Ion trap quantum computing with transverse phonon modes

Mahmoud Abdel‐Aty, Arthur R. McGurn

Shi-Liang Zhu, Christopher R. Monroe, Luming Duan

We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.

S. Charles Doret, Ashay N. Patel

Hiroki Takahashi

Yan‐Li Zhou

We present a scheme of quantum simulation of many-body interactions with trapped ions via the exchange of virtual phonons, where the motion from both the longitudinal and the transverse directions is considered. By tuning the detunings of Raman lasers, the long-range and locally tunable interaction is easily obtained between different spins. We show that the competing spin-spin couplings mediated by all motion modes can give rise to higher levels of frustration and richer phase transitions than the conventional approaches based on the longitudinal or the transverse phonon modes alone.

Subhra Mudli, Subhanka Mal, Anushree Dey +1 more

We theoretically show that when two largely separated trapped atoms interact with a trapped ion via Rydberg excitation of the atoms, the ion-mediated interaction between the atoms exceeds the direct atom-atom interaction by several orders of magnitude. Since the motion of the atoms is much slower than the motion of the ion, we resort to Born-Oppenheimer approximation to calculate the ion-mediated adiabatic potential. We also calculate the ion-mediated phonon modes of the atoms that are separated by more than 10 micron. For cylindrical geometry of the system and both the atoms being excited to the same Rydberg state, the stretched and center-of-mass (COM) axial or transverse phonon modes are found to be almost degenerate, while the phonon modes are non-degenerate when one atom is in a Rydberg state and the other in the ground state. We discuss the non-adiabatic effects in the system that give rise to a Gauge structure and associated geometric phase in the system. This study may open a new perspective in quantum computing and exploring molecular physics associated with a conical intersection using an ion-atom hybrid architecture.