# Lower ground state due to counter-rotating wave interaction in trapped ion system

## TL;DR

This paper analyzes a trapped ion system driven by two lasers beyond the rotating wave approximation, revealing a lower ground state energy and implications for quantum information processing.

## Contribution

It provides a complete eigensolution for the non-RWA Hamiltonian, enabling comparison with RWA results and exploring new quantum control possibilities.

## Key findings

- Ground state energy is lower without RWA.
- Complete eigensolutions for the non-RWA Hamiltonian.
- Potential applications in quantum information processing.

## Abstract

We consider a single ion confined in a trap under radiation of two traveling waves of lasers. In the strong-excitation regime and without the restriction of Lamb-Dicke limit, the Hamiltonian of the system is similar to a driving Jaynes-Cummings model without rotating wave approximation (RWA). The approach we developed enables us to present a complete eigensolutions, which makes it available to compare with the solutions under the RWA. We find that, the ground state in our non-RWA solution is energically lower than the counterpart under the RWA. If we have the ion in the ground state, it is equivalent to a spin dependent force on the trapped ion. Discussion is made for the difference between the solutions with and without the RWA, and for the relevant experimental test, as well as for the possible application in quantum information processing.