Exact Markovian and non-Markovian time dynamics in waveguide QED: collective interactions, bound states in continuum, superradiance and subradiance

Fatih Dinc1,2, İlke Ercan3, and Agata M. Brańczyk1

1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada
2Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
3Electrical & Electronics Engineering Department, Boğaziçi University, Istanbul, 34342, Turkey

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


We develop a formalism for modelling $exact$ time dynamics in waveguide quantum electrodynamics (QED) using the real-space approach. The formalism does not assume any specific configuration of emitters and allows the study of Markovian dynamics $\textit{fully analytically}$ and non-Markovian dynamics semi-analytically with a simple numerical integration step. We use the formalism to study subradiance, superradiance and bound states in continuum. We discuss new phenomena such as subdivision of collective decay rates into symmetric and anti-symmetric subsets and non-Markovian superradiance effects that can lead to collective decay stronger than Dicke superradiance. We also discuss possible applications such as pulse-shaping and coherent absorption. We thus broaden the range of applicability of real-space approaches beyond steady-state photon transport.

The quantum internet has the potential to revolutionize how computers talk to each other. Such systems could give people access to cloud-based quantum computers, and provide a level of privacy, security and computational power not possible with today’s internet. The ultimate vision of the quantum internet is a connection of potentially billions of quantum devices within the same network. A key challenge in designing such networks involves theoretical modelling. Existing models could only cope with very simple networks. We develop an approach for modelling complex networks of many devices, and use that method to make predictions in regimes not previously accessible.
Quantum networks will most likely be realized by sending quantum light through waveguides, such as optical fibres, that are connected to quantum devices—the most simple of which is a quantum bit (qubit). Various approaches have been explored for modelling interactions between quantum light and qubits in waveguides. Each method offers unique intuition and can be preferable over another depending on the problem of interest.
The virtue of our approach lies in providing analytical or semi-analytical (with a simple numerical integration step) results. This model makes it possible to study interactions between quantum light and qubits in complex waveguide geometries, with an unprecedented number of possibly non-identical qubits, using only a personal computer.
We expect that our method will benefit applications such as quantum logic, quantum memory, quantum photon routing, and quantum communication, bringing the ambitious vision of the quantum internet closer to realization.

► BibTeX data

► References

[1] Alp Sipahigil, Ruffin E Evans, Denis D Sukachev, Michael J Burek, Johannes Borregaard, Mihir K Bhaskar, Christian T Nguyen, Jose L Pacheco, Haig A Atikian, Charles Meuwly, et al. An integrated diamond nanophotonics platform for quantum-optical networks. Science, 354 (6314): 847–850, 2016. 10.1126/​science.aah6875.

[2] H Jeff Kimble. The quantum internet. Nature, 453 (7198): 1023, 2008. https:/​/​doi.org/​10.1038/​nature07127.

[3] Darrick E Chang, Anders S Sørensen, Eugene A Demler, and Mikhail D Lukin. A single-photon transistor using nanoscale surface plasmons. Nature Physics, 3 (11): 807, 2007. https:/​/​doi.org/​10.1038/​nphys708.

[4] Dibyendu Roy, Christopher M Wilson, and Ofer Firstenberg. Colloquium: Strongly interacting photons in one-dimensional continuum. Reviews of Modern Physics, 89 (2): 021001, 2017. 10.1103/​RevModPhys.89.021001.

[5] Huaixiu Zheng, Daniel J Gauthier, and Harold U Baranger. Waveguide QED: Many-body bound-state effects in coherent and fock-state scattering from a two-level system. Physical Review A, 82 (6): 063816, 2010. 10.1103/​PhysRevA.82.063816.

[6] Jung-Tsung Shen and Shanhui Fan. Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system. Physical Review Letters, 98 (15): 153003, 2007. 10.1103/​PhysRevLett.98.153003.

[7] Peter Bermel, Alejandro Rodriguez, Steven G Johnson, John D Joannopoulos, and Marin Soljačić. Single-photon all-optical switching using waveguide-cavity quantum electrodynamics. Physical Review A, 74 (4): 043818, 2006. 10.1103/​PhysRevA.74.043818.

