Entangling the lattice clock: Towards Heisenberg-limited timekeeping

A scheme is presented for entangling the atoms of an optical lattice to reduce the quantum projection noise of a clock measurement. The divalent clock atoms are held in a lattice at a “magic” wavelength that does not perturb the clock frequency—to maintain clock accuracy—while an open-shell $J=1/2$ “head” atom is coherently transported between lattice sites via the lattice polarization. This polarization-dependent “Archimedes’ screw” transport at magic wavelength takes advantage of the vanishing vector polarizability of the scalar, $J=0$, clock states of bosonic isotopes of divalent atoms. The on-site interactions between the clock atoms and the head atom are used to engineer entanglement and for clock readout.

Figure 1

Schematic of the entanglement process. (a) With $\varphi =0$ a single head atom (light orange circle) and several clock atoms (dark blue circles) are trapped in the minima of a one-dimensional (1D) optical lattice, with one or fewer atoms per site. Due to an intensity differential of the underlying lattices, the clock atoms couple strongly to the ${\sigma }_{+}$ lattice (solid blue line). The head atom is placed in a superposition of atomic states: one which couples strongly to the ${\sigma }_{+}$ lattice and one which couples strongly to the ${\sigma }_{-}$ lattice (dashed orange line). (b) As $\varphi$ is increased, the latter state spatially separates and is transported along the lattice. (c) This portion of the head atom is then brought into contact with a clock atom to entangle the two atoms. (d) The head atom is transported further to obtain entanglement with the remaining clock atoms in a similar manner.

Figure 2

Dynamic polarizability of Al as a function of lattice laser frequency. All values are given in atomic units. Marked points on the plot correspond to magic wavelengths for clock transitions in divalent atoms [23, 26].