Light-Matter Models
Light-matter model cards collect the standard few-mode Hamiltonians used in cavity QED, circuit QED, trapped-ion analogies, and quantum optics. The main distinctions are whether the field is quantized, whether the rotating-wave approximation has been made, and whether one or many emitters are coupled to the same mode.
Two-Level Atom derives the semiclassical driven-atom reduction and its validity tests. These cards begin where the electromagnetic mode is retained as a quantized degree of freedom.
Rabi Oscillations treats the distinct semiclassical experiment in which a prescribed field drives coherent population transfer; it should not be confused with the quantized single-mode Rabi model listed below.
| Model | Main lesson | Approximation status |
|---|---|---|
| Rabi Model | One two-level system coupled to one quantized mode including counter-rotating terms | no rotating-wave approximation |
| Jaynes–Cummings Model | Excitation exchange between one two-level system and one mode | rotating-wave approximation |
| Dicke Model | Collective coupling of many two-level systems to one mode | convention-dependent; may include or omit counter-rotating terms |
Shared Ingredients
Section titled “Shared Ingredients”- a two-level system or ensemble of two-level systems;
- a single bosonic oscillator or cavity mode;
- a coupling constant with convention-dependent normalization;
- detuning between matter and mode frequencies;
- a statement about the rotating-wave approximation;
- optional decay, drive, and open-system terms handled outside the closed Hamiltonian.
Common Mistakes
Section titled “Common Mistakes”- Calling Jaynes–Cummings the full light-matter Hamiltonian.
- Forgetting that depends on field normalization, dipole matrix elements, circuit variables, and convention.
- Treating closed Hamiltonian dynamics as a complete model of a lossy cavity experiment.
- Mixing Rabi, Jaynes–Cummings, Dicke, and Tavis-Cummings conventions without stating which terms are retained.
References
Section titled “References”- M. O. Scully and M. S. Zubairy, Quantum Optics, Cambridge University Press, 1997.
- D. F. Walls and G. J. Milburn, Quantum Optics, 2nd ed., Springer, 2008.
- C. Gerry and P. Knight, Introductory Quantum Optics, Cambridge University Press, 2005.