[8] Mu-Tian Cheng, Xiao-San Ma, Jia-Yan Zhang, and Bing Wang. Single photon transport in two waveguides chirally coupled by a quantum emitter. Optics Express, 24 (17): 19988–19993, 2016. 10.1364/​OE.24.019988.

[9] Yuecheng Shen, Zihao Chen, Yu He, Zhaohui Li, and Jung-Tsung Shen. Exact approach for spatiotemporal dynamics of spontaneous emissions in waveguide quantum electrodynamic systems. Journal of the Optical Society of America B, 35 (3): 607–616, 2018. 10.1364/​JOSAB.35.000607.

[10] Alexandre Roulet and Valerio Scarani. Solving the scattering of ${N}$ photons on a two-level atom without computation. New Journal of Physics, 18 (9): 093035, 2016. 10.1088/​1367-2630/​18/​9/​093035.

[11] Kevin A Fischer, Rahul Trivedi, Vinay Ramasesh, Irfan Siddiqi, and Jelena Vučković. Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system. Quantum, 2: 69, 2018. 10.22331/​q-2018-05-28-69.

[12] Tommaso Caneva, Marco T Manzoni, Tao Shi, James S Douglas, J Ignacio Cirac, and Darrick E Chang. Quantum dynamics of propagating photons with strong interactions: a generalized input–output formalism. New Journal of Physics, 17 (11): 113001, 2015. 10.1088/​1367-2630/​17/​11/​113001.

[13] Eden Rephaeli and Shanhui Fan. Dissipation in few-photon waveguide transport. Photonics Research, 1 (3): 110–114, 2013. 10.1364/​PRJ.1.000110.

[14] Shanhui Fan, Şükrü Ekin Kocabaş, and Jung-Tsung Shen. Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit. Physical Review A, 82 (6): 063821, 2010. 10.1103/​PhysRevA.82.063821.

[15] Tao Shi, Darrick E Chang, and J Ignacio Cirac. Multiphoton-scattering theory and generalized master equations. Physical Review A, 92 (5): 053834, 2015. 10.1103/​PhysRevA.92.053834.

[16] Ben Q Baragiola, Robert L Cook, Agata M Brańczyk, and Joshua Combes. ${N}$-photon wave packets interacting with an arbitrary quantum system. Physical Review A, 86 (1): 013811, 2012. 10.1103/​PhysRevA.86.013811.

[17] T Shi and CP Sun. Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays. Physical Review B, 79 (20): 205111, 2009. 10.1103/​PhysRevB.79.205111.

[18] T Shi, Shanhui Fan, CP Sun, et al. Two-photon transport in a waveguide coupled to a cavity in a two-level system. Physical Review A, 84 (6): 063803, 2011. 10.1103/​PhysRevA.84.063803.

[19] Joshua Combes and Daniel J Brod. Two-photon self-Kerr nonlinearities for quantum computing and quantum optics. Physical Review A, 98 (6): 062313, 2018. 10.1103/​PhysRevA.98.062313.

[20] Daniel J Brod, Joshua Combes, and Julio Gea-Banacloche. Two photons co- and counterpropagating through ${N}$ cross-Kerr sites. Physical Review A, 94 (2): 023833, 2016. 10.1103/​PhysRevA.94.023833.

[21] Guo-Zhu Song, Ewan Munro, Wei Nie, Leong-Chuan Kwek, Fu-Guo Deng, and Gui-Lu Long. Photon transport mediated by an atomic chain trapped along a photonic crystal waveguide. Physical Review A, 98 (2): 023814, 2018. 10.1103/​PhysRevA.98.023814.

[22] Sumanta Das, Vincent E Elfving, Florentin Reiter, and Anders S Sørensen. Photon scattering from a system of multilevel quantum emitters. II. application to emitters coupled to a one-dimensional waveguide. Physical Review A, 97 (4): 043838, 2018. 10.1103/​PhysRevA.97.043838.

[23] Guo-Zhu Song, Ewan Munro, Wei Nie, Fu-Guo Deng, Guo-Jian Yang, and Leong-Chuan Kwek. Photon scattering by an atomic ensemble coupled to a one-dimensional nanophotonic waveguide. Physical Review A, 96 (4): 043872, 2017. 10.1103/​PhysRevA.96.043872.

[24] Janne Ruostekoski and Juha Javanainen. Arrays of strongly coupled atoms in a one-dimensional waveguide. Physical Review A, 96 (3): 033857, 2017. 10.1103/​PhysRevA.96.033857.

