[{"volume":57,"ddc":["530"],"user_id":"458","_id":"52723","publisher":"IOP Publishing","has_accepted_license":"1","status":"public","oa":"1","external_id":{"isi":["001196678300001"]},"quality_controlled":"1","isi":"1","citation":{"chicago":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Derivation of Miller’s Rule for the Nonlinear Optical Susceptibility of a Quantum Anharmonic Oscillator.” <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i> 57, no. 9 (2024). <a href=\"https://doi.org/10.1088/1361-6455/ad369c\">https://doi.org/10.1088/1361-6455/ad369c</a>.","short":"M.T. Meyer, A. Schindlmayr, Journal of Physics B: Atomic, Molecular and Optical Physics 57 (2024).","ieee":"M. T. Meyer and A. Schindlmayr, “Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator,” <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>, vol. 57, no. 9, Art. no. 095001, 2024, doi: <a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>.","apa":"Meyer, M. T., &#38; Schindlmayr, A. (2024). Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator. <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>, <i>57</i>(9), Article 095001. <a href=\"https://doi.org/10.1088/1361-6455/ad369c\">https://doi.org/10.1088/1361-6455/ad369c</a>","bibtex":"@article{Meyer_Schindlmayr_2024, title={Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator}, volume={57}, DOI={<a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>}, number={9095001}, journal={Journal of Physics B: Atomic, Molecular and Optical Physics}, publisher={IOP Publishing}, author={Meyer, Maximilian Tim and Schindlmayr, Arno}, year={2024} }","ama":"Meyer MT, Schindlmayr A. Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator. <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>. 2024;57(9). doi:<a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>","mla":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Derivation of Miller’s Rule for the Nonlinear Optical Susceptibility of a Quantum Anharmonic Oscillator.” <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>, vol. 57, no. 9, 095001, IOP Publishing, 2024, doi:<a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>."},"file_date_updated":"2024-04-04T09:24:22Z","doi":"10.1088/1361-6455/ad369c","language":[{"iso":"eng"}],"article_number":"095001","intvolume":"        57","article_type":"original","date_updated":"2024-04-13T11:20:56Z","publication_status":"published","publication_identifier":{"eissn":["1361-6455"],"issn":["0953-4075"]},"author":[{"id":"77895","last_name":"Meyer","orcid":"0009-0003-4899-0920","first_name":"Maximilian Tim","full_name":"Meyer, Maximilian Tim"},{"last_name":"Schindlmayr","orcid":"0000-0002-4855-071X","first_name":"Arno","full_name":"Schindlmayr, Arno","id":"458"}],"year":"2024","title":"Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator","department":[{"_id":"296"},{"_id":"230"},{"_id":"15"},{"_id":"170"},{"_id":"35"}],"type":"journal_article","date_created":"2024-03-22T08:44:39Z","file":[{"relation":"main_file","date_updated":"2024-04-04T09:24:22Z","file_name":"Meyer_2024_J._Phys._B _At._Mol._Opt._Phys._57_095001.pdf","access_level":"open_access","file_size":358155,"title":"Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator","file_id":"53204","content_type":"application/pdf","creator":"schindlm","description":"Creative Commons Attribution 4.0 International Public License (CC BY 4.0)","date_created":"2024-04-04T09:24:22Z"}],"abstract":[{"text":"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.","lang":"eng"}],"issue":"9","publication":"Journal of Physics B: Atomic, Molecular and Optical Physics"}]