UNIVERSITY OF CALGARY Modelling Markovian light-matter interactions for quantum optical devices in the solid state by Stephen Christopher Wein A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN PHYSICS AND ASTRONOMY CALGARY, ALBERTA MARCH, 2021 © Stephen Christopher Wein 2021 Abstract The desire to understand the interaction between light and matter has stimulated centuries of research, leading to technological achievements that have shaped our world. One contemporary frontier of research into light-matter interaction considers regimes where quantum effects dominate. By understanding and manipulating these quantum effects, a vast array of new quantum-enhanced technologies become accessible. In this thesis, I explore and analyze fundamental components and processes for quantum optical devices with a focus on solid-state quantum systems. This includes indistinguishable single-photon sources, deterministic sources of entangled photonic states, photon- heralded entanglement generation between remote quantum systems, and deterministic optically- mediated entangling gates between local quantum systems. For this analysis, I make heavy use of an analytic quantum trajectories approach applied to a general Markovian master equation of an optically-active quantum system, which I introduce as a photon-number decomposition. This approach allows for many realistic system imperfections, such as emitter pure dephasing, spin decoherence, and measurement imperfections, to be taken into account in a straightforward and comprehensive way. ii Preface The content of this thesis was either directly developed for projects or indirectly inspired by projects that I was part of. Some of the content has already been published, some of it has not yet been published, and other parts may not be published other than in this thesis. In addition, some of the published material of which I was the primary author is presented verbatim, although it may be rearranged and modified as appropriate to suit the flow of this thesis. Other published material from works where I was a co-author but not the primary author is presented from my own perspective and cited appropriately. In every case, I have diligently detailed my contributions to all these original works to provide full transparency. The following is a full list of published and submitted papers that I have co-authored during my graduate studies. The list is presented in chronological order. For each entry, the PDF symbol provides a link to the corresponding arXiv manuscript and the chain symbol links to the journal article page if published and the arXiv abstract page if submitted. The asterisk symbol (∗) indicates equal contribution. [i] S. Wein, K. Heshami, C. A. Fuchs, H. Krovi, Z. Dutton, W. Tittel, and C. Simon. "Efficiency of an enhanced linear optical Bell-state measurement scheme with realistic imperfections." Phys. Rev. A 94, 032332 (2016). ® [ii] I. Dhand, A. D’Souza, V.Narasimhachar, N. Sinclair, S. Wein, P. Zarkeshian, A. Poostindouz, and C. Simon. "Understanding quantum physics through simple experiments: from wave- particle duality to Bell’s theorem." arXiv:1806.09958 (2018). ® Note: being developed into a textbook for Cambridge University Press. [iii] S. Wein, N. Lauk, R. Ghobadi, and C. Simon. “Feasibility of efficient room-temperature solid-state sources of indistinguishable single photons using ultrasmall mode volume cavi- ties.” Phys. Rev. B 97, 205418 (2018). ® [iv] F. Kimiaee Asadi, N. Lauk, S. Wein, N. Sinclair, C. O‘Brien, and C. Simon. “Quantum repeaters with individual rare-earth ions at telecommunication wavelengths.” Quantum 2, 93 (2018). ® iii [v] R. Ghobadi∗, S. Wein∗, H. Kaviani, P. Barclay, and C. Simon. “Progress toward cryogen-free spin-photon interfaces based on nitrogen-vacancy centers and optomechanics.” Phys. Rev. A 99, 053825 (2019). ® [vi] H. Ollivier, I. Maillette de Buy Wenniger, S. Thomas, S. C. Wein, A. Harouri, G. Coppola, P. Hilaire, C. Millet, A. Lemaître, I. Sagnes, O. Krebs, L. Lanco, J. C. Loredo, C. Antón, N. Somaschi, and P.Senellart. “Reproducibility of high-performance quantum dot single-photon sources.” ACS Photonics 7, 1050 (2020). ® [vii] F. Kimiaee Asadi, S. C. Wein, and C. Simon. “Cavity-assisted controlled phase-flip gates.” Phys. Rev. A 102, 013703 (2020). ® [viii] F. Kimiaee Asadi, S. C. Wein, and C. Simon. “Protocols for long-distance quantum com- munication with single 167Er ions.” Quantum Sci. Technol. 5, 045015 (2020). ® [ix] S. C. Wein, J.-W. Ji, Y.-F. Wu, F. Kimiaee Asadi, R. Ghobadi, and C. Simon.“Analyzing photon-count heralded entanglement generation between solid-state spin qubits by decom- posing the master-equation dynamics.” Phys. Rev. A 102, 033701 (2020). ® [x] S. E. Thomas, M. Billard, N. Coste, S. C. Wein, Priya, H. Ollivier, O. Krebs, L. Tazaïrt, A. Harouri, A. Lemaître, I. Sagnes, C. Antón, L. Lanco, N. Somaschi, J. C. Loredo, and P. Senel- lart. "Bright polarized single-photon source based on a linear dipole." arXiv:2007.04330 (2020). ® [xi] K. Sharman, F. Kimiaee Asadi, S. C. Wein, and C. Simon. "Quantum repeaters based on individual electron spins and nuclear-spin-ensemble memories in quantum dots." arXiv: 2010.13863 (2020). ® [xii] J.