Strong Purcell Effect on a Neutral Atom Trapped in an Open Fiber Cavity

We observe a sixfold Purcell broadening of the $D_2$ line of an optically trapped ${}^{87}\mathrm{Rb}$ atom strongly coupled to a fiber cavity. Under external illumination by a near-resonant laser, up to 90% of the atom’s fluorescence is emitted into the resonant cavity mode. The sub-Poissonian statistics of the cavity output and the Purcell enhancement of the atomic decay rate are confirmed by the observation of a strongly narrowed antibunching dip in the photon autocorrelation function. The photon leakage through the higher-transmission mirror of the single-sided resonator is the dominant contribution to the field decay ($\kappa \approx 2\pi \times 50\mathrm{MHz}$), thus offering a high-bandwidth, fiber-coupled channel for photonic interfaces such as quantum memories and single-photon sources.

Figure 1

Experimental setup. (a) Side- and (b) top-view technical drawing of the main components and the relevant light fields, showing the cavity- and side-probe configurations, respectively. The bottom inset shows a fluorescence image of two atoms coupled to the resonator (20 ms exposure time). (c) Probe power reflected from the cavity ($\kappa =2\pi \times 58\mathrm{MHz}$), showing the energy bands of the coupled atom-cavity system for a weakly-pumped single atom. The dashed lines display the dressed states of the addressed cycling transition ($|F,m_F⟩=|2,2⟩\leftrightarrow |3^{\prime },3^{\prime }⟩$). For each cavity frequency (${\omega }_{\mathrm{c}}$), the probe frequency ${\omega }_{\mathrm{p}}$ is scanned through resonance.

Figure 2

Purcell-induced broadening of the atomic line shape. (a) Simplified sketch of the measurement for coupled and uncoupled atoms. The $\text{lin}\perp \text{lin}$ probe light (purple) is scattered either into the cavity mode (red arrows) or into free space (blue arrows). (b) Free-space emission spectrum of atoms trapped outside the cavity mode, error bars indicate the one-sigma statistical error of the mean. The solid line is a fit to a Lorentzian curve, while the dashed line in the inset shows the negligible free-space contribution expected from atoms coupled to the cavity. (c) Emission line shape of the atom-cavity system displaying a clear Purcell broadening. The solid line represents a fit to a convolution of a Lorentzian curve of half-width ${\gamma }_{\mathrm{c}}^{\prime }=(1+g_{\mathrm{eff}}^2/\kappa \gamma )\gamma$ and a Gaussian distribution of coupling strengths with mean ${\overline{g}}_{\mathrm{eff}}$ and variance ${\sigma }_g$ (see main text). Differences in $m_F$-states population lead to an additional light shift. (d) and (e) are theoretical emission rates for an uncoupled atom in free space (${\tilde{R}}_0$, blue) and the cavity output of a coupled system (${\tilde{R}}_c$, red, $N_{\text{at}}=1$) using the fit parameters, both normalized to their maximum value. The dashed, black lines represent the eigenenergies of the system.

Figure 3

Cavity backaction on the atomic photoemission rate. (a) Simplified experimental scheme depicting the two (interfering) fields. (b) and (c) display the system’s emission in free space and into the cavity respectively, normalized to that of an uncoupled atom (dotted black line). The error bars are extracted from data bootstrapping and Monte Carlo error propagation. The uncertainties in (b) are a consequence of the small free-space collection efficiency and the short trapping lifetimes. The solid lines correspond to the fit to an expanded version of Eqs. (1a) (blue) and (1b) (red) including a convolution for different coupling strengths and optical pumping effects estimated from the master equation simulation (see the Supplemental Material [32]). (d) and (e) show the corresponding full spectra for the normalized emission into both free space and the cavity. The black dashed lines represent the ${\mathrm{\Delta }}_c{\mathrm{\Delta }}_a/(\kappa \gamma )=1+C$ region in (d), and the dressed eigenbands ${\mathrm{\Delta }}_c{\mathrm{\Delta }}_a/(\kappa \gamma )=2C$ in (e).

Figure 4

(a) Autocorrelation function of the cavity output showing the strongly narrowed antibunching dip in (b). The curve is a fit to the phenomenological model described in the Supplemental Material [32].