# Mollow Triplet

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The *Mollow triplet* is the lineshape of emission from a two-level system (such as an isolated electronic transition in an atom) that is resonantly excited by a continuous wave laser [1]. The triplet that arises from dressing the emitter by the strong laser field is one of the most famous and fundamental spectral lines of quantum optics.

Contributed by: Elena del Valle and Fabrice P. Laussy (December 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The result consists of a coherent (scattering) part and an incoherent (fluorescence) part. The first part becomes a delta function in the ideal detector case and has a Lorentzian shape with the same broadening as the detector otherwise. The second part displays three peaks near resonance () and in the high-intensity regime (), which is the *Mollow triplet* per se. They correspond to transitions between *dressed states* of the emitter, that is, quantum superpositions of the ground and excited states that result from the strong coupling with the laser. There are three peaks out of four possible transitions because two are degenerate. The transition energies corresponding to the satellite peaks are indicated by the dotted purple lines (the central peak is always pinned at the energy of the laser). When they merge into a single peak (at the laser frequency), signature of a transition to weak light-matter coupling, the spectrum is plotted in red.

The general solution presented here can be parametrized to describe various situations of interest. For instance, to describe the effect of finite temperature, one must carry out the parametrization and , where is the radiative decay rate at zero temperature and is the mean occupation of the thermal bath of temperature in contact with the emitter. To describe the Mollow triplet formed in cavity-QED, where the light field is also quantized, one must carry out the parametrization , where is the coupling strength between the emitter and the cavity mode, and is the mean cavity occupation number in the lasing regime. This is linked to the incoherent pump of the emitter: , where is the cavity decay rate [2, 3].

Units: The rate provides the units of the problem (if left at ) and the emitter frequency is taken as the origin of the frequencies. The spectra are always normalized to the total population of the emitter (between 0 and 1, given by the blue region in inset). The value on the axis multiplied by the value in parentheses gives the spectral density with rime dimension (as its integral over frequency is dimensionless, namely, the population of the emitter).

Snapshot 1: effect of detuning between the laser and emitter

Snapshot 2: effect of incoherent pumping on the detuned case (asymmetric triplet)

Snapshot 3: effect of incoherent pumping on the resonant case (symmetric but broadened triplet)

References

[1] B. R. Mollow, "Power Spectrum of Light Scattered by Two-Level Systems," *Physical Review*, 188(5), 1969 pp. 1969–1975. doi:10.1103/PhysRev.188.1969.

[2] E. del Valle and F. P. Laussy, "Mollow Triplet under Incoherent Pumping," *Physical Review Letters*, 105(23), 2010 233601. doi/10.1103/PhysRevLett.105.233601.

[3] E. del Valle and F. P. Laussy, "Regimes of Strong Light-Matter Coupling under Incoherent Excitation," *Physical Review A*, 84(4), 2011 043816. doi:10.1103/PhysRevA.84.043816.

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