Rotation Errors Due to Field Quantization for Simultaneously Driven Atoms

TL;DR

This paper analyzes how quantum field effects cause rotation errors in atomic ensembles during quantum gate operations, revealing error scaling behaviors and proposing mitigation strategies.

Contribution

It introduces a second order perturbation theory approach to quantify rotation errors due to field quantization for arbitrary atomic states and rotation angles.

Findings

Error scales as N for average initial states.

Error can scale as N^2 for certain entangled states.

Squeezed states and interaction time adjustments can reduce errors.

Abstract

When an electromagnetic field in a coherent or quasiclassical (e.g., squeezed) state is used to simultaneously drive an ensemble of two-level atoms, the quantum nature of the field will, in general, cause the final state of the atoms to differ from the one predicted for a totally classical field. This is a potential source of error in quantum logic gates in which the gate is the rotation of the atoms by a laser. In this paper, we use second order perturbation theory to find how this error scales with the number of atoms, $N$, being driven simultaneously, for an arbitrary rotation angle. The result depends on the initial atomic state: for some highly entangled states, and a field in a coherent state, the error may scale as $N^2$, yet we find that the average over a random distribution of initial states only scales as $N$. We discuss possible ways to mitigate the error, including the use of squeezed states, as well as adjusting the interaction time between the field and atoms to be different from what would be expected from the classical-field treatment.