# Casimir force and the quantum theory of lossy optical cavities

## Abstract

We present a derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are, in general, lossy and characterized by frequency-dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the Casimir force. The force is obtained as an integral over the real frequencies, including the contribution of evanescent waves besides that of ordinary waves, and then as an integral over imaginary frequencies. The demonstration relies only on general properties obeyed by real mirrors which also enforce general constraints for the variation of the Casimir force.

- Authors:

- Laboratoire Kastler Brossel, Unite de l'Ecole Normale Superieure, de l'Universite Pierre et Marie Curie, et du Centre National de la Recherche Scientifique, Case 74, Campus Jussieu, F-75252 Paris (France)

- Publication Date:

- OSTI Identifier:
- 20634029

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 67; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.67.043811; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; CASIMIR EFFECT; FLUCTUATIONS; FREQUENCY DEPENDENCE; MIRRORS; OPTICAL THEOREM; OPTICS; QUANTUM ELECTRODYNAMICS; QUANTUM MECHANICS; RADIATION PRESSURE; REFLECTION; SPECTRAL DENSITY; VISIBLE RADIATION

### Citation Formats

```
Genet, Cyriaque, Lambrecht, Astrid, and Reynaud, Serge.
```*Casimir force and the quantum theory of lossy optical cavities*. United States: N. p., 2003.
Web. doi:10.1103/PhysRevA.67.043811.

```
Genet, Cyriaque, Lambrecht, Astrid, & Reynaud, Serge.
```*Casimir force and the quantum theory of lossy optical cavities*. United States. doi:10.1103/PhysRevA.67.043811.

```
Genet, Cyriaque, Lambrecht, Astrid, and Reynaud, Serge. Tue .
"Casimir force and the quantum theory of lossy optical cavities". United States. doi:10.1103/PhysRevA.67.043811.
```

```
@article{osti_20634029,
```

title = {Casimir force and the quantum theory of lossy optical cavities},

author = {Genet, Cyriaque and Lambrecht, Astrid and Reynaud, Serge},

abstractNote = {We present a derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are, in general, lossy and characterized by frequency-dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the Casimir force. The force is obtained as an integral over the real frequencies, including the contribution of evanescent waves besides that of ordinary waves, and then as an integral over imaginary frequencies. The demonstration relies only on general properties obeyed by real mirrors which also enforce general constraints for the variation of the Casimir force.},

doi = {10.1103/PhysRevA.67.043811},

journal = {Physical Review. A},

issn = {1050-2947},

number = 4,

volume = 67,

place = {United States},

year = {2003},

month = {4}

}