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arXiv:1212.4385 · Physical Review Letters

s -Wave Collisional Frequency Shift of a Fermion Clock

E.L. Hazlett, Yi Zhang, Ronald W. Stites, Kurt Gibble, Kenneth M. O’Hara

Published Apr 15, 2013• 20 citations
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Abstract

We report an s-wave collisional frequency shift of an atomic clock based on fermions. In contrast to bosons, the fermion clock shift is insensitive to the population difference of the clock states, set by the first pulse area in Ramsey spectroscopy, θ(1). The fermion shift instead depends strongly on the second pulse area θ(2). It allows the shift to be canceled, nominally at θ(2)=π/2, but correlations perturb the null to slightly larger θ(2). The frequency shift is relevant for optical lattice clocks and increases with the spatial inhomogeneity of the clock excitation field, naturally larger at optical frequencies.

DOI
10.1103/physrevlett.110.160801

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Optical lattice clocks with extremely stable frequency are possible when many atoms are interrogated simultaneously, but this precision may come at the cost of systematic inaccuracy resulting from atomic interactions. Density-dependent frequency shifts can occur even in a clock that uses fermionic atoms if they are subject to inhomogeneous optical excitation. However, sufficiently strong interactions can suppress collisional shifts in lattice sites containing more than one atom. We demonstrated the effectiveness of this approach with a strontium lattice clock by reducing both the collisional frequency shift and its uncertainty to the level of 10(-17). This result eliminates the compromise between precision and accuracy in a many-particle system; both will continue to improve as the number of particles increases.
The effects of elastic collisions in optical-lattice atomic clocks are analyzed. Calculations are presented using a separated oscillatory fields clock arrangement. The interactions of atoms in multiply occupied lattice sites cause a linear frequency shift, and also generate asymmetric Ramsey fringe patterns, both complicate the determination of the resonance frequency and reduce the fringe visibility due to interparticle entanglement. A method of reducing these collisional effects in an optical lattice clock containing bosonic atoms by introducing a phase difference of π between the Ramsey driving fields in adjacent sites is developed. This configuration suppresses site-to-site hopping due to the interference of two tunneling pathways, without degrading the fringe visibility. The probability of double occupancy is, thereby, reduced and collisional shifts are, thus, ameliorated.
We develop a formalism to incorporate exchange symmetry considerations into the calculation of collisional frequency shifts for atomic clocks using a density-matrix formalism. The formalism is developed for both fermionic and bosonic atomic clocks. Numerical results for a finite-temperature 87{}^{87}87Sr 1S0{}^{1}{S}_{0}1S0​ (F=9/2F=9/2F=9/2) atomic clock in a magic wavelength optical lattice are presented.
We theoretically study the effects of elastic collisions on the determination of frequency standards via Ramsey-fringe spectroscopy in optical-lattice atom clocks. Interparticle interactions of bosonic atoms in multiply occupied lattice sites can cause a linear frequency shift, as well as generate asymmetric Ramsey-fringe patterns and reduce fringe visibility due to interparticle entanglement. We propose a method of reducing these collisional effects in an optical lattice by introducing a phase difference of $\ensuremath{\pi}$ between the Ramsey driving fields in adjacent sites. This configuration suppresses site-to-site hopping due to interference of two tunneling pathways, without degrading fringe visibility. Consequently, the probability of double occupancy is reduced, leading to cancellation of collisional shifts.