Single Photon Delayed Feedback: A Way to Stabilize Intrinsic Quantum Cavity Electrodynamics

We propose a scheme to control cavity quantum electrodynamics in the single photon limit by delayed feedback. In our approach a single emitter-cavity system, operating in the weak coupling limit, can be driven into the strong coupling-type regime by an external mirror: The external loop produces Rabi oscillations directly connected to the electron-photon coupling strength. As an expansion of typical cavity quantum electrodynamics, we treat the quantum correlation of external and internal light modes dynamically and demonstrate a possible way to implement a fully quantum mechanical time-delayed feedback. Our theoretical approach proposes a way to experimentally feedback control quantum correlations in the single photon limit.

Figure 1

Interaction scheme of a strongly coupled electron-photon dynamics in a microcavity with input-output coupling to a photon continuum in front of a mirror.

Figure 2

Dynamics in the single-excitation limit. Case (a): Without outcoupling, Rabi oscillations occur. In the weak coupling limit without external mirror (b) or with feedback in a bigger cavity (c), no Rabi oscillations occur. But in (d), although in the weak coupling limit, with an external mirror and a microcavity, the delayed feedback effect leads to Rabi oscillations again. Note, that in case (c) the occupation of the upper level $⟨E⟩$ is plotted, in cases (a),(b),(d) the photon density is $⟨c^{†}c⟩$.

Figure 3

Dynamics of the photon density (solid line) and total amount of excitation energy $N_c$ (dashed line) with parameters of Fig. 2d. The constant, nonvanishing amount of excitation inside the cavity leads to regular Rabi oscillations, revealing the electron-photon coupling $M$.

Figure 4

Robustness discussion: Dynamics of the photon density (solid line) and total amount of excitation energy $N_c$ (dashed line) for $\tau =\frac{11}{5}{M}^{-1}$. Even for fluctuating $N_c$, Rabi oscillations proportional to $M$ occur.