Trapped Ions in Rydberg-Dressed Atomic Gases

T. Secker, N. Ewald, J. Joger, H. Fürst, T. Feldker, and R. Gerritsma

Phys. Rev. Lett. 118, 263201 – Published 27 June 2017

Abstract

We theoretically study trapped ions that are immersed in an ultracold gas of Rydberg-dressed atoms. By off-resonant coupling on a dipole-forbidden transition, the adiabatic atom-ion potential can be made repulsive. We study the energy exchange between the atoms and a single trapped ion and find that Langevin collisions are inhibited in the ultracold regime for these repulsive interactions. Therefore, the proposed system avoids recently observed ion heating in hybrid atom-ion systems caused by coupling to the ion’s radio frequency trapping field and retains ultracold temperatures even in the presence of excess micromotion.

Received 13 December 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.263201

Physics Subject Headings (PhySH)

Ultracold collisions

Atomic gases Ions Rydberg atoms & molecules

Atom & ion cooling

Atomic, Molecular & Optical

Authors & Affiliations

T. Secker^1,2, N. Ewald¹, J. Joger¹, H. Fürst¹, T. Feldker¹, and R. Gerritsma¹

¹Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands
²Eindhoven University of Technology, Post Office Box 513, 5600 MB Eindhoven, Netherlands

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Issue

Vol. 118, Iss. 26 — 30 June 2017

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Images

Figure 1
A trapped ion (blue sphere) in a cloud of atoms (orange spheres); the atomic ground states $| g S ⟩$ are dressed with the Rydberg state $| n S ⟩$ with $n$ the principal quantum number and $Δ_{0}$ the laser detuning. By appropriate engineering of the Rydberg laser field, the adiabatic atom-ion potential can be made repulsive such that the atoms cannot get close enough to undergo Langevin collisions (as depicted by the sphere around the ion). To optically shield the ion in three dimensions, two laser fields are needed with linear and circular polarization, as explained in the text.
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Figure 2
The dressed potential $V_{d} (R)$ assuming coupling to the $| 19 S ⟩$ state of Rb with $Δ_{0} = 2 π$ 1.0 GHz. The dashed line is calculated from the Rydberg wave functions taken from Ref. [31] in first-order perturbation theory, within the dipole approximation, and neglecting spin-orbit coupling. Here, we assumed the defects of the $L - 1 / 2$ for the $L$ states and set the Rabi frequency on the $| 5 S ⟩ \to | 19 P ⟩$ transition to $Ω_{19 P, m_{L} = 0} = 2 π \times 200 MHz$ by tuning the laser intensity. The black dots are computed by diagonalization of the Rydberg manifold in the presence of the dressing laser and ion, in the rotating wave approximation, including spin-orbit coupling, up to charge-quadrupole order in the atom-ion interaction terms. The laser intensity was set to the same value as for the approximated potential. For both calculations, we took the Rydberg states $n = 10, \dots, 30$ into account [28].
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Figure 3
Collision dynamics for an ${}^{171}{Yb}^{+}$ ion in a Rydberg-dressed Rb gas with repulsive interactions and $T_{a} = 2 μ K$ . The ions heats up from $T_{ion} = 0$ to about $1.8 μ K$ , corresponding to near thermalization. Excess micromotion due to a dc field of $E_{EMM} = 0.05 V / m$ does not affect the thermalization dynamics, which is completely equivalent to that expected for an ion trapped in a time-independent trap with the same secular trap frequencies. For the curve starting at around $4 μ K$ , we gave the ion an initial velocity of 0.02(1,1,1) m/s and we simulate cooling towards the atomic gas temperature. The fastest thermalization curve shows the results for the combination ${}^{87}{Rb} − {}^{9}{Be}^{+}$ . The inset shows results for ground-state atoms, in which the interaction is attractive. Even without excess micromotion, the ion quickly heats up to temperatures higher than the atomic cloud, whereas within the secular approximation slow thermalization would occur. All results represent the average of 50–100 runs.
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