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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

s-Wave collisional frequency shift of a fermion clock

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

Published Jul 1, 2013• 1 citation
Publisher

Abstract

We have experimentally observed a collisional frequency shift of trapped ultracold fermions. We probe the distinguishing features of s-wave collisional frequency shifts of fermions by stepping the atomic interactions through zero near an s-wave Feshbach resonance.
DOI
10.1109/eftf-ifc.2013.6702258

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We excite spin waves with spatially inhomogeneous Ramsey pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped 87Rb. The density-dependent frequency shifts of the hyperfine transition simulate the s-wave collisional frequency shifts of fermions, including those of optical lattice clocks. As the spin polarizations oscillate in the trap, the frequency shift reverses and it depends on the area of the second Ramsey pulse, exhibiting a predicted beyond mean-field frequency shift. Numerical and analytic models illustrate these observed behaviors.
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.
Ultracold atoms--at temperatures of just a few nanokelvin--may serve as atomic "clocks" that can measure time with extremely high precision. Of the two types of atoms, bosons and fermions, the former have been pursued most actively as possible atomic clocks. In his Perspective, Inguscio draws attention to the possible advantages of fermions for such applications. He highlights the report by Gupta et al., who show that a fermion clock transition can be realized without collisional shifts. Radio-frequency spectroscopy turns out to be crucial for investigating interacting fermionic actoms as well as for probing the formations of ultracold molecules.
Radio-frequency techniques were used to study ultracold fermions. We observed the absence of mean-field "clock" shifts, the dominant source of systematic error in current atomic clocks based on bosonic atoms. This absence is a direct consequence of fermionic antisymmetry. Resonance shifts proportional to interaction strengths were observed in a three-level system. However, in the strongly interacting regime, these shifts became very small, reflecting the quantum unitarity limit and many-body effects. This insight into an interacting Fermi gas is relevant for the quest to observe superfluidity in this system.
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.