Light–Matter Interaction in Quantum Emitters: An Introduction Using QuTiP
Adrián Juan-Delgado
Download Paper
Base Information
Volume
V59 - N3 / 2026 Ordinario
Reference
52007
DOI
http://dx.doi.org/10.7149/OPA.59.3.52007
Language
English
Keywords
quantum optics, quantum emitters, QuTiP, numerical simulations, nanophotonics, open quantum systems, spontaneous emission, photon antibunching
Abstract
Quantum emitters constitute one of the most fundamental platforms for studying quantum light– matter interactions and play a central role in emerging quantum technologies. Here, we present an introduction for undergraduate and graduate students to the interaction between light and two-level quantum emitters based on numerical simulations implemented with QuTiP, an open-source Python framework for modelling open quantum systems. This tutorial combines numerical implementations with intuitive physical explanations and concise analytical derivations. The provided codes can be directly implemented and readily adapted to systematically explore the effects of different physical parameters, helping students develop physical intuition about quantum optical phenomena. The topics covered include spontaneous emission, coherent laser driving, the Mollow triplet, Rabi oscillations, photon antibunching, the Purcell effect, and the concept of polariton, among others. This tutorial is therefore intended as an accessible introduction to quantum optics for undergraduate and graduate students, while also providing a practical starting point for the numerical modelling of quantum emitters and nanophotonic systems using QuTiP.
References
B. Lounis and M. Orrit, Single-photon sources, Rep. Prog. Phys. 68, 1129 (2005).
C. Couteau, S. Barz, T. Durt, T. Gerrits, J. Huwer, R. Prevedel, J. Rarity, A. Shields, and G. Weihs, Applications of single photons to quantum communication and computing, Nat. Rev. Phys. 5, 326 (2023).
H. J. Kimble, M. Dagenais, and L. Mandel, Photon Antibunching in Resonance Fluorescence, Phys. Rev. Lett. 39, 691 (1977).
F. Diedrich and H. Walther, Nonclassical radiation of a single stored ion, Phys. Rev. Lett. 58, 203 (1987).
A. Kuhn, M. Hennrich, and G. Rempe, Deterministic Single-Photon Source for Distributed Quantum Networking, Phys. Rev. Lett. 89, 067901 (2002).
D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003).
W. E. Moerner and L. Kador, Optical detection and spectroscopy of single molecules in a solid, Phys. Rev. Lett. 62, 2535 (1989).
C. Toninelli et al., Single organic molecules for photonic quantum technologies, Nat. Mater. 20, 1615 (2021).
P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, A Quantum Dot Single-Photon Turnstile Device, Science 290, 2282 (2000).
S. Buckley, K. Rivoire, and J. Vučković, Engineered quantum dot single-photon sources, Rep. Prog. Phys. 75, 126503 (2012).
A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. von Borczyskowski, Scanning Confocal Optical Microscopy and Magnetic Resonance on Single Defect Centers, Science 276, 2012 (1997).
I. Aharonovich, S. Castelletto, D. A. Simpson, C.-H. Su, A. D. Greentree, and S. Prawer, Diamond-based single-photon emitters, Rep. Prog. Phys. 74, 076501 (2011).
G. Grosso, H. Moon, B. Lienhard, S. Ali, D. K. Efetov, M. M. Furchi, P. Jarillo-Herrero, M. J. Ford, I. Aharonovich, and D. Englund, Tunable and high-purity room temperature single-photon emission from atomic defects in hexagonal boron nitride, Nat. Commun. 8, 705 (2017).
M. Toth and I. Aharonovich, Single Photon Sources in Atomically Thin Materials, Annu. Rev. Phys. Chem. 70, 123 (2019).
J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An open-source Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
N. Lambert et al., QuTiP 5: The Quantum Toolbox in Python, Phys. Rep. 1153, 1 (2026).
R. Loudon and R. Loudon, The Quantum Theory of Light, Third Edition, Third Edition (Oxford University Press, Oxford, New York, 2000).
C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics (John Wiley & Sons, 2024).
P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic Press, 2013).
A. Juan Delgado, Photon Statistics and Entanglement from Two Interacting Quantum Emitters, PhD Thesis, Universidad del País Vasco (2025).
V. A. Kovarskii, Quantum processes in biological molecules. Enzyme catalysis, Phys.-Uspekhi 42, 797 (1999).
D. L. Andrews and P. Allcock, Optical Harmonics in Molecular Systems: Quantum Electrodynamical Theory (Wiley-VCH, 2002).
F. Oster, C. H. Keitel, and M. Macovei, Generation of correlated photon pairs in different frequency ranges, Phys. Rev. A 85, 063814 (2012).
W. J. Meath and E. A. Power, On the effects of diagonal dipole matrix elements in multi-photon resonance profiles using two-level systems as models, Mol. Phys. 51, 585 (1984).
W. J. Meath and E. A. Power, On the importance of permanent moments in multiphoton absorption using perturbation theory, J. Phys. B At. Mol. Phys. 17, 763 (1984).
C. Groiseau, A. I. Fernández-Domínguez, D. Martín-Cano, and C. S. Muñoz, Single-Photon Source Over the Terahertz Regime, PRX Quantum 5, 010312 (2024).
H.-P. Breuer, and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, New York, 2002).