[25] Zeyang Liao, Hyunchul Nha, and M Suhail Zubairy. Dynamical theory of single-photon transport in a one-dimensional waveguide coupled to identical and nonidentical emitters. Physical Review A, 94 (5): 053842, 2016a. 10.1103/​PhysRevA.94.053842.

[26] Zeyang Liao, Xiaodong Zeng, Shi-Yao Zhu, and M Suhail Zubairy. Single-photon transport through an atomic chain coupled to a one-dimensional nanophotonic waveguide. Physical Review A, 92 (2): 023806, 2015. 10.1103/​PhysRevA.92.023806.

[27] Lan Zhou, ZR Gong, Yu-xi Liu, CP Sun, Franco Nori, et al. Controllable scattering of a single photon inside a one-dimensional resonator waveguide. Physical Review Letters, 101 (10): 100501, 2008. 10.1103/​PhysRevLett.101.100501.

[28] Imran M Mirza and John C Schotland. Multiqubit entanglement in bidirectional-chiral-waveguide QED. Physical Review A, 94 (1): 012302, 2016. 10.1103/​PhysRevA.94.012302.

[29] Mu-Tian Cheng, Jingping Xu, and Girish S Agarwal. Waveguide transport mediated by strong coupling with atoms. Physical Review A, 95 (5): 053807, 2017. 10.1103/​PhysRevA.95.053807.

[30] Zeyang Liao, Xiaodong Zeng, Hyunchul Nha, and M Suhail Zubairy. Photon transport in a one-dimensional nanophotonic waveguide QED system. Physica Scripta, 91 (6): 063004, 2016b. 10.1088/​0031-8949/​91/​6/​063004.

[31] Yimin Wang, Jiří Minář, Lana Sheridan, and Valerio Scarani. Efficient excitation of a two-level atom by a single photon in a propagating mode. Physical Review A, 83 (6): 063842, 2011. 10.1103/​PhysRevA.83.063842.

[32] Yao-Lung L Fang, Francesco Ciccarello, and Harold U Baranger. Non-Markovian dynamics of a qubit due to single-photon scattering in a waveguide. New Journal of Physics, 20 (4): 043035, 2018. 10.1088/​1367-2630/​aaba5d.

[33] Huaixiu Zheng and Harold U Baranger. Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions. Physical Review Letters, 110 (11): 113601, 2013. 10.1103/​PhysRevLett.110.113601.

[34] C Gonzalez-Ballestero, Francisco J García-Vidal, and Esteban Moreno. Non-Markovian effects in waveguide-mediated entanglement. New Journal of Physics, 15 (7): 073015, 2013. 10.1088/​1367-2630/​15/​7/​073015.

[35] T. S. Tsoi and C. K. Law. Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide. Physical Review A, 78: 063832, Dec 2008. 10.1103/​PhysRevA.78.063832.

[36] Paolo Facchi, MS Kim, Saverio Pascazio, Francesco V Pepe, Domenico Pomarico, and Tommaso Tufarelli. Bound states and entanglement generation in waveguide quantum electrodynamics. Physical Review A, 94 (4): 043839, 2016. 10.1103/​PhysRevA.94.043839.

[37] Giuseppe Calajó, Yao-Lung L Fang, Harold U Baranger, Francesco Ciccarello, et al. Exciting a bound state in the continuum through multiphoton scattering plus delayed quantum feedback. Physical Review Letters, 122 (7): 073601, 2019. 10.1103/​PhysRevLett.122.073601.

[38] C Gonzalez-Ballestero, Esteban Moreno, and FJ Garcia-Vidal. Generation, manipulation, and detection of two-qubit entanglement in waveguide QED. Physical Review A, 89 (4): 042328, 2014. 10.1103/​PhysRevA.89.042328.

[39] Stefano Longhi. Bound states in the continuum in a single-level Fano-Anderson model. The European Physical Journal B, 57 (1): 45–51, 2007. 10.1140/​epjb/​e2007-00143-2.

[40] S Tanaka, S Garmon, Gonzalo Ordonez, and T Petrosky. Electron trapping in a one-dimensional semiconductor quantum wire with multiple impurities. Physical Review B, 76 (15): 153308, 2007. 10.1103/​PhysRevB.76.153308.

