Decoherence and Collisional Frequency Shifts of Trapped Bosons and Fermions

TL;DR

This paper provides exact calculations of collisional frequency shifts in trapped bosons and fermions, clarifying the factor of 2 controversy and highlighting the importance of spatial variations and decoherence effects.

Contribution

It offers a comprehensive analysis of collisional shifts using singlet and triplet bases, resolving the factor of 2 controversy for bosons and emphasizing spatial variation effects.

Findings

The factor of 2 for bosons' frequency shift is confirmed.

Spatial variations critically affect fermions' collision shifts.

Decoherence impacts frequency shifts in trapped particles.

Abstract

We perform exact calculations of collisional frequency shifts for several fermions or bosons using a singlet and triplet basis for pairs of particles. The "factor of 2 controversy" for bosons becomes clear - the factor is always 2. Decoherence is described by singlet states and they are unaffected by spatially uniform clock fields. Spatial variations are critical, especially for fermions which were previously thought to be immune to collision shifts. The spatial variations lead to decoherence and a novel frequency shift that is not proportional to the partial density of internal states.