Cooling dynamics of a free ion in a Bose-Einstein condensate

Abstract

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 $T_{\mathrm{ion}}$, 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 $10^{13}{\mathrm{cm}}^{-3}$ and $10^{14}{\mathrm{cm}}^{-3}$. We characterize this behavior by defining the duration at half maximum as the time required by $T_{\mathrm{ion}}$ 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.

arXiv comment16 pages, 11 figures

References in corpus (48)

• Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
• A Straightforward Introduction to Continuous Quantum Measurement
• Metastability and Coherence of Repulsive Polarons in a Strongly Interacting Fermi Mixture
• Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate
• Attractive and repulsive Fermi polarons in two dimensions
• Bose polarons in the strongly interacting regime
• Repulsive Fermi polarons in a resonant mixture of ultracold ${}^6$Li atoms
• Cold hybrid ion-atom systems
• Bose polarons near quantum criticality
• Mesoscopic molecular ions in Bose-Einstein condensates
• Micromotion-induced Limit to Atom-Ion Sympathetic Cooling in Paul Traps
• Controlling chemical reactions of a single particle
• Sympathetic and swap cooling of trapped ions by cold atoms in a MOT
• Cold atom-ion experiments in hybrid traps
• Emulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms
• A single ion as a three-body reaction center in an ultracold atomic gas
• Observation of Feshbach resonances between a single ion and ultracold atoms
• Buffer gas cooling of a trapped ion to the quantum regime
• An ionic impurity in a Bose-Einstein condensate at sub-microkelvin temperatures
• Controlled collisions of a single atom and ion guided by movable trapping potentials
• Universal properties in ultracold ion-atom interactions
• Optical Traps for sympathetic Cooling of Ions with ultracold neutral Atoms
• Ionic polaron in a Bose-Einstein condensate
• Unraveling the Structure of Ultracold Mesoscopic Molecular Ions
• Transport of a single cold ion immersed in a Bose-Einstein condensate
• Observation of Rydberg Blockade Induced by a Single Ion
• Description of ion motion in a Paul trap immersed in a cold atomic gas
• Spatial imaging of a novel type of molecular ions
• Charged polarons and molecules in a Bose-Einstein Condensate
• Quantum dynamics of an atomic double-well system interacting with a trapped ion
• A pulsed ion microscope to probe quantum gases
• Cold chemistry: a few-body perspective on impurity physics of a single ion in an ultracold bath
• Many-body bound states and induced interactions of charged impurities in a bosonic bath
• Inelastic collision dynamics of a single cold ion immersed in a Bose-Einstein condensate
• Absolute strong-field ionization probabilities of ultracold rubidium atoms
• Prospects of reaching the quantum regime in Li-Yb${}^{+}$ mixtures
• Capture Dynamics of Ultracold Atoms in the Presence of an Impurity Ion
• A high resolution ion microscope for cold atoms
• Mediated interactions between ions in quantum degenerate gases
• Generalised Kronig-Penney model for ultracold atomic quantum systems
• Observation of trap-assisted formation of atom-ion bound states
• Ultrafast Electron Cooling in an Expanding Ultracold Plasma
• Quantum-limited thermometry of a Fermi gas with a charged spin particle
• Quantum simulation of extended polaron models using compound atom-ion systems
• Compound atom-ion Josephson junction: Effects of finite temperature and ion motion
• Experimental setup for studying an ultracold mixture of trapped Yb${}^{+}$-${}^6$Li
• Ion-induced interactions in a Tomonaga-Luttinger liquid
• Charged ultralong-range Rydberg trimers

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