The best atomic clocks are based on ensembles of independent atoms. For these systems, clock precision cannot be better than the standard quantum limit, which scales as *N*^{½} (where *N* is the number of atoms) [1].

However, a certain class of entangled states known as “squeezed states” are known to have precision better than the standard quantum limit [2,3]. Operating a clock with these states is bound by the ultimate limit to measurement precision, namely the Heisenburg limit. The Heisenburg limit is enhanced over the standard quantum limit by a factor of *N*^{½}, meaning that this limit scales as *N*. This can result in clock precision that is orders of magnitude better than traditional clocks.

We are exploring a novel scheme for squeezing atoms using Rydberg states [4]. Starting with an ultracold gas of strontium trapped in an optical lattice potential, the excited state of the strontium clock transition is dressed by a laser that couples to a Rydberg level. The Rydberg interaction creates state-dependent correlations, which squeezes the atoms. Using this squeezed state, the improvement in clock precision can be demonstrated by performing spectroscopy of the clock transition with an ultrastable laser.

References:

[1] Itano, et al. “Quantum projection noise: Population fluctuations in two level systems.” *Physical Review A* **47**, 3554 (1993).

[2] M. Kitagawa and M. Ueda. Squeezed spin states. *Physical Review A* **47**, 5138 (1993).

[3] D.J. Wineland, et al. Squeezed atomic states and projection noise in spectroscopy. *Physical Review A* **50**, 67 (1994).

[4] L.I.R. Gil, et al. Spin squeezing in a Rydberg lattice clock. *Physical Review Letters* **112**, 103601 (2014).