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.

16 pages, 11 figures

References in corpus (13)

• Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
• A Straightforward Introduction to Continuous Quantum Measurement
• Attractive and repulsive Fermi polarons in two dimensions
• Repulsive Fermi polarons in a resonant mixture of ultracold ${}^6$Li atoms
• Controlling chemical reactions of a single particle
• Controlled collisions of a single atom and ion guided by movable trapping potentials
• Universal properties in ultracold ion-atom interactions
• Quantum dynamics of an atomic double-well system interacting with a trapped ion
• Inelastic collision dynamics of a single cold ion immersed in a Bose-Einstein condensate
• Generalised Kronig-Penney model for ultracold atomic quantum systems
• Quantum-limited thermometry of a Fermi gas with a charged spin particle
• Quantum simulation of extended polaron models using compound atom-ion systems
• Experimental setup for studying an ultracold mixture of trapped Yb${}^{+}$-${}^6$Li