Recoil-Free Spectroscopy of Neutral Sr Atoms in the Lamb-Dicke Regime

Recoil-free as well as Doppler-free spectroscopy was demonstrated on the ${}^{1}S_0-{}^{3}P_1$ transition of Sr atoms confined in a one-dimensional optical lattice. By investigating the wavelength and polarization dependence of the ac Stark shift acting on the ${}^{1}S_0$ and ${}^{3}P_1(m_J=0)$ states, we determined the wavelength where the Stark shifts for both states coincide. This Stark-free optical lattice, allowing the purturbation-free spectroscopy of trapped atoms, may keep neutral-atom based optical standards competitive with single-ion standards.

Figure 1

(a) Level diagram and optical coupling related to the ${}^{1}S_0-{}^{3}P_1$ clock transition. The ${}^{1}S_0$ state is dominantly coupled to ${}^{1}P_1$, while the ${}^{3}P_1$ state is coupled to the upper triplet states of ${}^{3}S$, ${}^{3}P$, and ${}^{3}D$. The latter couplings strongly depend on the light polarization, as depicted by the thickness of arrows. (b) Schematic diagram of the 1D optical lattice. A bias magnetic field ${\overrightarrow{B}}_0$ was applied parallel to the probe electric field ${\overrightarrow{E}}_p$ with a wave vector ${\overrightarrow{k}}_p$ parallel to that of the lattice beam $\pm {\overrightarrow{k}}_L$. $\theta$ represents an angle between ${\overrightarrow{B}}_0$ and the electric field $\overrightarrow{E}$ of the lattice. The probe laser was introduced parallel to $\pm {\overrightarrow{k}}_L$, along which the spatial modulation of the ac Stark shift confines atoms in the LDR, as depicted in (a).

Figure 2

(a) Fluorescence spectra of Sr atoms confined in a 1D optical lattice for different polarization orientation $\theta$ at ${\lambda }_L=830\mathrm{n}\mathrm{m}$. At $\theta \approx \pi /4$ (A), the narrower spectrum was observed as the Stark shifts on the clock transition nearly canceled out, whereas nonzero differential Stark shift introduced a frequency shift and broadening for $\theta \approx \pi /2$ ($B$). (b) The change of the Stark shift as the angular orientation $\theta$ of the lattice-laser polarization with respect to a bias magnetic field. Since the light shift of the ${}^{3}P_1(m_J=0)$ depends on the lattice laser polarization, the frequency varies sinusoidally depending on the components of $\pi$ and the ${\sigma }^{+}+{\sigma }^{-}$ intensity. The dashed lines show the differential Stark shifts for atoms in the $n_v=0,1,2$ vibrational states.

Figure 3

Differential Stark shift for the ${}^{1}S_0-{}^{3}P_1(m=0)$ transition. The shift depends on the trap laser wavelength ${\lambda }_L$, the polarization rotation $\theta$, and the vibrational state $n_v$, indicated by dashed lines. Different symbols correspond to the measurements on different days. The inset shows the intensity dependence of the shifts measured for several wavelengths ${\lambda }_L$ at $\theta =\pi /2$. By linearly extrapolating to zero laser power, the atomic resonance frequency was obtained.

Figure 4

Laser-induced fluorescence of atoms (a) confined in a 1D optical lattice and (b) in free fall. The dashed line shows a Gaussian fit to the data points (b). The confinement suppressed the Doppler width of 83 kHz and gave a narrow Lorentzian linewidth of 11 kHz, which was limited by the saturation broadening. A slight blueshift of the center frequency in (b) is caused by the photon recoil shift.