V. Weisskopf and E. Wigner, Berechnung der natürlichen Linienbreite auf Grund der Diracschen Lichttheorie, Z. Für Phys. 63, 54 (1930).
A. Juan-Delgado, G. Giedke, J. Aizpurua, and R. Esteban, Generation of polarization-entangled photon pairs from two interacting quantum emitters, Phys. Rev. A 112, 052434 (2025).
T. von Foerster, Quantum Theory of a Damped Two-Level Atom, Am. J. Phys. 40, 854 (1972).
L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University Press, Cambridge, 2012).
L. A. Khalfin, Contribution To The Decay Theory Of A Quasi-Stationary State, Sov. Phys. JETP 6, 1053 (1958).
P. L. Knight and P. W. Milonni, Long-time deviations from exponential decay in atomic spontaneous emission theory, Phys. Lett. A 56, 275 (1976).
D. Manzano, A short introduction to the Lindblad master equation, AIP Adv. 10, 025106 (2020).
F. Bloch and A. Siegert, Magnetic Resonance for Nonrotating Fields, Phys. Rev. 57, 522 (1940).
D. Fregenal, E. Horsdal-Pedersen, L. B. Madsen, M. Førre, J. P. Hansen, and V. N. Ostrovsky, Multiphoton intrashell resonances in Rydberg atoms: Bloch-Siegert shifts and widths, Phys. Rev. A 69, 031401 (2004).
J. Tuorila, M. Silveri, M. Sillanpää, E. Thuneberg, Y. Makhlin, and P. Hakonen, Stark Effect and Generalized Bloch-Siegert Shift in a Strongly Driven Two-Level System, Phys. Rev. Lett. 105, 257003 (2010).
Y. Yan, Z. Lü, and H. Zheng, Bloch-Siegert shift of the Rabi model, Phys. Rev. A 91, 053834 (2015).
I. I. Rabi, Space Quantization in a Gyrating Magnetic Field, Phys. Rev. 51, 652 (1937).
B. R. Mollow, Power Spectrum of Light Scattered by Two-Level Systems, Phys. Rev. 188, 1969 (1969).
C. Cohen-Tannoudji and S. Reynaud, Dressed-atom description of resonance fluorescence and absorption spectra of a multi-level atom in an intense laser beam, J. Phys. B At. Mol. Phys. 10, 345 (1977).
R. J. Glauber, The Quantum Theory of Optical Coherence, Phys. Rev. 130, 2529 (1963).
R. J. Glauber, Nobel Lecture: One hundred years of light quanta, Rev. Mod. Phys. 78, 1267 (2006).
A. Juan-Delgado, R. Esteban, Á. Nodar, J.-B. Trebbia, B. Lounis, and J. Aizpurua, Tailoring the statistics of light emitted from two interacting quantum emitters, Phys. Rev. Res. 6, 023207 (2024).
A. Juan-Delgado, J.-B. Trebbia, R. Esteban, Q. Deplano, P. Tamarat, R. Avriller, B. Lounis, and J. Aizpurua, Addressing the Correlation of Stokes-Shifted Photons Emitted from Two Quantum Emitters, Phys. Rev. Lett. 135, 163602 (2025).
E. M. Purcell, H. C. Torrey, and R. V. Pound, Resonance Absorption by Nuclear Magnetic Moments in a Solid, Phys. Rev. 69, 37 (1946).
C. Navarrete-Benlloch, Introduction to Quantum Optics, arXiv:2203.13206 (2022).
C. Gonzalez-Ballestero, Tutorial: projector approach to master equations for open quantum systems, Quantum 8, 1454 (2024).
D. A. Steck, Quantum and Atom Optics, available online at http://steck.us/teaching (2007).
F. Toffoletti and E. Collini, Coherent phenomena in exciton–polariton systems, J. Phys. Mater. 8, 022002 (2025).
D. G. Baranov, M. Wersäll, J. Cuadra, T. J. Antosiewicz, and T. Shegai, Novel Nanostructures and Materials for Strong Light–Matter Interactions, ACS Photonics 5, 24 (2018).
P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, Ultrastrong coupling regimes of light-matter interaction, Rev. Mod. Phys. 91, 025005 (2019).
A. Ulhaq, S. Weiler, S. M. Ulrich, R. Roßbach, M. Jetter, and P. Michler, Cascaded single-photon emission from the Mollow triplet sidebands of a quantum dot, Nat. Photonics 6, 238 (2012).
H.-T. Chen, T. E. Li, A. Nitzan, and J. E. Subotnik, Predictive Semiclassical Model for Coherent and Incoherent Emission in the Strong Field Regime: The Mollow Triplet Revisited, J. Phys. Chem. Lett. 10, 1331 (2019).
B. Zhu, J. Schachenmayer, M. Xu, F. Herrera, J. G. Restrepo, M. J. Holland, and A. M. Rey, Synchronization of interacting quantum dipoles, New J. Phys. 17, 083063 (2015).
M. Reitz, F. Mineo, and C. Genes, Energy transfer and correlations in cavity-embedded donor-acceptor configurations, Sci. Rep. 8, 9050 (2018).
J. Zirkelbach, M. Mirzaei, I. Deperasińska, B. Kozankiewicz, B. Gurlek, A. Shkarin, T. Utikal, S. Götzinger, and V. Sandoghdar, High-resolution vibronic spectroscopy of a single molecule embedded in a crystal, J. Chem. Phys. 156, 104301 (2022).