-W. Ji, Y.-F. Wu, S. C. Wein, F. Kimiaee Asadi, R. Ghobadi, and C. Simon. "Proposal for room-temperature quantum repeaters with nitrogen-vacancy centers and optomechanics." arXiv:2012.06687 (2020). ® [xiii] H. Ollivier∗, S. E. Thomas∗, S. C. Wein, I. Maillette de Buy Wenniger, N. Coste, J. C. Loredo, N. Somaschi, A. Harouri, A. Lemaître, I. Sagnes, L. Lanco, C. Simon, C. Antón, O. Krebs, and P. Senellart. "Hong-Ou-Mandel interference with imperfect single photon sources." Phys. Rev. Lett. 126, 063602 (2021). ® [xiv] S. C. Wein, J. C. Loredo, M. Maffei, P. Hilaire A. Harouri, N. Somaschi, A. Lemaître, I. Sagnes, L. Lanco, O. Krebs, A. Auffèves, C. Simon, P. Senellart, and C. Antón-Solanas. "Photon-number entanglement generated by sequential excitation of a two-level atom." In preparation (2021). iv Throughout this thesis, I will be using the above roman numeral references whenever citing works where I am a co-author. However, not all of these papers are relevant to the present topic. The papers [iii] and [ix] are the only two that are entirely included in this thesis, and the author contributions for these works are summarized below. Please also see appendixC for copyright permissions. Author contributions for [iii]—SW and CS conceived the idea. SW and RG developed the methods. SW performed the analysis and wrote the manuscript with guidance from NL and RG. NL and CS provided critical feedback. All authors contributed to editing the manuscript. Author contributions for [ix]—SCW and CS conceived the idea. SCW developed the methods. SCW performed the analysis and wrote the manuscript with help from JWJ, YFW, and FKA. RG and CS provided critical feedback. All authors contributed to editing the manuscript. A portion of supplementary theory material from [xiii] and [xiv] are also described in this thesis under fair dealing, as I was the primary author of that material within those experimental papers. Moreover, I will include unpublished research related to my contributions to [vii] and [viii]. Both of these latter papers have already appeared in the thesis of the primary author, Dr. Faezeh Kimiaee Asadi. Because of this, I will make clear what material deviates from the published material and present any material from those published papers in my own original words with the appropriate citations. The remaining original material in this thesis is tangentially related to my other publications and I will detail those relationships as they become relevant. The content of [iii] appears in section 3.1 and appendixB. In addition, [ix] appears in chapter 2 and section 4.1. Some supplementary material related to [xiii] and [xiv] is included in chapter 3. The material related to [vii] and [viii] appears in section 4.2. Aside from the introduction, the remaining material that is not attributed to a paper is, to the best of my knowledge, original unpublished research that serves to aggregate my published works into a consistent framework. v Acknowledgements I am genuinely grateful to everyone who has contributed to my personal and academic de- velopment, allowing for the completion of this milestone in my life. Although I cannot mention everyone, I hope to highlight those who have had the most significant impact. I would like to express my heartfelt thanks to all the people who have mentored me through my studies. Most importantly, to my advisor Prof. Christoph Simon, whose wisdom and mindful guidance has undoubtedly shaped both my career and my life. To Dr. Dean Kokonas, whose words—“you just need to find your groove" said to me when I was failing grade 10 math— echo in my head whenever I struggle with a concept. To Mr. Bob Shoults, who never failed to pique my curiosity for physics. To Prof. Michael Wieser, whose lectures on quantum mechanics inspired me to switch undergraduate programs and study physics. And to Prof. David Feder, whose enthusiasm brought me into physics research. This work would not be as it is without the influence from many of my collaborators, colleagues, and peers. I would like to thank all past and present members of Prof. Simon’s theory group who have shaped my research environment; and also Prof. Pascale Senellart and all members of GOSS at the Centre for Nanosciences and Nanotechnologies for inspiring discussions and projects. In particular, I am very grateful to Prof. Khabat Heshami for guidance on my first research paper, to Prof. Sandeep Goyal for initiating my interest in open quantum systems, and Dr. Faezeh Kimiaee Asadi for the many productive discussions and successful collaborations. The completion of my doctorate would not have been possible without my family and friends. I am foremost indebted to my parents, Beverly and Marcus Wein, who are the source of my confidence and continue to teach me to think critically.