Cavity QED beyond the Jaynes-Cummings model

TL;DR

This work questions the adequacy of the Jaynes–Cummings single‑mode model for modern atom–cavity systems by treating mirrors as elements that modify local field dynamics rather than truncating the field Hilbert space. Using a quantum optical master equation for a single atom coupled to a structured vacuum, it derives environment‑dependent decay rates Γ that can surpass or match the free‑space rate Γ_free due to interference with reflected fields, especially in subwavelength plasmonic cavities. The authors show that, in general, Γ_cav ≈ Γ_free for planar cavities, explaining why strong coupling is challenging, while subwavelength metallic mirrors can dramatically boost or suppress emission depending on phase upon reflection. The results provide a unified framework for understanding emission modifications across free space, partially reflecting interfaces, and multi‑mirror cavities, with implications for designing cavities that truly exploit cooperativity and re‑absorption effects.

Abstract

As atom-cavity systems are becoming more sophisticated, the limitations of the Jaynes-Cummings model are becoming more apparent. In this paper, we therefore take a more dynamical approach to the modelling of atom-cavity systems and do not reduce the electromagnetic field inside the resonator to a single mode. Our approach shows that the decay rate Gamma_cav of an emitter inside a subwavelength cavity with metallic mirrors can be much larger than its free space decay rate Gamma_free due to constructive interference effects of the emitted light. In general, however, we find that Gamma_cav = Gamma_free to a very good approximation which might explain why many atom-cavity experiments have not been able to operate in the so-called strong coupling regime.

Figures (9)

• Figure 1: [Colour online] Standard view of atom-cavity systems in quantum optics, as promoted by the Jaynes-Cummings Hamiltonian in Eq. (\ref{['I1']}) and the corresponding master equations in Eq. (\ref{['I2']}). When placed inside an optical cavity with a matching cavity frequency, the atom couples resonantly to a single standing wave mode of the quantised electromagnetic field and exchanges energy with the mode in a controlled way. Moreover, there are two decay channels: photons might leak out through the resonator mirrors with a decay rate $\kappa$ or might come directly from the atom which has the spontaneous decay rate $\Gamma$.
• Figure 2: [Colour online] Schematic view of an atom at a position $\boldsymbol{r}_0 = (x_0, 0, 0)$ with ${x_0>0}$ in the presence of a partially transparent mirror in the $x=0$ plane. Light emitted towards the mirror surface is reflected, and seems to come from the position $\tilde{\boldsymbol r}_0 = (-x_0, 0, 0)$ of the mirror image of the atom and interferes with light emitted away from the mirror. For small atom-mirror distances, interference is mostly destructive and the spontaneous decay rate of the atom decreases. Here $r_a$ and $t_a$ denote the (complex) reflection and transmission rates of the mirror interface.
• Figure 3: The spontaneous decay rate $\Gamma_{\text{mir }}$ in Eq. (\ref{['E42']}) as a function of the emitter-mirror distance $d$ for different reflection coefficients $r_a$. Here we consider dielectric mirrors with real and negative reflection rates $r_a$, since the incoming light accumulates a minus sign upon reflection. The graph highlights the relatively strong dependence of $\Gamma_{\text{mir }}$ on both the emitter-mirror distance and the reflectivity of the surface.
• Figure 4: The spontaneous decay rate $\Gamma_{\text{mir }}$ in Eq. (\ref{['E42']}) as a function of the emitter-mirror distance $d$ for different reflection coefficients $r_a$. Here we consider a plasmonic mirror surface with positive reflection rates $r_a$, i.e. the incoming light does not experience a phase shift upon reflection. Now the spontaneous decay rate of the emitter can be twice its free space value.
• Figure 5: [Colour online] Schematic view of an atom placed at the centre of of a cavity which consists of two partially transparent planar mirrors a distance $d$ away from each other. Now $r_a$, $r_b$, $t_a$ and $t_b$ denote the (complex) reflection and (real) transmission rates of the interface AMC. Compared to the setup in Fig. \ref{['figpaperlogo3']}, light emitted from the atom now might get reflected many times before leaving the setup eventually. Now there are infinitely many path which contribute to light emission into the same final direction of propagation and the interference of the outgoing light is strongly enhanced, thereby altering the spontaneous decay rate of the atom.