Multi-normal-mode splitting of a cavity in the presence of atoms: A step towards the superstrong-coupling regime

Multi-normal-mode splitting peaks are experimentally observed in a system with Doppler-broadened two-level atoms inside a relatively long optical cavity. In this system, the atom-cavity interaction can reach the “superstrong-coupling” condition with atom-cavity coupling strength $g\sqrt{N}$ to be near or larger than the cavity free-spectral range ${\Delta }_{\text{FSR}}$. In such case, normal-mode splitting can occur in many cavity longitudinal modes to generate the multi-normal-mode splitting peaks, which can be well explained by the linear-dispersion enhancement due to the largely increased atomic density in the cavity. Many new interesting phenomena might come out of this superstrong atom-cavity coupling regime.

Figure 1

(Color online) Theoretical calculations of the transmission spectra of the coupled atom-cavity system with the Doppler-broadened two-level atoms with different absorption coefficients. For comparison, the cavity transmission spectrum for the empty cavity (blue dashed) is plotted in (a)–(d). The vertical scale is normalized to the light intensity transmitted through the empty cavity. This is for an optical cavity with ${\Delta }_{\text{FSR}}=2\pi \times 850\text{MHz}$. $m=0,\pm 1,\pm 2,\dots$ label the multi-normal-mode splitting peaks coming from the FSR cavity modes. The finesse of the empty cavity $F=20$ and $\lambda =780\text{nm}$. (a) $a_0{L}_a=12$ (corresponding to $N_D{L}_a=9.4\times {10}^{15}$ $m^{-2}$); (b) $a_0{L}_a=70(N_D{L}_a=5.5\times {10}^{16}$ $m^{-2}$); (c) $a_0{L}_a=130(N_D{L}_a=1.0\times {10}^{17}$ $m^{-2}$); (d) $a_0{L}_a=170(N_D{L}_a=1.3\times {10}^{17}$ $m^{-2}$); and (e) and (f) are the replots of (b) and (d), respectively.

Figure 2

(Color online) Schematic of the experimental setup of the coupled atom-cavity system. $\lambda /2$: half-wave plate. $D1,D2,D3$: detectors. HV-AMP: high-voltage amplifier. PZT: piezoelectric transducer. PBS: polarized beam splitter. $L1,L2$: optical lens.

Figure 3

(Color online) Experimentally measured transmission spectra of the coupled atom-cavity system with the Doppler-broadened two-level atoms at different temperatures of the atomic cell. The curves (a)–(d) correspond to (e) with a narrow frequency detuning range. For comparison, the cavity transmission spectrum for the empty cavity (blue dashed) is added in (a)–(d). The vertical scale is normalized to the light intensity transmitted through the empty cavity. (a) $T=105°\text{C}$; (b) $T=110°\text{C}$; (c) $T=115°\text{C}$; (d) $T=120°\text{C}$; and (e) the saturated absorption spectroscopy (curve 1) and the corresponding cavity transmission spectra (curve 2) of the coupled atom-cavity system. $T=120°\text{C}$.