---
_id: '52723'
abstract:
- lang: eng
  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.
article_number: '095001'
article_type: original
author:
- first_name: Maximilian Tim
  full_name: Meyer, Maximilian Tim
  id: '77895'
  last_name: Meyer
  orcid: 0009-0003-4899-0920
- first_name: Arno
  full_name: Schindlmayr, Arno
  id: '458'
  last_name: Schindlmayr
  orcid: 0000-0002-4855-071X
citation:
  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>'
  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} }'
  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>.'
  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>.'
  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>.'
  short: 'M.T. Meyer, A. Schindlmayr, Journal of Physics B: Atomic, Molecular and
    Optical Physics 57 (2024).'
date_created: 2024-03-22T08:44:39Z
date_updated: 2024-04-13T11:20:56Z
ddc:
- '530'
department:
- _id: '296'
- _id: '230'
- _id: '15'
- _id: '170'
- _id: '35'
doi: 10.1088/1361-6455/ad369c
external_id:
  isi:
  - '001196678300001'
file:
- access_level: open_access
  content_type: application/pdf
  creator: schindlm
  date_created: 2024-04-04T09:24:22Z
  date_updated: 2024-04-04T09:24:22Z
  description: Creative Commons Attribution 4.0 International Public License (CC BY
    4.0)
  file_id: '53204'
  file_name: Meyer_2024_J._Phys._B _At._Mol._Opt._Phys._57_095001.pdf
  file_size: 358155
  relation: main_file
  title: Derivation of Miller's rule for the nonlinear optical susceptibility of a
    quantum anharmonic oscillator
file_date_updated: 2024-04-04T09:24:22Z
has_accepted_license: '1'
intvolume: '        57'
isi: '1'
issue: '9'
language:
- iso: eng
oa: '1'
publication: 'Journal of Physics B: Atomic, Molecular and Optical Physics'
publication_identifier:
  eissn:
  - 1361-6455
  issn:
  - 0953-4075
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum
  anharmonic oscillator
type: journal_article
user_id: '458'
volume: 57
year: '2024'
...