Ion Coulomb Crystals Research Articles

Trapping and Sympathetic Cooling of Conformationally Selected Molecular Ions.

We report the generation, trapping, and sympathetic cooling of individual conformers of molecular ions with the example of cis- and trans- meta-aminostyrene. Following conformationally selective photoionization, the incorporation of the conformers into a Coulomb crystal of laser-cooled calcium ions was confirmed by fluorescence imaging, mass spectrometry, and molecular dynamics simulations. We deduce the molecules to be stable in the trap environment for more than ten minutes. The present results pave the way for the spectroscopy and controlled chemistry of distinct ionic conformers in traps.

Heat transport in an ion Coulomb crystal with a topological defect

Heat transport in an ion Coulomb crystal with a topological defect

Dynamics Simulation and Light-Sheet Tomography of Multispecies Ion Coulomb Crystals

Ions in coulomb crystals are sufficiently cooled and well isolated from the environment, which makes them an ideal platform for the research of high precision spectroscopy. Ion coulomb crystals (ICC) constituted by multispecies ions can provide important information about the nucleus, such as isotope shifts and hyperfine splittings. In order to extract the spectroscopic data with a high precision, the status of ICC needs to be properly evaluated. In this paper, we utilize the molecular dynamics simulation software LAMMPS and the (py) Lion package to simulate the dynamics of ICC with multispecies ions. To make a better comparison between the simulation results and experimental observations, we propose an ICC tomography scheme with the fluorescence light-sheet microscopy. This work can be applied to make better estimation on dynamic parameters of both laser cooled and sympathetically cooled ions.

Improved bounds on Lorentz violation from composite pulse Ramsey spectroscopy in a trapped ion

In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the 2F7/2 manifold of an Yb+ ion, extending the coherence time from 200 μs to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the 2F7/2 state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10−21 level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.

Number-resolved detection of dark ions in Coulomb crystals

While it is straightforward to count laser-cooled trapped ions by fluorescence imaging, detecting the number of dark ions embedded and sympathetically cooled in a mixed ion crystal is more challenging. We demonstrate a method to track the number of dark ions in real time with single-particle sensitivity. This is achieved by observing discrete steps in the amount of fluorescence emitted from the coolant ions while exciting secular motional resonances of dark ions. By counting the number of fluorescence steps, we can identify the number of dark ions without calibration and without relying on any physical model of the motional excitation. We demonstrate the scheme by detecting H$_2^+$ and H$_3^+$ ions embedded in a Be$^+$ ion Coulomb crystal in a linear radio frequency trap. Our method allows observing the generation and destruction of individual ions simultaneously for different types of ions. Besides high-resolution spectroscopy of dark ions, another application is the detection of chemical reactions in real time with single-particle sensitivity. This is demonstrated in this work.

Dynamics of vortex defect formation in two-dimensional Coulomb crystals

We study the non-equilibrium dynamics of two dimensional planar ion Coulomb crystals undergoing a structural buckling transition to a three plane configuration, driven by a reduction of the transverse confining frequency. This phase transition can be theoretically modeled using a mapping to a two dimensional Ginzburg-Landau theory with complex order parameter field. We demonstrate that finite rate quenches result in creation of stable topological vortices, which are localized point regions around which the phase of the order parameter field winds a multiple of 2{\pi}. The density of the defects as a function of quench rate is investigated using molecular dynamics simulations and its scaling is shown to be consistent with Kibble-Zurek theory of defect formation. Following the quench, the annihilation of vortex and anti-vortex pairs results in the relaxation of defect density that follows a diffusive scaling with a logarithmic correction. This work highlights the potential for investigating complex non-equilibrium statistical physics of topological defects in an experimentally accessible ion trap setting.

Quantum nanofriction in trapped ion chains with a topological defect

Trapped ion systems constitute a well controllable scenario for the study and emulation of nanofriction, and in particular of Frenkel-Kontorova-like models. This is in particular the case when a topological defect is created in a zigzag ion Coulomb crystal, which results in an Aubry transition from free sliding to pinned phase as a function of the trap aspect ratio. We explore the quantum effects of the Aubry transition by means of an effective simplified model, in which the defect is treated like a single quantum particle that experiences an effective Peierls-Nabarro potential and a position-dependent mass. We demonstrate the relevance of quantum tunneling in a finite range of aspect ratios close the critical point, showing that the quantum effects may be observed in the kink dynamics for sufficiently low temperatures. Finally, we discuss the requirements to reveal quantum effects at the Aubry transition in future experiments on trapped ions.

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

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.

Tunable transverse spin–motion coupling for quantum information processing

Laser-controlled entanglement between atomic qubits (‘spins’) and collective motion in trapped ion Coulomb crystals requires conditional momentum transfer from the laser. Since the spin-dependent force is derived from a spatial gradient in the spin–light interaction, this force is typically longitudinal—parallel and proportional to the average laser k-vector (or two beams’ k-vector difference), which constrains both the direction and relative magnitude of the accessible spin–motion coupling. Here, we show how momentum can also be transferred perpendicular to a single laser beam due to the gradient in its transverse profile. By controlling the transverse gradient at the position of the ion through beam shaping, the relative strength of the sidebands and carrier can be tuned to optimize the desired interaction and suppress undesired, off-resonant effects that can degrade gate fidelity. We also discuss how this effect may already be playing an unappreciated role in recent experiments.