[41] Tommaso Tufarelli, Francesco Ciccarello, and MS Kim. Dynamics of spontaneous emission in a single-end photonic waveguide. Physical Review A, 87 (1): 013820, 2013. 10.1103/​PhysRevA.87.013820.

[42] Andreas Albrecht, Loïc Henriet, Ana Asenjo-Garcia, Paul B Dieterle, Oskar Painter, and Darrick E Chang. Subradiant states of quantum bits coupled to a one-dimensional waveguide. New Journal of Physics, 21 (2): 025003, 2019. 10.1088/​1367-2630/​ab0134.

[43] A Asenjo-Garcia, M Moreno-Cardoner, A Albrecht, HJ Kimble, and DE Chang. Exponential improvement in photon storage fidelities using subradiance and “selective radiance” in atomic arrays. Physical Review X, 7 (3): 031024, 2017. 10.1103/​PhysRevX.7.031024.

[44] Yao Zhou, Zihao Chen, and Jung-Tsung Shen. Single-photon superradiant emission rate scaling for atoms trapped in a photonic waveguide. Physical Review A, 95 (4): 043832, 2017. 10.1103/​PhysRevA.95.043832.

[45] A Goban, C-L Hung, JD Hood, S-P Yu, JA Muniz, O Painter, and HJ Kimble. Superradiance for atoms trapped along a photonic crystal waveguide. Physical Review Letters, 115 (6): 063601, 2015. 10.1103/​PhysRevLett.115.063601.

[46] D Valente, MFZ Arruda, and T Werlang. Non-Markovianity induced by a single-photon wave packet in a one-dimensional waveguide. Optics Letters, 41 (13): 3126–3129, 2016. 10.1364/​OL.41.003126.

[47] Kanupriya Sinha, Pierre Meystre, Elizabeth A Goldschmidt, Fredrik K Fatemi, Steven L Rolston, and Pablo Solano. Non-Markovian collective emission from macroscopically separated emitters. arXiv preprint arXiv:1907.12017, 2019. URL https:/​/​arxiv.org/​abs/​1907.12017.

[48] Fatih Dinç and İ. Ercan. Quantum mechanical treatment of two-level atoms coupled to continuum with an ultraviolet cutoff. Journal of Physics A: Mathematical and Theoretical, 51 (35): 355301, 2018. 10.1088/​1751-8121/​aad165.

[49] David J. Griffiths and Darrell F. Schroeter. Introduction to Quantum Mechanics. Cambridge University Press, 3 edition, 2018. 10.1017/​9781316995433.

[50] Jung-Tsung Shen and Shanhui Fan. Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits. Physical Review Letters, 95 (21): 213001, 2005. 10.1103/​PhysRevLett.95.213001.

[51] Jung-Tsung Shen, Shanhui Fan, et al. Theory of single-photon transport in a single-mode waveguide. I. coupling to a cavity containing a two-level atom. Physical Review A, 79 (2): 023837, 2009. 10.1103/​PhysRevA.79.023837.

[52] Paolo Facchi, Davide Lonigro, Saverio Pascazio, Francesco V. Pepe, and Domenico Pomarico. Bound states in the continuum for an array of quantum emitters. Physical Review A, 100: 023834, Aug 2019. 10.1103/​PhysRevA.100.023834.

[53] Clemens Müller, Joshua Combes, Andrés Rosario Hamann, Arkady Fedorov, and Thomas M Stace. Nonreciprocal atomic scattering: A saturable, quantum Yagi-Uda antenna. Physical Review A, 96 (5): 053817, 2017. 10.1103/​PhysRevA.96.053817.

[54] Arjan F Van Loo, Arkady Fedorov, Kevin Lalumière, Barry C Sanders, Alexandre Blais, and Andreas Wallraff. Photon-mediated interactions between distant artificial atoms. Science, 342 (6165): 1494–1496, 2013. 10.1126/​science.1244324.

[55] Maciej Zworski. Mathematical study of scattering resonances. Bulletin of Mathematical Sciences, 7 (1): 1–85, 2017. 10.1007/​s13373-017-0099-4.

