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# Understanding the nature of mean-field semiclassical light-matter dynamics: An investigation of energy transfer, electron-electron correlations, external driving, and long-time detailed balance

## Abstract

Semiclassical electrodynamics (with quantum matter plus classical electrodynamics fields) is an appealing approach for studying light-matter interactions, especially for realistic molecular systems. However, there is no unique semiclassical scheme. On the one hand, intermolecular interactions can be described instantaneously by static two-body interactions connecting two different molecules, while a classical transverse E field acts as a spectator at short distance; we will call this Hamiltonian no. I. On the other hand, intermolecular interactions can also be described as effects that are mediated exclusively through a classical one-body Ε field without any quantum effects at all (assuming we ignore electronic exchange); we will call this Hamiltonian no. II. Moreover, one can also mix these two different Hamiltonians into a third, hybrid Hamiltonian, which preserves quantum electron-electron correlations for lower excitations but describes higher excitations in a mean-field way. To investigate which semiclassical scheme is most reliable for practical use, here we study the real-time dynamics of a minimalistic many-site model—a pair of identical two-level systems (TLSs)—undergoing either resonance energy transfer (RET) or collectively driven dynamics. While both approaches (no. 1 and no. 2) perform reasonably well when there is no strong external excitation, we find that no single approach is perfectmore »

- Authors:

- Univ. of Pennsylvania, Philadelphia, PA (United States)

- Publication Date:

- Research Org.:
- Univ. of Pennsylvania, Philadelphia, PA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1595484

- Grant/Contract Number:
- SC0019397; AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review A

- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 6; Journal ID: ISSN 2469-9926

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Light-matter interaction; Strong electromagnetic field effects

### Citation Formats

```
Li, Tao E., Chen, Hsing-Ta, Nitzan, Abraham, and Subotnik, Joseph E. Understanding the nature of mean-field semiclassical light-matter dynamics: An investigation of energy transfer, electron-electron correlations, external driving, and long-time detailed balance. United States: N. p., 2019.
Web. doi:10.1103/PhysRevA.100.062509.
```

```
Li, Tao E., Chen, Hsing-Ta, Nitzan, Abraham, & Subotnik, Joseph E. Understanding the nature of mean-field semiclassical light-matter dynamics: An investigation of energy transfer, electron-electron correlations, external driving, and long-time detailed balance. United States. doi:10.1103/PhysRevA.100.062509.
```

```
Li, Tao E., Chen, Hsing-Ta, Nitzan, Abraham, and Subotnik, Joseph E. Fri .
"Understanding the nature of mean-field semiclassical light-matter dynamics: An investigation of energy transfer, electron-electron correlations, external driving, and long-time detailed balance". United States. doi:10.1103/PhysRevA.100.062509.
```

```
@article{osti_1595484,
```

title = {Understanding the nature of mean-field semiclassical light-matter dynamics: An investigation of energy transfer, electron-electron correlations, external driving, and long-time detailed balance},

author = {Li, Tao E. and Chen, Hsing-Ta and Nitzan, Abraham and Subotnik, Joseph E.},

abstractNote = {Semiclassical electrodynamics (with quantum matter plus classical electrodynamics fields) is an appealing approach for studying light-matter interactions, especially for realistic molecular systems. However, there is no unique semiclassical scheme. On the one hand, intermolecular interactions can be described instantaneously by static two-body interactions connecting two different molecules, while a classical transverse E field acts as a spectator at short distance; we will call this Hamiltonian no. I. On the other hand, intermolecular interactions can also be described as effects that are mediated exclusively through a classical one-body Ε field without any quantum effects at all (assuming we ignore electronic exchange); we will call this Hamiltonian no. II. Moreover, one can also mix these two different Hamiltonians into a third, hybrid Hamiltonian, which preserves quantum electron-electron correlations for lower excitations but describes higher excitations in a mean-field way. To investigate which semiclassical scheme is most reliable for practical use, here we study the real-time dynamics of a minimalistic many-site model—a pair of identical two-level systems (TLSs)—undergoing either resonance energy transfer (RET) or collectively driven dynamics. While both approaches (no. 1 and no. 2) perform reasonably well when there is no strong external excitation, we find that no single approach is perfect for all conditions (and all methods fail when a strong external field is applied). Each method has its own distinct problems: Hamiltonian no. I performs best for RET but behaves in a complicated manner for driven dynamics; Hamiltonian no. II is always stable, but obviously fails for RET at short distances. One key finding is that, for externally driven dynamics, a full configuration-interaction description of Hamiltonian no. I strongly overestimates the long-time electronic energy, highlighting the not obvious fact that, if one plans to merge quantum molecules with classical light, a full, exact treatment of electron-electron correlations can actually lead to worse results than a simple mean-field electronic structure treatment. Future work will need to investigate (i) how these algorithms behave in the context of more than a pair of TLSs and (ii) whether or not these algorithms can be improved in general by including crucial aspects of spontaneous emission.},

doi = {10.1103/PhysRevA.100.062509},

journal = {Physical Review A},

number = 6,

volume = 100,

place = {United States},

year = {2019},

month = {12}

}

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