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arXiv:2109.03143 · Physical Review A

Dynamics of a trapped ion in a quantum gas: Effects of particle statistics

Lorenzo Oghittu, Melf Johannsen, Antonio Negretti, R. Gerritsma

Published Nov 17, 2021• 13 citations
arXivHTMLPDF

Abstract

We study the quantum dynamics of an ion confined in a radio-frequency trap in interaction with either a Bose or spin-polarized Fermi gas. To this end, we derive quantum optical master equations in the limit of weak coupling and the Lamb-Dicke approximations. For the bosonic bath, we also include the so-called ``Lamb-shift'' correction to the ion trap due to the coupling to the quantum gas as well as the extended Fr\"ohlich interaction within the Bogolyubov approximation that have been not considered in previous studies. We calculate the ion kinetic energy for various atom-ion scattering lengths as well as gas temperatures by considering the intrinsic micromotion and we analyze the damping of the ion motion in the gas as a function of the gas temperature. We find that the ion's dynamics depends on the quantum statistics of the gas and that a fermionic bath enables to attain lower ionic energies.

DOI
10.1103/physreva.104.053314

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We study the quantum dynamics of an ion confined in a radio-frequency trap in interaction with either a Bose or spin-polarized Fermi gas. To this end, we derive quantum optical master equations in the limit of weak coupling and the Lamb-Dicke approximations. For the bosonic bath, we also include the so-called ``Lamb-shift'' correction to the ion trap due to the coupling to the quantum gas as well as the extended Fr"ohlich interaction within the Bogolyubov approximation that have been not considered in previous studies. We calculate the ion kinetic energy for various atom-ion scattering lengths as well as gas temperatures by considering the intrinsic micromotion and we analyze the damping of the ion motion in the gas as a function of the gas temperature. We find that the ion's dynamics depends on the quantum statistics of the gas and that a fermionic bath enables to attain lower ionic energies.
We investigate confinement-induced resonances in atom-ion quantum mixtures confined in hybrid traps for small atom-ion mass ratios. Specifically, we consider an ion confined in a time-dependent radio-frequency Paul trap with linear geometry, while the atom is constrained to move into a quasi-one-dimensional optical waveguide within the ion trap. We evaluate the impact of the ion intrinsic micromotion on the resonance position. Thus, we solve the atom-ion dynamics semiclassically, namely, the atom dynamics is governed by the three-dimensional time-dependent Schr\"odinger equation, whereas the ion motion is described by the classical Hamilton equations. We find that the energy of the ion provided by the oscillating radio-frequency fields can affect the resonance position substantially. Notwithstanding, the peculiar phenomenology of those resonances regarding perfect transmission and reflection is still observable. These findings indicate that the intrinsic micromotion of the ion is not detrimental for the occurrence of the resonance and that its position can be controlled by the radio-frequency fields. This provides an additional means for tuning atom-ion interactions in low spatial dimensions. The study represents an important advancement in the scattering physics of compound atomic quantum systems in time-dependent traps.
Abstract Reaching ultracold temperatures within hybrid atom–ion systems is a major limiting factor for control and exploration of the atom–ion interaction in the quantum regime. In this work, we present results on numerical simulations of trapped ion buffer gas cooling using an ultracold atomic gas in a large number of experimentally realistic scenarios. We explore the suppression of micromotion-induced heating effects through optimization of trap parameters for various radio-frequency (rf) traps and rf driving schemes including linear and octupole traps, digital Paul traps, rotating traps and hybrid optical/rf traps. We find that very similar ion energies can be reached in all of them even when considering experimental imperfections that cause so-called excess micromotion. Moreover we look into a quantum description of the system and show that quantum mechanics cannot save the ion from micromotion-induced heating in an atom–ion collision. The results suggest that buffer gas cooling can be used to reach close to the ion’s groundstate of motion and is even competitive when compared to some sub-Doppler cooling techniques such as Sisyphus cooling. Thus, buffer gas cooling is a viable alternative for ions that are not amenable to laser cooling, a result that may be of interest for studies into cold controlled quantum chemistry and charged impurity physics.
We investigate the dynamics of an ion moving through a homogeneous Bose-Einstein condensate (BEC) after an initial momentum is imparted. For this, we derive a master equation in the weak-coupling limit and Lamb-Dicke approximation for the reduced density matrix of the ion. We study the time evolution of the ion's kinetic energy and observe that its expectation value, identified as the ion temperature Tion , is reduced by several orders of magnitude in a time on the order of microseconds for a condensate density in the experimentally relevant range between 1013cm−3 and 1014cm−3 . We characterize this behavior by defining the duration at half maximum as the time required by Tion to reach half of its initial value, and study its dependence on the system parameters. Similarly, we find that the expectation value of the ion's momentum operator is reduced by nine orders of magnitude on the same timescale, making the ion's position converge to a final value. Based on these results, we conclude that the interaction with the bosonic bath allows for cooling and pinning of the ion by decreasing the expectation value of its kinetic energy and velocity, which constitutes a result of direct relevance for current atom-ion experiments. Published by the American Physical Society 2024
A kinetic theory based on the Boltzmann equation is developed for the trapping of atomic ions in a radio-frequency quadrupole ion trap containing enough neutral atoms that ion-neutral collisions cannot be ignored. The collisions are treated at the same level of sophistication and detail as is used to deal with the time- and space-dependent electric fields in the trap. As a result, microscopic definitions are obtained for the damping and stochastic forces that originate from such collisions. These definitions contrast with corresponding phenomenological terms added ad hoc in previous treatments to create damped Mathieu and Langevin equations, respectively. Furthermore, the theory indicates that either collisional cooling or heating of the ions is possible, depending upon details of the ion-neutral mass ratios and interaction potential. The kinetic theory is not dependent on any special assumptions about the electric field strengths, the ion-neutral interaction potentials, or the ion-neutral mass ratio. It also provides an ab initio way to describe the ion kinetic energies, temperatures, and other properties by a series of successive approximations.
We investigate the problem of a single ion in a radio-frequency trap and immersed in an ultracold Bose gas either in condensed or non-condensed phase. We develop master equation formalism describing the sympathetic cooling and we determine the cooling rates and final energies of ions. We show that cold atomic reservoir modifies the stability diagram of the ion in the Paul trap creating the regions where the ion is either cooled or heated due to the energy quanta exchanged with the time-dependent potential. Our calculation indicates that micromotion constitutes an important source of heating limiting the final temperature of ions to values higher than 100μ\muμK for parameters of present experiments.
The immersion of a single ion confined by a radiofrequency (RF) trap in an ultracold atomic gas extends the concept of buffer gas cooling to a new temperature regime. The steady-state energy distribution of the ion is determined by its kinetics in the RF field rather than the temperature of the buffer gas. Moreover, the finite size of the ultracold gas facilitates the observation of back-action of the ion onto the buffer gas. We numerically investigate the system's properties depending on atom–ion mass ratio, trap geometry, differential cross-section and non-uniform neutral atom density distribution. Experimental results are well reproduced by our model considering only elastic collisions. We identify excess micromotion to set the typical scale for the ion energy statistics and explore the applicability of the mobility collision cross-section to the ultracold regime.