[56] Anatolii V Andreev, Vladimir I Emelyanov, and Yu A Ilinski ̆ı. Collective spontaneous emission (Dicke superradiance). Soviet Physics Uspekhi, 23 (8): 493–514, aug 1980. 10.1070/​pu1980v023n08abeh005024.

[57] Debsuvra Mukhopadhyay and Girish S. Agarwal. Multiple Fano interferences due to waveguide-mediated phase coupling between atoms. Phys. Rev. A, 100: 013812, Jul 2019. 10.1103/​PhysRevA.100.013812.

[58] Yoshiya Sato, Yoshinori Tanaka, Jeremy Upham, Yasushi Takahashi, Takashi Asano, and Susumu Noda. Strong coupling between distant photonic nanocavities and its dynamic control. Nature Photonics, 6 (1): 56, 2012. 10.1038/​nphoton.2011.286.

[59] Yuntian Chen, Martijn Wubs, Jesper Mørk, and A Femius Koenderink. Coherent single-photon absorption by single emitters coupled to one-dimensional nanophotonic waveguides. New Journal of Physics, 13 (10): 103010, 2011. 10.1088/​1367-2630/​13/​10/​103010.

[60] Yuwen Wang, Yongyou Zhang, Qingyun Zhang, Bingsuo Zou, and Udo Schwingenschlogl. Dynamics of single photon transport in a one-dimensional waveguide two-point coupled with a Jaynes-Cummings system. Scientific Reports, 6: 33867, 2016. 10.1038/​srep33867.

[61] Eden Rephaeli, Jung-Tsung Shen, and Shanhui Fan. Full inversion of a two-level atom with a single-photon pulse in one-dimensional geometries. Physical Review A, 82 (3): 033804, 2010. 10.1103/​PhysRevA.82.033804.

[62] Enrico Fermi. Quantum theory of radiation. Reviews of Modern Physics, 4 (1): 87, 1932. 10.1103/​RevModPhys.4.87.

[63] Gerhard C Hegerfeldt. Causality problems for Fermi’s two-atom system. Physical Review Letters, 72 (5): 596, 1994. 10.1103/​PhysRevLett.72.596.

[64] PW Milonni, DFV James, and H Fearn. Photodetection and causality in quantum optics. Physical Review A, 52 (2): 1525, 1995. 10.1103/​PhysRevA.52.1525.

[65] Juan Ignacio Cirac, Peter Zoller, H Jeff Kimble, and Hideo Mabuchi. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Physical Review Letters, 78 (16): 3221, 1997. 10.1103/​PhysRevLett.78.3221.

[66] K Stannigel, P Rabl, Anders Søndberg Sørensen, MD Lukin, and P Zoller. Optomechanical transducers for quantum-information processing. Physical Review A, 84 (4): 042341, 2011. 10.1103/​PhysRevA.84.042341.

[67] Fatih Dinc, Lauren E. Hayward, and Agata M. Brańczyk. ``Photon-mediated interactions in high-dimensional quantum networks'', Manuscript under preparation, 2019.

[68] Alexander I Lvovsky, Barry C Sanders, and Wolfgang Tittel. Optical quantum memory. Nature Photonics, 3 (12): 706, 2009. 10.1038/​nphoton.2009.231.

[69] Itay Shomroni, Serge Rosenblum, Yulia Lovsky, Orel Bechler, Gabriel Guendelman, and Barak Dayan. All-optical routing of single photons by a one-atom switch controlled by a single photon. Science, 345 (6199): 903–906, 2014. 10.1126/​science.1254699.

[70] Lan Zhou, Li-Ping Yang, Yong Li, CP Sun, et al. Quantum routing of single photons with a cyclic three-level system. Physical Review Letters, 111 (10): 103604, 2013. 10.1103/​PhysRevLett.111.103604.

[71] Christian L Degen, F Reinhard, and P Cappellaro. Quantum sensing. Reviews of Modern Physics, 89 (3): 035002, 2017. 10.1103/​RevModPhys.89.035002.

[72] Gilbert Grynberg, Alain Aspect, Claude Fabre, and Claude Cohen-Tannoudji. Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light. Cambridge University Press, 2010. 10.1017/​CBO9780511778261.

[73] Magdalena Stobińska, Gernot Alber, and Gerd Leuchs. Perfect excitation of a matter qubit by a single photon in free space. EPL (Europhysics Letters), 86 (1): 14007, 2009. 10.1209/​0295-5075/​86/​14007.

