Strong coupling on a forbidden transition in strontium and nondestructive atom counting

We observe strong collective coupling between an optical cavity and the forbidden spin singlet to triplet optical transition ${}^{1}S_0$ to ${}^{3}P_1$ in an ensemble of ${}^{88}\text{Sr}$. Despite the transition being 1000 times weaker than a typical dipole transition, we observe a well-resolved vacuum Rabi splitting. We use the observed vacuum Rabi splitting to make nondestructive measurements of atomic population with the equivalent of projection-noise limited sensitivity between subsequent measurements and with minimal heating [$<0.01$ (photon recoils)/atom]. This technique may be used to enhance the performance of optical lattice clocks by generating entangled states and reducing dead time.

Figure 1

(a) Experimental diagram. ${}^{88}\text{Sr}$ atoms are confined by 1D optical lattice in high-finesse cavity. $\pi$ polarized probe light is coupled through cavity and is detected on a single-photon counting module. This probe interacts only with the ${}^{1}S_0$ to ${}^{3}P_1, m_J=0$ transition. A magnetic field $B$ shifts the $m_J=\pm 1$ Zeeman sublevels by $\pm 15$ MHz. (b) Relevant level structure of ${}^{88}\text{Sr}$, showing dipole forbidden transitions at 689 nm and 698 nm, and dipole allowed transition at 461 nm.

Figure 2

Observation of the collective strong-coupling regime on the forbidden ${}^{1}S_0$ to ${}^{3}P_1$ transition. (a) We characterize the vacuum Rabi splitting by recording transmitted power as probe frequency is swept. Traces correspond to different cavity detunings ${\delta }_c$. (b) Detected fluorescence versus vacuum Rabi splitting $\mathrm{\Omega }$. (c) Fitted linewidths ${\kappa }_{\pm }^{\prime }$ of the two resonances at ${\omega }_{+}$ (red) and ${\omega }_{-}$ (blue) versus ${\delta }_c$, with prediction based on known atomic linewidth $\gamma$, measured $\mathrm{\Omega }$, and cavity linewidth $\kappa$.

Figure 3

(a) To probe the vacuum Rabi splitting, two probe tones at ${\omega }_{p\pm }$ are simultaneously swept across the two normal mode resonances at ${\omega }_{\pm }$ while total transmitted power is recorded. (b) The noise power spectra relative to photon shot noise for cavity probe with a single tone (red trace) and two tones (black trace), demonstrate noise cancellation of two-tone probing.

Figure 4

(a) Black points show measurement noise relative to hypothetical projection noise in adjacent windows $R$, versus length of a measurement window. The lowest two points represent $R=-2.4_{1.1}^{0.9}$ dB. Red line shows the number of scattered photons per atom $m_s$ in a single measurement window. (b) Fractional change in ${\mathrm{\Omega }}^2=4g^{2}N$ due to additional sweep $\epsilon \equiv ({\mathrm{\Omega }}_0^2-{\mathrm{\Omega }}_s^2)/{\mathrm{\Omega }}_0^2$, versus $M_t$, the number of photons in the additional sweep. ${\mathrm{\Omega }}_s$ and ${\mathrm{\Omega }}_0$ are the measured vacuum Rabi splittings with and without the additional scattering sweep. Solid red line is fit to data, with shaded region representing $1\sigma$ error on the fit. Dashed line represents a prediction based on the theoretically predicted free space scattering. The number of photons used in two typical $100-\mu \text{s}$ windows is represented by the thickness of the left axis.