Franck–Condon physics in a single trapped ion

Y M Hu,W L Yang,C Lee,M Feng,F Zhou,L Chen,K L Gao,Y Y Xu

doi:10.1088/1367-2630/13/5/053037

Abstract

We propose a way to explore the Franck–Condon (FC) physics using a single ion confined in a spin-dependent potential, formed by the combination of a Paul trap and a magnetic field gradient. A correlation between electronic and vibrational degrees of freedom, called electron–vibron coupling, is induced by a non-zero gradient. In the case of a sufficiently strong electron–vibron coupling, FC blockade of low-lying vibronic transitions takes place. We examine the feasibility of observing FC physics in a single trapped ion and demonstrate many potential applications of ionic FC physics in quantum state engineering and quantum information processing.

Highlights

The Franck-Condon (FC) principle is a well-known fundamental law to explain the intensity of vibronic transitions in molecules [1, 2], in which the transition intensity is proportional to the FC factor defined by the square of the overlap integral between the vibrational wavefunctions of the two involved states
Our discussion above focused on the FC blockade, the strong electron-vibron coupling would probably be useful for quantum simulation of, e.g., Dirac equation [26] or quantum walk [27]
We argue that our study would be useful for further understanding FC physics and its application

Summary

INTRODUCTION

The Franck-Condon (FC) principle is a well-known fundamental law to explain the intensity of vibronic transitions in molecules [1, 2], in which the transition intensity is proportional to the FC factor defined by the square of the overlap integral between the vibrational wavefunctions of the two involved states. Even for a system of no inter-particle interaction, due to the intrinsic nature of a spin-dependent optical lattice, the unavoidable coupling between next-nearest-neighboring sites may destroy the FC physics and induce complex quantum transport along the lattice axis. Compared to the electron-vibron coupling generated by radiation of non-resonant laser beams on the ion, which is too weak to observe the FC physics, the MFG-induced electron-vibron coupling is controllable and could be strong enough to observe. We may apply this coupling to suppress or even block some undesired transitions, called FC blockade, or to enhance some desirable transitions. Beyond the fundamental interests in various fields from quantum spectroscopy to quantum transport, the ionic FC physics is of promising applications in quantum state engineering

MODEL AND FC BLOCKADE

OBSERVATION OF FC BLOCKADE VIA CNOT GATES

Preparation of Fock states

Modification in single-qubit gate operations

EXPERIMENTAL FEASIBILITY AND CHALLENGE

CONCLUSIONS