Lattice-Induced Frequency Shifts in Sr Optical Lattice Clocks at the10−17Level

Abstract

We present a comprehensive study of the frequency shifts associated with the lattice potential in a Sr lattice clock by comparing two such clocks with a frequency stability reaching 5×10(-17) after a 1 h integration time. We put the first experimental upper bound on the multipolar M1 and E2 interactions, significantly smaller than the recently predicted theoretical upper limit, and give a 30-fold improved upper limit on the effect of hyperpolarizability. Finally, we report on the first observation of the vector and tensor shifts in a Sr lattice clock. Combining these measurements, we show that all known lattice related perturbations will not affect the clock accuracy down to the 10(-17) level, even for lattices as deep as 150 recoil energies.

Experimental realization of an optical second with strontium lattice clocks

“…This strong confinement regime (Lamb-Dicke regime) dramatically reduces the motional effects. The lattice induces a light shift of several 10 5 Hz on the energy levels, but, as anticipated in the initial proposal 9 , we can control the differential shift at the mHz level 22 when the lattice is operated at the magic wavelength. Together with the J ¼ 0 nature of the clock states, this leads to a spectroscopy almost immune to fluctuations in trapping power or polarization.…”

“…With a waist of 56 mm and an intracavity power of 14 W, the second clock features potentials as deep as 5000 E r . The magic frequency, f magic ¼ 368,554,725 (5) MHz, ensures only the cancellation of the scalar part of the differential polarizability; a tensor correction 22 depending on the angle a between the lattice polarization and the quantization axis defined along the magnetic field can shift noticeably the effective magic point (from f magic À 268 MHz to f magic þ 134 MHz). This angle also defines the sensitivity of the clocks to residual lattice polarization fluctuations.…”

“…The resonators forming the lattices allow trap depths as large as 5000 E r , E r being the recoil energy of a strontium atom absorbing a lattice photon. This provides an important leverage to explore the residual effects of the lattice 22 . We could thus resolve the second-order light shift, equal to 0.45 (10) mHz/E 2 r for a lattice polarization parallel to the quantization axis.…”

“…We have built two OLCs 12,22,30 based on the transition at 698 nm between the ground state 1 S 0 and the metastable state 3 P 0 of neutral 87 Sr atoms, with a natural linewidth of 1 mHz. The atoms are tightly confined in a few thousand wells of an optical lattice formed by a standing wave in an optical resonator.…”

Atomic fountains and optical clocks at SYRTE: Status and perspectives

“…It enabled us to explore systematic effects induced by the trapping laser light. These effects are specific to OLCs, and we have demonstrated that they can be controlled to better than 10 −17 , even with a significant trapping depth [27,28], thus validating the concept of OLCs. In particular, we have determined the precise value for the "magic wavelength" for which the impact of the trapping light is canceled to first order, and resolved or upperbounded a number of higher order effects.…”