WOLFRAM|DEMONSTRATIONS PROJECT

Cavity Quantum Electrodynamics with Bosons: Emission Spectra in the Strong and Weak Coupling Regimes

​
coupling strength g
1
cavity decay
γ
a
2
emitter decay
γ
b
1
pumping
cavity
P
a
0.1
emitter
P
b
0.001
emission
cavity
emitter
dressed states
ω
min
-5
ω
max
5
z
Placing an optical emitter—like an excited atom—in a cavity alters its emission properties. Its decay can thus be enhanced (returning to its ground state more rapidly) or inhibited (staying in the excited state for a longer time). This manifests in the optical emission as a broadening or narrowing of the lineshape, respectively (a δ line in a spectrum corresponds to a system with infinite lifetime). When the coupling of the emitter to the cavity becomes large enough, the probability of reabsorbing its emitted photon becomes important, and a sequence of emissions and absorptions can take place. This regime is non-perturbative, and instead of a mere renormalization of the lifetime, a new quantum regime is reached where the atom and the photon vanish to give rise to new quantum states, known as dressed states (in the atomic community) or polariton states (in the solid-state community). The optical emission of these systems is a spectral doublet, known as the Rabi doublet after the Rabi oscillations of the excitation between the atom and the cavity.
This Demonstration allows you to investigate Rabi doublets in the cavity-quantum electrodynamics regime for boson emitters. Their spectral line is shown with the emitted intensity on the
y
axis as a function of the energy (or frequency) relative to the bare cavity energy,
ω-
ω
a
, on the
x
axis. The system is either in weak (renormalization of the lifetime) or strong (line splitting) coupling regime, depending on the coupling strength
g
of the emitter to the cavity, the lifetime of a cavity photon (cavity decay rate
γ
a
) and of the emitter
(
γ
b
), as well as of the pumping rates of the cavity,
P
a
, and of the emitter,
P
b
. The cavity photon's energy provides the origin from which the emitter can be detuned by dragging the vertical line of the display. One can also decompose the total luminescence spectrum into its dressed state emission (in green) and an additional contribution due to their coupling (in dark red). The spectrum is shown in blue when in strong coupling and in red when in weak coupling. A rich variety of lineshapes as well as the transition between strong and weak couplings can be investigated in both the cavity and the emitter direct emissions.