[74] Jon M. Bendickson, Jonathan P. Dowling, and Michael Scalora. Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures. Phys. Rev. E, 53: 4107–4121, Apr 1996. 10.1103/​PhysRevE.53.4107.

[75] Andrey E. Miroshnichenko, Sergej Flach, and Yuri S. Kivshar. Fano resonances in nanoscale structures. Rev. Mod. Phys., 82: 2257–2298, Aug 2010. 10.1103/​RevModPhys.82.2257.

Cited by

[1] Zeyang Liao, Yunning Lu, and M. Suhail Zubairy, "Multiphoton pulses interacting with multiple emitters in a one-dimensional waveguide", Physical Review A 102 5, 053702 (2020).

[2] Davide Lonigro, Paolo Facchi, Andrew D. Greentree, Saverio Pascazio, Francesco V. Pepe, and Domenico Pomarico, "Photon-emitter dressed states in a closed waveguide", Physical Review A 104 5, 053702 (2021).

[3] Yuto Ashida, Takeru Yokota, Ataç İmamoğlu, and Eugene Demler, "Nonperturbative waveguide quantum electrodynamics", Physical Review Research 4 2, 023194 (2022).

[4] P. Solano, P. Barberis-Blostein, and K. Sinha, "Dissimilar collective decay and directional emission from two quantum emitters", Physical Review A 107 2, 023723 (2023).

[5] Z. Y. Li and H. Z. Shen, "Non-Markovian dynamics with a giant atom coupled to a semi-infinite photonic waveguide", Physical Review A 109 2, 023712 (2024).

[6] Debsuvra Mukhopadhyay and Girish S. Agarwal, "Transparency in a chain of disparate quantum emitters strongly coupled to a waveguide", Physical Review A 101 6, 063814 (2020).

[7] Rahul Trivedi, Daniel Malz, Shuo Sun, Shanhui Fan, and Jelena Vučković, "Optimal two-photon excitation of bound states in non-Markovian waveguide QED", Physical Review A 104 1, 013705 (2021).

[8] Hyok Sang Han, Ahreum Lee, Kanupriya Sinha, Fredrik K. Fatemi, and S. L. Rolston, "Observation of Vacuum-Induced Collective Quantum Beats", Physical Review Letters 127 7, 073604 (2021).

[9] Anita Dąbrowska, Dariusz Chruściński, Sagnik Chakraborty, and Gniewomir Sarbicki, "Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket", New Journal of Physics 23 12, 123019 (2021).

[10] Kisa Barkemeyer, Andreas Knorr, and Alexander Carmele, "Heisenberg treatment of multiphoton pulses in waveguide QED with time-delayed feedback", Physical Review A 106 2, 023708 (2022).

[11] Qing-Yang Qiu, Ying Wu, and Xin-You Lü, "Collective radiance of giant atoms in non-Markovian regime", Science China Physics, Mechanics & Astronomy 66 2, 224212 (2023).

[12] Fatih Dinc, "Diagrammatic approach for analytical non-Markovian time evolution: Fermi's two-atom problem and causality in waveguide quantum electrodynamics", Physical Review A 102 1, 013727 (2020).

[13] Guo-Zhu Song, Jin-Liang Guo, Wei Nie, Leong-Chuan Kwek, and Gui-Lu Long, "Optical properties of a waveguide-mediated chain of randomly positioned atoms", Optics Express 29 2, 1903 (2021).

[14] Wenfang Li, Dylan Brown, Alexey Vylegzhanin, Zohreh Shahrabifarahani, Aswathy Raj, Jinjin Du, and Síle Nic Chormaic, "Atom-light interactions using optical nanofibres—a perspective", Journal of Physics: Photonics 6 2, 021002 (2024).

[15] Kisa Barkemeyer, Andreas Knorr, and Alexander Carmele, "Strongly entangled system-reservoir dynamics with multiphoton pulses beyond the two-excitation limit: Exciting the atom-photon bound state", Physical Review A 103 3, 033704 (2021).

[16] Ning Liu, Xin Wang, Xia Wang, Xiao-San Ma, and Mu-Tian Cheng, "Tunable single photon nonreciprocal scattering based on giant atom-waveguide chiral couplings", Optics Express 30 13, 23428 (2022).

