Excited-Band Coherent Delocalization for Improved Optical Lattice Clock Performance

We implement coherent delocalization as a tool for improving the two primary metrics of atomic clock performance: systematic uncertainty and instability. By decreasing atomic density with coherent delocalization, we suppress cold-collision shifts and two-body losses. Atom loss attributed to Landau-Zener tunneling in the ground lattice band would compromise coherent delocalization at low trap depths for our ${}^{171}\mathrm{Yb}$ atoms; hence, we implement for the first time delocalization in excited lattice bands. Doing so increases the spatial distribution of atoms trapped in the vertically oriented optical lattice by $\sim 7$ times. At the same time, we observe a reduction of the cold-collision shift by 6.5(8) times, while also making inelastic two-body loss negligible. With these advantages, we measure the trap-light-induced quenching rate and natural lifetime of the ${{}^{3}P}_0$ excited state as $5.7(7)\times {10}^{-4}{E}_r^{-1}{\mathrm{s}}^{-1}$ and 19(2) s, respectively.

Figure 1

Shaken vertical optical lattice potential. The tunneling rate between neighboring lattice sites, shown as the strength of the yellow bars, increases for higher longitudinal bands.

Figure 2

The population of atoms remaining after ramping to various applied trap depths from $57(1)E_r$. Atoms are prepared in different longitudinal bands using ARP, with the targeted lattice band labeled as $n_z$. Dashed lines are theoretically determined populations, $P_{\mathrm{LZ}}(U,n_z)$, which show LZ tunneling leads to loss as the depth is lowered. The slight persistence in percent-level survival rates at low trap depths seen in $n_z=2$, 3 is due to the percent-level impurity in the targeted lattice band.

Figure 3

(a) We numerically integrate Eq. (3) to find the theoretical maximum tunneling rates in each motional band. Note the presence of effective trap depth scaling in the tunneling rate. We assume that the trap depth at any point during AM must not be lower than the cutoff depth, where $P_{\mathrm{LZ}}(U,n_z)=1/e$. For a given band, this sets a maximum $\alpha$ for depths above the cutoff depth. (b) Averaged fluorescence images of the delocalized Yb sample (right) and original sample (left). Delocalization is applied at the experimentally determined optimal conditions for 1 s. The tilt is imperfect alignment of the camera’s vertical axis to the lattice axis and makes a negligible contribution to the determined size of the delocalized sample.

Figure 4

We measure the shift of the clock transition frequency between two non-spin-polarized samples of different atom numbers, with delocalized samples in blue squares and nondelocalized samples in red triangles. For the nondelocalized sample, data were taken at atom number differences larger than 3000, which are not plotted but still contribute to the fit. The red (blue) line gives a linear fit to the nondelocalized (delocalized) measurements and shaded regions are $1\text{−}\sigma$ statistical uncertainty. Atom number is calibrated through fluorescence measurements, and all measurements are taken between $55E_r$ and $62E_r$.

Figure 5

(a) We measure the reduction in two-body loss from delocalization at $U=60(1)E_r$. Black triangles are $n_e(t)$ in nondelocalized samples, orange squares are $n_e(t)$ in delocalized samples, and the orange line is the fit to Eq. (4) for the delocalized sample. Both samples have identical atom numbers to begin. (b) Excited-state total decay rates are plotted versus the effective trap depth. Hollow red (solid blue) points are taken on different apparatus, and the solid red (dashed blue) line indicates the linear fit to each dataset. The gray line is a previous measurement of the clock state natural lifetime [50]. Excited-state total decay rates are computed from fits such as the representative one in the inset, which was taken at $U=59.8(5)E_r$, corresponding to $U_{\mathrm{eff}}=50.1E_r$. For atoms beginning in the ground state (${{}^{1}S}_0$), $n_g$ are in blue triangles, and the blue line is a fit to $n_g(t)=n_g(t=0)\exp (-{\mathrm{\Gamma }}_{\mathrm{loss}}t)$. For atoms beginning in the excited ${{}^{3}P}_0$ state, $n_e$ ($n_g$) are plotted in red squares (green circles), and the red (green) line is the fit to Eq. (4) [Eq. (5)], with ${\mathrm{\Gamma }}_{\mathrm{loss}}$ shared among all three fits for a given trap depth. The shaded areas are the $1\text{−}\sigma$ statistical uncertainty regions.

Figure 6

We measure a Rabi line by sweeping the frequency of our 578-nm laser over the clock transition. The normalized population is measured using electron shelving, with ${{}^{1}S}_0$ atoms first measured using 399-nm fluorescence and ${{}^{3}P}_0$ atoms then measured by transferring them to ${{}^{1}S}_0$ then measuring 399-nm fluorescence. We move atoms via the normal repump method (${{}^{3}P}_0-{{}^{3}D}_1$ 1388-nm laser), shown in red triangles, or by ARP on the carrier transition, shown in blue squares.

Figure 7

Coherence in tunneling is demonstrated. (a) The vertical size of the atomic sample is plotted versus time. The red line shows a fit to the expected coherent tunneling dynamics of $\sqrt{{\sigma }_0+v^2{t}^2}$, with the shaded region at $1\text{−}\sigma$ statistical uncertainty. The vertical size is measured via Gaussian fit. The tunneling parameters are atoms in $n_z=0$ at $10E_r$ with $\alpha =0.4$. (b) Reversal of coherent tunneling is demonstrated. A Loschmidt echo [two pulses of coherent delocalization (AM) separated by a freezing time $t_{\mathrm{fr}}$] is performed during the dark time of Ramsey spectroscopy. The contrast of the Ramsey line shape is measured to have a period of the freezing time, indicating that the coherent tunneling dynamics can be reversed. Lines are a guide to the eye.