Superstrong coupling regime of cavity quantum electrodynamics

We describe a qualitatively different regime of cavity quantum electrodynamics, the superstrong coupling regime. This regime is characterized by atom-field coupling strengths of the order of the free spectral range of the cavity, resulting in a significant change in the spatial mode functions of the light field. It can be reached in practice for cold atoms trapped in an optical dipole potential inside the resonator. We present a nonperturbative scheme that allows us to calculate the frequencies and linewidths of the modified field modes, thereby providing a good starting point for a quantization of the theory.

Figure 1

Schematic of atoms trapped in an optical lattice potential in a cavity. Also shown are the effective mirror at $z_a$ representing the atoms and the boundary conditions for the incoming and outgoing fields at this mirror.

Figure 2

Logarithmic plot of ${\mid D\left(\omega \right)\mid }^{-2}$ for the parameters given in the text, with the dark regions corresponding to very small $D$ signifying resonant behavior. The inset shows the linewidth $\Gamma$ as a function of $z_a$, with the reflection coefficients of the atoms taken into account (solid line) and neglected (dashed line). The labeled dots mark the frequencies and atomic positions for which the field envelopes are shown in Fig. 3.

Figure 3

(Color online) Field envelopes across the optical lattice for frequency detunings from an empty cavity resonance of $\omega =$ (a) $-0.074{\omega }_{\mathrm{FSR}}$, (b) and (c) 0, and (d) $0.39{\omega }_{\mathrm{FSR}}$ and the corresponding atomic positions as shown in Fig. 2. For parameters see text.