Nondestructive measurement of the transition probability in a Sr optical lattice clock

We present the experimental demonstration of nondestructive probing of the ${{}^{1}S}_0\text{−}{{}^{3}P}_0$ clock transition probability in an optical lattice clock with ${}^{87}\text{S}\text{r}$ atoms. It is based on the phase shift induced by the atoms on a weak off-resonant laser beam. The method we propose is a differential measurement of this phase shift on two modulation sidebands with opposite detuning with respect to the ${{}^{1}S}_0\text{−}{{}^{1}P}_1$ transition, allowing a detection limited by the photon shot noise. We have measured an atomic population of ${10}^4$ atoms with a signal-to-noise ratio of 100 per cycle, while keeping more than 95% of the atoms in the optical lattice with a depth of 0.1 mK. The method proves simple and robust enough to be operated as part of the whole clock setup. This detection scheme enables us to reuse atoms for subsequent clock state interrogations, dramatically reducing the loading time and thereby improving the clock frequency stability.

Figure 1

(Color online) Energy levels of Sr of interest in this Rapid Communication. A typical spectroscopy of the clock transition using the nondestructive detection is inset. The transition is saturated and power broadened so that the blue detuned lattice motional sideband is visible. The red detuned sideband is absent because most of the atoms are in the fundamental state of the lattice.

Figure 2

(Color online) Theoretical phase shift ${\phi }^{\text{at}}S/N$ for the ${{}^{1}S}_0\text{−}{{}^{1}P}_1$ transition with a zero magnetic field and a linearly polarized probe. It takes into account the three different $F^{\prime }=7/2$, 9/2, and 11/2 levels of ${{}^{1}P}_1$, spanning over 60 MHz around their average frequency (center of the plot). The phase shift is represented for equally populated $m_F$ states (solid red curve) and spin-polarized atoms in $m_F=9/2$ or $m_F=-9/2$ states (dashed blue curve). For a 90 MHz detuning, these phase shifts are comparable and amount to a few tens of mrad with typical parameters $N={10}^4$ atoms and $S=2.8\times {10}^3\mu {\text{m}}^2$.

Figure 3

(Color online) Experimental setup. The number of atoms in the optical lattice is proportional to the phase shift of the RF component at the modulation frequency $f$, filtered by a bandpass filter (BPF). The harmonic at frequency $2f$ is used to lock the phase of the interferometer and hence maximizing the RF power of the signal component.

Figure 4

(Color online) Detection noise $\left(\frac{1}{2}\sqrt{⟨\delta {\phi }_1^2⟩+⟨\delta {\phi }_{-1}^2⟩}\right)$ power spectral density at 125 Hz and 1 kHz. The signal is shot noise limited [blue line, from Eq. (4)] for powers up to 30 nW. The inset shows the full phase noise spectrum for a typical detected optical power $\eta P=5\text{nW}$, corresponding to a white noise level of ${10}^{-10}{\text{rad}}^2/\text{Hz}$.

Figure 5

(Color online) Atomic loss due to the probe laser for different lattice depths, measured by fluorescence detection after the nondestructive probing. The solid curve is a fit of the fluorescence points with Eq. (6). This fit gives $n_{\gamma }=103$ photons per atom, in good agreement with the value of 81 photons per atom deduced from Eq. (5) and the measured optical power ($P=14\text{nW}$, $T=3\text{ms}$).