@article{52723,
  abstract     = {{Miller's rule is an empirical relation between the nonlinear and linear optical coefficients that applies to a large class of materials but has only been rigorously derived for the classical Lorentz model with a weak anharmonic perturbation. In this work, we extend the proof and present a detailed derivation of Miller's rule for an equivalent quantum-mechanical anharmonic oscillator. For this purpose, the classical concept of velocity-dependent damping inherent to the Lorentz model is replaced by an adiabatic switch-on of the external electric field, which allows a unified treatment of the classical and quantum-mechanical systems using identical potentials and fields. Although the dynamics of the resulting charge oscillations, and hence the induced polarizations, deviate due to the finite zero-point motion in the quantum-mechanical framework, we find that Miller's rule is nevertheless identical in both cases up to terms of first order in the anharmonicity. With a view to practical applications, especially in the context of ab initio calculations for the optical response where adiabatically switched-on fields are widely assumed, we demonstrate that a correct treatment of finite broadening parameters is essential to avoid spurious errors that may falsely suggest a violation of Miller's rule, and we illustrate this point by means of a numerical example.}},
  author       = {{Meyer, Maximilian Tim and Schindlmayr, Arno}},
  issn         = {{1361-6455}},
  journal      = {{Journal of Physics B: Atomic, Molecular and Optical Physics}},
  number       = {{9}},
  publisher    = {{IOP Publishing}},
  title        = {{{Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator}}},
  doi          = {{10.1088/1361-6455/ad369c}},
  volume       = {{57}},
  year         = {{2024}},
}

@article{37934,
  author       = {{Mukamel, Shaul and Freyberger, Matthias and Schleich, Wolfgang and Bellini, Marco and Zavatta, Alessandro and Leuchs, Gerd and Silberhorn, Christine and Boyd, Robert W and Sánchez-Soto, Luis Lorenzo and Stefanov, André and Barbieri, Marco and Paterova, Anna and Krivitsky, Leonid and Shwartz, Sharon and Tamasaku, Kenji and Dorfman, Konstantin and Schlawin, Frank and Sandoghdar, Vahid and Raymer, Michael and Marcus, Andrew and Varnavski, Oleg and Goodson, Theodore and Zhou, Zhi-Yuan and Shi, Bao-Sen and Asban, Shahaf and Scully, Marlan and Agarwal, Girish and Peng, Tao and Sokolov, Alexei V and Zhang, Zhe-Dong and Zubairy, M Suhail and Vartanyants, Ivan A and del Valle, Elena and Laussy, Fabrice}},
  issn         = {{0953-4075}},
  journal      = {{Journal of Physics B: Atomic, Molecular and Optical Physics}},
  keywords     = {{Condensed Matter Physics, Atomic and Molecular Physics, and Optics}},
  number       = {{7}},
  publisher    = {{IOP Publishing}},
  title        = {{{Roadmap on quantum light spectroscopy}}},
  doi          = {{10.1088/1361-6455/ab69a8}},
  volume       = {{53}},
  year         = {{2020}},
}

@article{26308,
  author       = {{Kröger, Johannes and Ahrens, Thomas and Sperling, Jan and Vogel, Werner and Stolz, Heinrich and Hage, Boris}},
  issn         = {{0953-4075}},
  journal      = {{Journal of Physics B: Atomic, Molecular and Optical Physics}},
  title        = {{{High intensity click statistics from a 10 × 10 avalanche photodiode array}}},
  doi          = {{10.1088/1361-6455/aa8e68}},
  year         = {{2017}},
}

@article{26315,
  author       = {{Sperling, Jan and Agudelo, E and Walmsley, I A and Vogel, W}},
  issn         = {{0953-4075}},
  journal      = {{Journal of Physics B: Atomic, Molecular and Optical Physics}},
  title        = {{{Quantum correlations in composite systems}}},
  doi          = {{10.1088/1361-6455/aa7438}},
  year         = {{2017}},
}

@article{26306,
  author       = {{Perez-Leija, Armando and Leon-Montiel, Roberto de J and Sperling, Jan and Moya-Cessa, Hector and Szameit, Alexander and Busch, Kurt}},
  issn         = {{0953-4075}},
  journal      = {{Journal of Physics B: Atomic, Molecular and Optical Physics}},
  title        = {{{Two-particle four-point correlations in dynamically disordered tight-binding networks}}},
  doi          = {{10.1088/1361-6455/aa9aa1}},
  year         = {{2017}},
}

@article{26047,
  author       = {{Stefszky, Michael and Mow-Lowry, Conor M and McKenzie, Kirk and Chua, Sheon and Buchler, Ben C and Symul, Thomas and McClelland, David E and Lam, Ping Koy}},
  issn         = {{0953-4075}},
  journal      = {{Journal of Physics B: Atomic, Molecular and Optical Physics}},
  title        = {{{An investigation of doubly-resonant optical parametric oscillators and nonlinear crystals for squeezing}}},
  doi          = {{10.1088/0953-4075/44/1/015502}},
  year         = {{2010}},
}