Unified theory of consequences of spontaneous emission in a $\Lambda$ system

In a $\Lambda$ system with two nearly degenerate ground states and one excited state in an atom or quantum dot, spontaneous radiative decay can lead to a range of phenomena, including electron-photon entanglement, spontaneously generated coherence, and two-pathway decay. We show that a treatment of the radiative decay as a quantum evolution of a single physical system composed of a three-level electron subsystem and photons leads to a range of consequences depending on the electron-photon interaction and the measurement. Different treatments of the emitted photon channel the electron-photon system into a variety of final states. The theory is not restricted to the three-level system.

Figure 1

The energy levels of the $\Lambda$ system consisting of the two electron spin states (lower levels) and the light-hole trion polarized along the $+x$ direction. The solid line represents the laser pulse, which propagates along $z$ and is linearly polarized in the $y$ direction. The wavy lines denote the spontaneously emitted photons from the transitions $\mid {\tau }_l⟩\to \mid +⟩$ and $\mid {\tau }_l⟩\to \mid -⟩$, which are elliptically polarized in the $yz$ plane and linearly polarized along $x$, respectively.

Figure 2

(a) and (b) are the energy diagrams and possible electron-trion transitions caused by $\sigma +$-polarized photons with the electron spin quantized in $z$ and $x$ directions, re- spectively. (c) The Raman coherence generated by the pump pulse, and (d) Schematic depiction of interference between the Raman coherence and the spin coherence generated by sponta- neous emission, under a magnetic field applied along the $x$ direction.

Figure 3

(a) The amplitude and (b) the phase shift of the spin beat (shown in the insert) as functions of the Zeeman splitting in units of the trion state width, $\Gamma$. The filled circle and solid lines include the SGC effect, calculated with and without the short-pulse approximation, respectively. The diamond and dotted lines are the results without the SGC effect, calculated with and without the short-pulse approximation, respectively.