Many-body treatment of the collisional frequency shift in fermionic atoms

TL;DR

This paper presents a first-principles many-body theoretical framework to understand density-dependent frequency shifts in fermionic alkaline-earth atoms, explaining experimental data and proposing a new measurement method for scattering lengths.

Contribution

It introduces a non-equilibrium many-body theory for interaction frequency shifts in fermionic atoms, linking microscopic interactions to observable density shifts and measurement effects.

Findings

The theory explains experimental density shift data.

It reveals the role of excitation inhomogeneity and many-body dynamics.

Proposes a method to measure the second scattering length.

Abstract

Recent clock experiments have measured density-dependent frequency shifts in polarized fermionic alkaline-earth atoms using 1S0-3P0 Rabi spectroscopy. Here we provide a first-principles non-equilibrium theoretical description of the interaction frequency shifts starting from the microscopic many-body Hamiltonian. Our formalism describes the dependence of the frequency shift on excitation inhomogeneity, interactions, and many-body dynamics, provides a fundamental understanding of the effects of the measurement process, and explains the observed density shift data. We also propose a method to measure the second of the two 1S0-3P0 scattering lengths, whose knowledge is essential for quantum information processing and quantum simulation applications.