333$ (green line) at $γ t = 4000$ .
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Figure 5
The mean gap ratio, PR and DPLR under different sizes and clean-disordered zone ratios. (a) The mean gap ratio under $D = 0$ , (b) $P R / N$ under $D = 0.2, and γ t = 4000$ with different quantum emitter numbers and $\bar{w}$ for $ξ = 0.25 π$ and $N_{c} = N_{d} .$ (c) $P R / N_{d}$ with different $N$ in (b). (d) DPLR for $N = 50, 100, 150, 200$ under different disorder strength with equal size in clean order zone and disordered zone size. (e) The mean gap ratio with $D = 0$ (f) PR with $D = 0.2 and γ t = 4000$ varies $N_{c}$ and $\bar{w}$ while $N = 500$ and $ξ = 0.25 π$ . [(g) and (h)] PR and DPLR with different size of clean zone while $N_{d} = 50, ξ = 0.25 π, D = 0.2, and γ t = 4000 .$ The red dots in (a) and (e) represents the localization crossover points.
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