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arXiv:2010.13621 · Physical Review A

Trapping, shaping, and isolating of an ion Coulomb crystal via state-selective optical potentials

Pascal Weckesser, Fabian Thielemann, Daniel Hoenig, Alexander Lambrecht, Leon Karpa, Tobias Schaetz

Published Jan 21, 2021• 23 citations
arXivHTMLPDF

Abstract

For conventional ion traps, the trapping potential is close to independent of the electronic state, providing confinement for ions dependent primarily on their charge-to-mass ratio $Q/m$. In contrast, storing ions within an optical dipole trap results in state-dependent confinement. Here we experimentally study optical dipole potentials for $^{138}\mathrm{Ba}^{+}$ ions stored within two distinctive traps operating at 532 and 1064 nm. We prepare the ions in either the electronic ground ($6{S}_{1/2}$) or one of the metastable excited states ($5{D}_{3/2}$ or $5{D}_{5/2}$) and probe the relative strength and polarity of the potential. On the one hand, we apply our findings to selectively remove ions from a Coulomb crystal, despite all ions sharing the same $Q/m$. On the other hand, we deterministically purify the trapping volume from parasitic ions in higher-energy orbits, resulting in reliable isolation of Coulomb crystals down to a single ion within a radio-frequency trap.

DOI
10.1103/physreva.103.013112

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For conventional ion traps, the trapping potential is close to independent of the electronic state, providing confinement for ions dependent primarily on their charge-to-mass ratio Q/mQ/mQ/m. In contrast, storing ions within an optical dipole trap results in state-dependent confinement. Here we experimentally study optical dipole potentials for 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ ions stored within two distinctive traps operating at 532 and 1064 nm. We prepare the ions in either the electronic ground (6S1/26{S}_{1/2}6S1/2​) or one of the metastable excited states (5D3/25{D}_{3/2}5D3/2​ or 5D5/25{D}_{5/2}5D5/2​) and probe the relative strength and polarity of the potential. On the one hand, we apply our findings to selectively remove ions from a Coulomb crystal, despite all ions sharing the same Q/mQ/mQ/m. On the other hand, we deterministically purify the trapping volume from parasitic ions in higher-energy orbits, resulting in reliable isolation of Coulomb crystals down to a single ion within a radio-frequency trap.
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta.Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task.For many applications, linear chains of ions in conventional traps are ideally suited to address this problem.However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems.Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields.We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal.As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap.Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion.Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one-and two-dimensional crystals.
Abstract Isolating neutral and charged particles from the environment is essential in precision experiments. For decades, this has been achieved by trapping ions with radio-frequency (RF) fields and neutral particles with optical fields. Recently, the trapping of ions by interaction with light has been demonstrated. This might permit the advantages of optical trapping and ions to be combined. For example, we would benefit from superimposing optical traps to investigate ensembles of ions and atoms in the absence of any RF fields and from the versatile and scalable trapping geometries featured by optical lattices. In particular, ions provide individual addressability, and electronic and motional degrees of freedom that can be coherently controlled and detected via high-fidelity, state-dependent operations. Their long-range Coulomb interaction is significantly larger compared to those of neutral atoms and molecules. This enables ultra-cold interaction and the chemistry of trapped ions and atoms to be studied, as well as providing a novel platform for higher-dimensional experimental quantum simulations. The aim of this topical review is to present the current state of the art and to discuss the current challenges and prospects of the emerging field.