A study of metastable ion Coulomb crystals in a polychromatic all-optical trap

Metastable ion Coulomb crystal (ICC) in the polychromatic optical superlattice (OSL) created by so-called rectified gradient forces is studied. Our analysis is based on the numerical solution of the nonlinear stochastic differential equations taking into account the trapping and dissipative forces, their quantum fluctuations, and Coulomb repulsion of ions. The key question is how long will this metastable highly ordered crystalline structure persist. The critical parameter determining the ICC destruction times td is the OSL period L (at fixed intensity values of the optical fields). Our simulations demonstrate that td of the ICC, consisting of several tens of mercury ions, experiences giant changes (by four orders of magnitude) at relatively slight variations of the optical superlattice period L in the range from 0.35 to 0.70 mm. We have shown that the dependence td (L) can be approximated by the Arrhenius-like equation with an effective activation energy which is nonlinearly dependent on the OSL period L. These results explain the ultrahigh sensitivity td (L) to the OSL period L and show how to adjust L to ensure all-optical confinement of ICC in the OSL from a fraction of a second to one and half minutes.

Controlling the potential landscape and normal modes of ion Coulomb crystals by a standing-wave optical potential

Light-induced control of ions within small Coulomb crystals is investigated. By intense intracavity optical standing wave fields, subwavelength localization of individual ions is achieved for one-, two-, and three-dimensional crystals. Based on these findings, we illustrate numerically how the application of such optical potentials can be used to tailor the normal mode spectra and patterns of multi-dimensional Coulomb crystals. The results represent, among others, important steps towards controlling the crystalline structure of Coulomb crystals, investigating heat transfer processes at the quantum limit and quantum simulations of many-body systems.

Probing Time Dilation in Coulomb Crystals in a High-Precision Ion Trap

Trapped-ion optical clocks are capable of achieving systematic fractional frequency uncertainties of $10^{-18}$ and possibly below. However, the stability of current ion clocks is fundamentally limited by the weak signal of single-ion interrogation. We present an operational, scalable platform for extending clock spectroscopy to arrays of Coulomb crystals consisting of several tens of ions, while allowing systematic shifts as low as $10^{-19}$. Using a newly developed technique, we observe 3D excess micromotion amplitudes inside a Coulomb crystal with atomic spatial resolution and sub-nanometer amplitude uncertainties. We show that in ion Coulomb crystals of 400$\mu$m and 2mm length, time dilation shifts of In${}^+$ ions due to micromotion can be close to $1\times10^{-19}$ and below $10^{-18}$, respectively. In previous ion traps, excess micromotion would have dominated the uncertainty budget for spectroscopy of even a few ions. By minimizing its contribution and providing a means to quantify it, this work opens up the path to precision spectroscopy in many-body ion systems, enabling entanglement-enhanced ion clocks and providing a well-controlled, strongly coupled quantum system.

Nanofriction and motion of topological defects in self-organized ion Coulomb crystals

We study nanofriction in an ion Coulomb crystal under the presence of a topological defect. We have previously observed signatures of the pinning to sliding transition i.e. the symmetry breaking at the critical point and the existence of a vibrational soft mode. Here we discuss how they depend on the position of the topological defect and how external potentials, such as anharmonic trapping potentials or differential light pressure, can be used to change the defect position. The resulting forces tend to break the intrinsic crystal symmetry, thereby reducing mode softening near the transition. We show that the topological defect mode is sensitive to differential forces at the 10−24 N level. We find that the local structure and position of the topological defect is essential for the presence of the soft mode and illustrate how the defect changes its properties, when it moves through the crystal.

Spectroscopy of Molecular Ions in Coulomb Crystals.

In this Perspective, we examine the use of laser-cooled atomic ions and sympathetically cooled molecular ions in Coulomb crystals for molecular spectroscopy. Coulomb crystals are well-isolated environments that provide localization and long storage times for sensitive measurements of weak signals and cold temperatures for precise spectroscopy. Coulomb crystals of molecular and atomic ions enable the detection of single-photon molecular ion transitions at a range of wavelengths by a change in atomic ion fluorescence at visible wavelengths. We give an overview of the state of the art from action spectroscopy to quantum logic spectroscopy for a wide range of molecular transitions from rotational sublevels separated by 10-7 cm-1 to rovibronic transitions at 25 000 cm-1. We emphasize how this system allows for unparalleled control of the molecular ion state for precision spectroscopy with applications in astrochemistry and fundamental physics. We conclude with an outlook of the use of this control in cold molecular ion reactions.

