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Laser Physics

Collisional shifts in an optical-lattice atomic clock

Y. B. Band, Amichay Vardi

Published Mar 1, 2008• 2 citations
Publisher

Abstract

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.

DOI
10.1134/s1054660x08030195

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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 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.
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.
We discuss two possible configurations for optical lattice clocks; a one-dimensional (1D) lattice loaded with spinpolarized fermions, and a three-dimensional (3D) lattice loaded with bosons. In the former scheme, collisional frequency shifts are suppressed by the quantum statistical property of identical fermions. This Pauli blocking of collisions is critically dependent on the degree of spin polarization of the fermionic atoms, which we carefully investigated in the Rabi excitation process of the clock transition. In the latter scheme, a single occupancy lattice suppresses bunching of bosons and collisional frequency shifts. We demonstrate a frequency comparison of these two optical lattice clocks based on fermionic 87Sr and bosonic 88Sr. Operating these clocks parallely has yielded a stability approaching 10−17. Such measurements are an important step to ascertain the lattice clocks' uncertainty at the 10−17 level and beyond.
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.
Collisions with background gas particles can shift the resonance frequencies of atoms in atomic clocks. The internal quantum states of atoms can also become entangled with their motional states due to the recoil imparted by a collision, which leads to a further shift of the clock frequency through the relativistic Doppler shift. It can be complicated to evaluate the Doppler and collisional frequency shifts for clock atoms in such entangled states, but estimates of these shifts are essential in order to improve the accuracy of optical atomic clocks. We present a formalism that describes collisions and relativistic Doppler shifts in a unified manner, and can therefore be used to accurately estimate collisional frequency shifts in trapped-atom clocks.