Micromotion in trapped atom-ion systems

Abstract

We examine the validity of the harmonic approximation, where the radio-frequency ion trap is treated as a harmonic trap, in the problem regarding the controlled collision of a trapped atom and a single trapped ion. This is equivalent to studying the effect of the micromotion since this motion must be neglected for the trapped ion to be considered as a harmonic oscillator. By applying the transformation of Cook and Shankland we find that the micromotion can be represented by two periodically oscillating operators. In order to investigate the effect of the micromotion on the dynamics of a trapped atom-ion system, we calculate (i) the coupling strengths of the micromotion operators by numerical integration and (ii) the quasienergies of the system by applying the Floquet formalism, a useful framework for studying periodic systems. It turns out that the micromotion is not negligible when the distance between the atom and the ion traps is shorter than a characteristic distance. Within this range the energy diagram of the system changes remarkably when the micromotion is taken into account, which leads to undesirable consequences for applications that are based on an adiabatic process of the trapped atom-ion system. We suggest a simple scheme for bypassing the micromotion effect in order to successfully implement a quantum controlled phase gate proposed previously and create an atom-ion macromolecule. The methods presented here are not restricted to trapped atom-ion systems and can be readily applied to studying the micromotion effect in any system involving a single trapped ion.

25 pages, 8 figures

References in corpus (3)

• Quantum theory of ultracold atom-ion collisions
• Atom-ion quantum gate
• Controlled collisions of a single atom and ion guided by movable trapping potentials

Cited by in corpus (24)

• Cold hybrid ion-atom systems
• Micromotion-induced Limit to Atom-Ion Sympathetic Cooling in Paul Traps
• Cold atom-ion experiments in hybrid traps
• Emulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms
• Observation of collisions between cold Li atoms and Yb${}^{+}$ ions
• Formation of molecular ions by radiative association of cold trapped atoms and ions
• Controlled long-range interactions between Rydberg atoms and ions
• Description of ion motion in a Paul trap immersed in a cold atomic gas
• Ground state properties of ultracold trapped bosons with an immersed ionic impurity
• Dynamics of a single ion spin impurity in a spin-polarized atomic bath
• Trapping Ions and Atoms Optically
• Quantum dynamics of an atomic double-well system interacting with a trapped ion
• Trapped ions in Rydberg-dressed atomic gases
• Impact of ion motion on atom-ion confinement-induced resonances in hybrid traps
• Buffer gas cooling of ions in time-dependent traps using ultracold atoms
• Dynamics of a trapped ion in a quantum gas: effects of particle statistics
• Compound atom-ion Josephson junction: Effects of finite temperature and ion motion
• Minimizing rf-induced excess micromotion of a trapped ion with the help of ultracold atoms
• RF-induced heating dynamics of non-crystallized trapped ions
• Bound states of an ultracold atom interacting with a set of stationary impurities
• Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperature
• Singularities of Floquet Scattering and Tunneling
• Quantum reactive scattering in the long-range ion-dipole potential
• Radio-Frequency Pseudo-Null Induced by Light in an Ion Trap