Properties of magnetized Coulomb crystals of ions with polarizable electron background

We have studied phonon and thermodynamic properties of a body-centered cubic (bcc) Coulomb crystal of ions with weakly polarized electron background in a uniform magnetic field B. At B = 0, the difference between phonon moments calculated using the Thomas-Fermi (TF) and random phase approximations is always less than 1% and for description of phonon properties of a crystal, TF formalism was used. This formalism was successfully applied to investigate thermodynamic properties of magnetized Coulomb crystals. It was shown that the influence of the polarization of the electron background is significant only at κTFa>0.1 and T≪Tp(1+h2)−1/2, where κTF is the Thomas-Fermi wavenumber, a is the ion sphere radius, Tp≡ℏωp is the ion plasma temperature, h≡ωB/ωp, ωB is the ion cyclotron frequency, and ωp is the ion plasma frequency.

Transient dynamics in cavity electromagnetically induced transparency with ion Coulomb crystals

We experimentally investigate the transient dynamics of an optical cavity field interacting with large ion Coulomb crystals in a situation of electromagnetically induced transparency (EIT). EIT is achieved by injecting a probe field at the single photon level and a more intense control field with opposite circular polarization into the same mode of an optical cavity to couple Zeeman substates of a metastable level in ions. The EIT interaction dynamics are investigated both in the frequency-domain – by measuring the probe field steady state reflectivity spectrum – and in the time-domain – by measuring the progressive buildup of transparency. The experimental results are observed to be in excellent agreement with theoretical predictions taking into account the inhomogeneity of the control field in the interaction volume, and confirm the high degree of control on light-matter interaction that can be achieved with ion Coulomb crystals in optical cavities.

Phonons in a magnetized Coulomb crystal of ions with polarizable electron background

We have studied phonon modes of a body-centered cubic (bcc) Coulomb crystal of ions in the presence of a uniform magnetic field B taking into account the polarizability of the electron background (electron screening) described by the Thomas-Fermi formalism. For k≫κTF (k and κTF are the phonon wavevector and Thomas-Fermi wavenumber, respectively), electron polarizability is not important. At k≪κTF, the electron response results in a pronounced effect. One of the three available modes is acoustic. For orthogonal propagation (k⊥B), its frequency Ω is independent of B and κTF. For k∥B, Ω∝1/κTF and is independent of B. Another mode is quadratic. Its frequency is ∝1/(BκTF) for orthogonal propagation and ∝1/B and independent of κTF for the parallel case. The third mode is optic with Ω≈ωB (ωB is the ion cyclotron frequency). A general expression is derived for the dynamic matrix of a Coulomb crystal with a polarizable background and more than one ion in the primitive cell. It is employed for a study of a magnetized hexagonal close-packed Coulomb crystal. We have also presented an analysis of phonon polarization vectors in a magnetized bcc crystal with or without screening. The results obtained can be used for realistic calculations of electron-phonon scattering rates and electron thermal and electrical conductivities in neutron star crusts.

Sideband cooling of small ion Coulomb crystals in a Penning trap

We have recently demonstrated the laser cooling of a single ion to the motional ground state in a Penning trap using the resolved-sideband cooling technique on the electric quadrupole transition S D. Here we report on the extension of this technique to small ion Coulomb crystals made of two or three ions. Efficient cooling of the axial motion is achieved outside the Lamb-Dicke regime on a two-ion string along the magnetic field axis as well as on two- and three-ion planar crystals. Complex sideband cooling sequences are required in order to cool both axial degrees of freedom simultaneously. We measure a mean excitation after cooling of for the centre of mass (COM) mode and for the breathing mode of the two-ion string with corresponding heating rates of 11(2) and at a trap frequency of 162 kHz. The occupation of the ground state of the axial modes () is above 75% for the two-ion planar crystal and the associated heating rates 0.8(5) at a trap frequency of 355 kHz.

Sympathetic cooling in two-species ion crystals in a Penning trap

We have studied the formation and properties of two-species ion Coulomb crystals in the Penning trap of the SpecTrap experiment. These crystals have been formed by injection of admixture ions from an external source into a previously confined and laser-cooled cloud of magnesium ions. This kind of study, performed over a range of the admixture ions’ charge-to-mass ratios, indicates the conditions for their sympathetic cooling and the formation of two-species ion crystals. This mechanism allows efficient cooling of the admixed species such as highly charged ions which do not feature suitable laser-cooling transitions, and thus make them accessible to high-resolution laser spectroscopy.

Nonequilibrium quantum thermodynamics in Coulomb crystals

We present an in-depth study of the non-equilibrium statistics of the irreversible work produced during sudden quenches in proximity to the structural linear-zigzag transition of ion Coulomb crystals in 1+1 dimensions. By employing both an analytical approach based on a harmonic expansion and numerical simulations, we show the divergence of the average irreversible work in proximity to the transition. We show that the non-analytic behaviour of the work fluctuations can be characterized in terms of the critical exponents of the quantum Ising chain. Due to the technological advancements in trapped ion experiments, our results can be readily verified.