Abstract We study a method for mass-selective removal of ions from a Paul trap by parametric excitation. This can be achieved by applying an oscillating electric quadrupole field at twice the secular frequency ωsec\omega _{\text {sec}}ωsec​ ω sec using pairs of opposing electrodes. While excitation near the resonance with the secular frequency ωsec\omega _{\text {sec}}ωsec​ ω sec only leads to a linear increase of the amplitude with excitation duration, parametric excitation near 2 ωsec2\, \omega _{\text {sec}}2ωsec​ 2 ω sec results in an exponential increase of the amplitude. This enables efficient removal of ions from the trap with modest excitation voltages and narrow bandwidth, therefore, substantially reducing the disturbance of ions with other charge-to-mass ratios. We numerically study and compare the mass selectivity of the two methods. In addition, we experimentally show that the barium isotopes with 136 and 137 nucleons can be removed from small ion crystals and ejected out of the trap while keeping 138Ba+^{138}\text {Ba}^{+}138Ba+ 138 Ba + ions Doppler cooled, corresponding to a mass selectivity of better than Δm/m=1/138\Delta m / m = 1/138Δm/m=1/138 Δ m / m = 1 / 138 . This method can be widely applied to ion trapping experiments without major modifications since it only requires modulating the potential of the ion trap.
We investigate numerically the structural dynamics of ion Coulomb crystals confined in a three-dimensional harmonic trap when influenced by an additional one-dimensional optically induced periodical potential. We demonstrate that transitions between thermally excited crystal structures, such as body-centered cubic and face-centered cubic, can be suppressed by a proper choice of the potential depth and periodicity. Furthermore, by varying the harmonic trap parameters and/or the optical potential in time, controlled transitions between crystal structures can be obtained with close to unit efficiency.
Superradiant lasers have emerged as a promising platform for optical frequency references due to their potential to achieve exceptionally narrow linewidths with reduced sensitivity to cavity noise. Trapped ion Coulomb crystals provide an attractive emitting medium due to their long coherence times, great environmental isolation and precise control over their motional dynamics. However, scaling trapped ion systems to the large ion numbers required for strong collective emission introduces new challenges, including crystal stability and position-dependent decoherence mechanisms. This work presents a numerical framework for modelling large Coulomb crystals confined within a linear Paul trap and assessing their suitability for superradiant lasing. A numerical simulation was developed to generate equilibrium crystal configurations, followed by a normal mode analysis to verify crystal’s dynamical stability and characterise the collective motional spectrum. The dependence of the crystal properties on the trapping parameters was examined, while the damping coefficient and integration timestep used in the numerical relaxation procedure were systematically optimised to obtain equilibrium configurations. The decoherence mechanisms expected to influence superradiant operation, including RF micromotion and electric quadrupole shifts, were also investigated as functions of ion number and trapping conditions. The simulations can produce accurate models of mechanically stable Coulomb crystals with up to 10,000 ions under appropriate relaxation conditions. They also show how the collective motional spectrum evolves across the trapping parameter space where they were also compared with the theoretical lasing threshold to assess the suitability of the trapping conditions for superradiant operation. Although the largest micromotion amplitudes increase with crystal size, a significant fraction of the ions remain confined close to the RF null, suggesting that large ion numbers may still be compatible with superradiant operation. The developed framework also provides a means of quantifying the quadrupole shift, indicating that the resulting frequency shifts are relatively small for the trapping parameters considered here, although further optimisation of the operating conditions is required to fully assess their influence on superradiant perfomance. Overall, the computational suite developed here establishes a versatile platform for studies of large Coulomb ion crystals and provides the tools to determine whether superradiant lasing thresholds can be reached with trapped ion crystals.
Coulomb crystallisation of laser-cooled ensembles of ions in harmonic traps has been studied experimentally with many spectacular results in recent years. It is well known that for sufficiently large numbers of ions the ground state of a Coulomb crystal in such a system has a body-centred cubic (bcc) structure. However, in experiments with crystals of up to a few 104 ions, structural transitions between bcc and, for example, face centred cubic (fee) or hexagonal close packed (hep) structures are observed. For constant ion densities, the lattice spacing of the planes of highest density differs only by about 3% between bcc and fee structures and simulations predict very small energy differences, thus thermal effects even at temperatures in the mK regime are sufficient to excite these transitions. Here we study numerically the possibility of controlling and switching the crystal structure with the help of periodic potentials generated by the dipole forces of standing-wave light fields.