Subrecoil Clock-Transition Laser Cooling Enabling Shallow Optical Lattice Clocks

Laser cooling is a key ingredient for quantum control of atomic systems in a variety of settings. In divalent atoms, two-stage Doppler cooling is typically used to bring atoms to the $\mu \mathrm{K}$ regime. Here, we implement a pulsed radial cooling scheme using the ultranarrow ${{}^1\mathrm{S}}_0\text{−}{{}^3\mathrm{P}}_0$ clock transition in ytterbium to realize subrecoil temperatures, down to tens of nK. Together with sideband cooling along the one-dimensional lattice axis, we efficiently prepare atoms in shallow lattices at an energy of 6 lattice recoils. Under these conditions key limits on lattice clock accuracy and instability are reduced, opening the door to dramatic improvements. Furthermore, tunneling shifts in the shallow lattice do not compromise clock accuracy at the ${10}^{-19}$ level.

Figure 1

(a) Energy levels used in the cooling. Note that spontaneous decay from ${{}^3\mathrm{D}}_1$ (lifetime $330\mathrm{ns}$ [40]) follows the branching ratios 0.64 (${{}^3\mathrm{P}}_0$), 0.35 (${{}^3\mathrm{P}}_1$), and 0.01 (${{}^3\mathrm{P}}_2$, not shown). ${{}^3\mathrm{P}}_1$ population decays to the ground state with a $870$-ns lifetime [40]. (b) Atomic excitation as a function of laser detuning from the 578-nm transition for a laser propagating along the $x$ (red) and $z$ (blue) axes at 560-${\mathrm{E}}_{\mathrm{r}}$ lattice depth. (c) Measured linewidth of velocity selection profiles as a function of the first 578-nm laser pulse duration and for different trap depths [48 ${\mathrm{E}}_{\mathrm{r}}$ (green circle), 115 ${\mathrm{E}}_{\mathrm{r}}$ (cyan square), and 560 ${\mathrm{E}}_{\mathrm{r}}$ (red diamond)] and cooling conditions [560 ${\mathrm{E}}_{\mathrm{r}}$ after three-dimensional (3D) cooling (blue triangle)]. The magenta triangle data are measured with free-space atoms, and the black dashed line is the calculated Fourier-limited linewidth for different pulse durations. The right ordinate indicates the corresponding temperature of the selected atoms, from free-space Doppler theory.

Figure 2

(a) Radial spectra before (red) and after (blue) pulsed radial cooling at 560 ${\mathrm{E}}_{\mathrm{r}}$. The same cooling process was also realized at 48 ${\mathrm{E}}_{\mathrm{r}}$ (green) and 115 ${\mathrm{E}}_{\mathrm{r}}$ (orange). The corresponding radial temperatures of atoms are 17.4(4) $\mu \mathrm{K}$, 250(10) nK, 90(10) nK, and 90(10) nK, respectively. The total cooling time for each trap depth is 84 ms, 93 ms, and 96 ms, respectively. Temperature is derived from the width of a Voigt line shape fit [41]. (b) Measured radial temperature as a function of cooling time at 560 ${\mathrm{E}}_{\mathrm{r}}$. The cooling time is adjusted by varying the number of pulse cycles applied. The solid line is the exponential fit. The black dashed line is the recoil-limited temperature of 410 nK. (c) Longitudinal sideband spectra at 560 ${\mathrm{E}}_{\mathrm{r}}$ after 3D cooling. Red sideband, carrier, and blue sideband transitions are highlighted with the red, gray, and blue line, respectively. (d) Blue sidebands at 560 ${\mathrm{E}}_{\mathrm{r}}$ under conditions of no clock-transition cooling (red), longitudinal sideband cooling alone ($z$ cooling, brown), radial cooling alone (xy cooling, green), and 3D cooling (blue). In the green trace, we resolve transitions from different longitudinal lattice bands, whose frequency splitting is given by the trap anharmonicity.

Figure 3

(a) Remaining atomic fraction after adiabatically ramping to the indicated trap depth from 560 ${\mathrm{E}}_{\mathrm{r}}$ after 3D cooling at 560 ${\mathrm{E}}_{\mathrm{r}}$ (blue circle), after longitudinal sideband cooling alone (cyan square), or with no clock transition cooling at all (green diamond). Also included is the case of direct loading to a fixed lattice of indicated trap depth with no adiabatic ramp (magenta triangle). (b) Longitudinal temperature ($T_z$, blue circle) and radial temperature ($T_r$, red diamond) after adiabatically ramping to the indicated trap depth from 560 ${\mathrm{E}}_{\mathrm{r}}$ after 3D cooling at 560 ${\mathrm{E}}_{\mathrm{r}}$. The dashed lines are fit with the expected adiabatic scaling.

Figure 4

(a) Longitudinal sideband and Bloch oscillation spectrum at 12 ${\mathrm{E}}_{\mathrm{r}}$. First-order Bloch oscillations ($\pm 1$) are observed not only around the carrier transition but also around the blue sideband. (b) 30-ms $\pi$ pulse Rabi spectroscopy at 6 ${\mathrm{E}}_{\mathrm{r}}$. Insets: enlarged views of the carrier spectrum and the first-order Bloch oscillation spectrum. (c) Measured relative Rabi frequencies of the carrier and the first-order Bloch oscillation transition as a function of trap depth. Dashed lines are theoretical calculations.