[17] Wenju Gu, Lei Chen, Zhen Yi, Sujing Liu, and Gao-xiang Li, "Tunable photon-photon correlations in waveguide QED systems with giant atoms", Physical Review A 109 2, 023720 (2024).

[18] Kanupriya Sinha, Pierre Meystre, Elizabeth A. Goldschmidt, Fredrik K. Fatemi, S. L. Rolston, and Pablo Solano, "Non-Markovian Collective Emission from Macroscopically Separated Emitters", Physical Review Letters 124 4, 043603 (2020).

[19] Kanupriya Sinha, Alejandro González-Tudela, Yong Lu, and Pablo Solano, "Collective radiation from distant emitters", Physical Review A 102 4, 043718 (2020).

[20] Alireza Tavanfar, Aliasghar Parvizi, and Marco Pezzutto, "Unitary Evolutions Sourced By Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories", Quantum 7, 1007 (2023).

[21] Lezhi Lo and C. K. Law, "Retardation-dependent decaying modes of a single excitation in an atomic array coupled to a one-dimensional waveguide", Physical Review A 105 3, 033703 (2022).

[22] Kiryl Piasotski and Mikhail Pletyukhov, "Diagrammatic approach to scattering of multiphoton states in waveguide QED", Physical Review A 104 2, 023709 (2021).

[23] Yongguan Ke, Jiaxuan Huang, Wenjie Liu, Yuri Kivshar, and Chaohong Lee, "Topological Inverse Band Theory in Waveguide Quantum Electrodynamics", Physical Review Letters 131 10, 103604 (2023).

[24] W. Z. Jia and Q. Y. Cai, "Multiple electromagnetically induced transparency without a control field in an atomic array coupled to a waveguide", The European Physical Journal Plus 137 9, 1082 (2022).

[25] Daniele De Bernardis, Francesco S. Piccioli, Peter Rabl, and Iacopo Carusotto, "Chiral Quantum Optics in the Bulk of Photonic Quantum Hall Systems", PRX Quantum 4 3, 030306 (2023).

[26] Y. P. Peng and W. Z. Jia, "Single-photon scattering from a chain of giant atoms coupled to a one-dimensional waveguide", Physical Review A 108 4, 043709 (2023).

[27] Fatih Dinc and Agata M. Brańczyk, "Non-Markovian super-superradiance in a linear chain of up to 100 qubits", Physical Review Research 1 3, 032042 (2019).

[28] Lingzhen Guo, Anton Frisk Kockum, Florian Marquardt, and Göran Johansson, "Oscillating bound states for a giant atom", Physical Review Research 2 4, 043014 (2020).

[29] Shangjie Guo, Yidan Wang, Thomas Purdy, and Jacob Taylor, "Beyond spontaneous emission: Giant atom bounded in the continuum", Physical Review A 102 3, 033706 (2020).

[30] Fatih Dinc, Lauren E. Hayward, and Agata M. Brańczyk, "Multidimensional super- and subradiance in waveguide quantum electrodynamics", Physical Review Research 2 4, 043149 (2020).

[31] Alexander Carmele, Nikolett Nemet, Victor Canela, and Scott Parkins, "Pronounced non-Markovian features in multiply excited, multiple emitter waveguide QED: Retardation induced anomalous population trapping", Physical Review Research 2 1, 013238 (2020).

[32] Ahreum Lee, Hyok Sang Han, Fredrik K. Fatemi, S. L. Rolston, and Kanu Sinha, "Collective quantum beats from distant multilevel emitters", Physical Review A 107 1, 013701 (2023).

[33] Lei Du, Mao-Rui Cai, Jin-Hui Wu, Zhihai Wang, and Yong Li, "Single-photon nonreciprocal excitation transfer with non-Markovian retarded effects", Physical Review A 103 5, 053701 (2021).

[34] Paolo Facchi, Davide Lonigro, Saverio Pascazio, Francesco V. Pepe, and Domenico Pomarico, "Bound states in the continuum for an array of quantum emitters", Physical Review A 100 2, 023834 (2019).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-25 02:47:54) and SAO/NASA ADS (last updated successfully 2024-05-25 02:47:55). The list may be incomplete as not all publishers provide suitable and complete citation data.