Vibrational Bloch-Siegert effect in trapped ions

TL;DR

This paper investigates the vibrational Bloch-Siegert effect in trapped ions, deriving explicit formulas for frequency shifts caused by off-resonant laser interactions, and compares these with numerical simulations to deepen understanding of the phenomenon.

Contribution

It introduces the vibrational Bloch-Siegert shift concept, providing explicit analytic expressions and analyzing its relation to the traditional Bloch-Siegert shift in trapped ions.

Findings

Analytic expressions for vibrational Bloch-Siegert shifts are derived.

Numerical results confirm the validity of the analytic formulas.

The study clarifies differences between vibrational and traditional Bloch-Siegert shifts.

Abstract

When trapped atoms are illuminated by weak lasers, off-resonant transitions cause shifts in the frequencies of the vibrational-sideband resonances. These frequency shifts may be understood in terms of Stark-shifts of the individual levels or, as proposed here, as a vibrational Bloch-Siegert shift, an effect closely related to the usual (radio-frequency or optical) Bloch-Siegert shift and associated with rapidly oscillating terms when the Rotating Wave Approximation is not made. Explicit analytic expressions are derived and compared to numerical results, and the similarities and differences between the usual and the vibrational Bloch-Siegert shifts are also spelled out.