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arXiv:1908.01151 · Physical Review A

Impact of ion motion on atom-ion confinement-induced resonances in hybrid traps

Vladimir S. Melezhik, Zbigniew Idziaszek, Antonio Negretti

Published Dec 3, 2019• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.100.063406

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Scholarly review .•Oct 3, 2025•0 citations
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.
We have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V.S. Melezhik et. al., Phys. Rev. A100, 063406 (2019)). The important element of the hybrid atom-ion systems is the electromagnetic Paul trap confining the charged ion. The oscillating motion of the confined ion is defined by two frequencies of the Paul trap. It is the frequency of the order of 100 kHz due to the constant electric field and the radio-frequency of about 1-2 MHz defined by the alternating electromagnetic field of the ion trap. The necessity to accurately treat the ion motion in the combined field with two time scales defined by these two very different frequencies has demanded to develop the stable computational scheme for integration of the classical Hamilton equations for the ion motion. Moreover, the scheme must be stable on rather long time-interval of the ion collision with the cold atom ∼ 10 × 2/ defined by the atomic trap frequency ∼ 10 kHz and in the moment of the atom-ion collision when the Hamilton equations are strongly coupled. The developed numerical method takes into account all these features of the problem and makes it possible to integrate the system of coupled quantum-semiclassical equations with the necessary accuracy and quantitatively describes the processes of atomic-ion collisions in hybrid traps, including resonance effects.
We investigate confinement-induced resonances in a system composed of a tightly trapped ion and a moving atom in a waveguide. We determine the conditions for the appearance of such resonances in a broad region---from the ``long-wavelength'' limit to the opposite case when the typical length scale of the atom-ion polarization potential essentially exceeds the transverse waveguide width. We find considerable dependence of the resonance position on the atomic mass which, however, disappears in the ``long-wavelength and zero-energy'' limit, where the known result for the confined atom-atom scattering is reproduced. We also derive an analytic and a semianalytic formula for the resonance position in the long-wavelength and zero-energy limit and we investigate numerically the dependence of the resonance condition on the finite atomic colliding energy. Our results, which can be investigated experimentally in the near future, could be used to determine the atom-ion scattering length, to determine the temperature of the atomic ensemble in the presence of an ion impurity, and to control the atom-phonon coupling in a linear ion crystal in interaction with a quasi-one-dimensional atomic quantum gas.
We present a theoretical study of trapping an electron in a two-frequency Paul trap, motivated by future hybrid architecture consisting of a doubly charged calcium ion (Ca2+^{2+}2+) and an electron. By isolating the electron from ionic-electron interactions, we formulate the equations of motion for the electron in the time-dependent trap potentials and cast them in the Hill form. Stability and dynamics are then analysed in terms of the dimensionless q-parameters, which encode the applied voltages, drive frequencies, trap geometry, and the particle's charge-to-mass ratio. Under the combined action of the two radio-frequency fields, the trapped electron's classical motion is shown to be approximated well by a slow secular oscillation modulated by two distinct motion sidebands originating from the low- and high-frequency RF drives. The approximation method presented here enables a quick evaluation of the relation between the device-design q-parameters and the electron motion. It offers a crucial foundation for developing physical models of electron-ion interactions in electron-ion traps.
We consider a system composed of a trapped atom and a trapped ion. The ion charge induces in the atom an electric dipole moment, which attracts it with an ${r}^{\ensuremath{-}4}$ dependence at large distances. In the regime considered here, the characteristic range of the atom-ion interaction is comparable or larger than the characteristic size of the trapping potential, which excludes the application of the contact pseudopotential. The short-range part of the interaction is described in the framework of quantum-defect theory, by introducing some short-range parameters, which can be related to the sss-wave scattering length. When the separation between traps is changed we observe trap-induced shape resonances between molecular bound states and vibrational states of the external trapping potential. Our analysis is extended to quasi-one-dimensional geometries, when the scattering exhibit confinement-induced resonances, similar to the ones studied before for short-range interactions. For quasi-one-dimensional systems we investigate the effects of coupling between the center of mass and relative motion, which occurs for different trapping frequencies of atom and ion traps. Finally, we show how the two types of resonances can be employed for quantum state control and spectroscopy of atom-ion molecules.
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.
Ion traps and optical tweezers have emerged as highly promising technologies in the development of quantum computing, enabling precise control over qubits through electromagnetic and optical confinement. This paper explores the fundamental principles, advantages, and limitations of ion traps, including Paul and Penning configurations, and evaluates their role in modern quantum architectures. Particular emphasis is placed on coherence time, fidelity, and all-to-all connectivity, which make trapped ions a leading qubit candidate despite challenges in scalability and optical complexity. The work also examines optical tweezers, which use tightly focused laser beams to trap and manipulate ions and atoms with high precision, facilitating scalable arrays of qubits. Furthermore, hybrid traps that integrate optical tweezers with Paul traps are discussed as promising solutions to mitigate Radio-Frequency (RF) micromotion and enhance stability for cold ion–atom systems. Python-based simulations are presented to illustrate ion dynamics under Brownian motion, electric fields, and Gaussian laser traps, demonstrating how trap strength directly affects oscillation amplitude and confinement. Results confirm that stronger optical potentials reduce oscillation amplitude, while weaker traps lead to ion escape, aligning with theoretical predictions. Overall, this study highlights how the interplay of electromagnetic and optical techniques advances the frontier of quantum information science, with direct implications for computation, communication, and simulation.