S. A. Rangwala

Deviations from both the ideal linear Paul trap (LPT) geometry as well as the ideal quadrupole driving scheme introduce imperfections to ion trapping potentials. We investigate the effects of these imperfections in a LPT operated in a conventional dipole-drive configuration. We demonstrate the trapping of the Li$^+$ ions along the axial direction with zero and negative end-cap voltages. This occurs due to the modified axial $a-q$ space resulting from radial-to-axial coupling of the electric field. The dipole drive configuration lifts the degeneracy of the radial trapping potentials, resulting in unequal radial secular frequencies, and this is demonstrated experimentally. The combined effects of dipole drive and trap dimensions are summarized in a two-dimensional map that quantifies deviations from ideal behaviour. Based on this map, we propose a geometric modification that significantly reduces radial-to-axial coupling of the potential.

We present the design and fabrication of an endcap-type Paul trap. The trap is designed for studies with Ca$^{+}$ and Yb$^{+}$. The design, fabrication process, and characterization are presented in detail with a focus on trapping a single compensated ion at the rf node. A custom-built imaging system of $NA = 0.14$ and magnification $\approx 22 \times$ performs close to diffraction-limit and resolves multi-ion clusters. Controlled ion loading and characterization of the trap are performed using $^{40}$Ca$^{+}$. The experimentally determined quadrupole coefficient of the trap is $\approx 0.3$, which is very close to the design value. The relative frequency shift along the spectroscopy beam due to excess micromotion (EMM) is at the level of $3.5\times 10^{-18}$ for $^{40}$Ca$^{+}$. Applications of this trap encompass single-ion-based optical frequency standards, tests of fundamental physics, the study of mesoscopic Coulomb clusters, and the controlled interaction of a single ion with co-trapped atoms.

Laser-cooled ions confined in electromagnetic traps provide a unique, tunable mesoscopic system where the interplay of the trapping potential, nonlinear Coulomb interactions, and laser-ion scattering generates rich, collective dynamics. In this work, we engineer thermally activated switching between two oppositely oriented, square-pyramidal configurations of five laser-cooled ions in a Paul trap. For identical ions ($^{40}\mathrm{Ca}^{+}$), the inversions proceed via a \textit{Berry pseudo-rotation} mechanism with a low activation barrier, enabled by the permutation symmetry, in contrast to the \textit{umbrella inversion} observed in ammonia. The experimentally measured inversion rates, spanning two orders of magnitude, are accurately captured by the multidimensional Kramers-Langer theory, enabling thermometry of the Doppler-cooled ion cluster at $1.8 \pm 0.1$ mK. By substituting the apex ion with a heavier isotope ($^{44}\mathrm{Ca}^{+}$), we break the permutation symmetry and observe a suppression of thermally activated inversions. Numerical analysis reveals that this symmetry breaking closes the low-barrier channel, forcing the system to invert through a high-barrier \textit{turnstile rotation}. Thus, we demonstrate a structural analogue of molecular kinetic isotope effects, establishing trapped ions as a versatile platform to explore symmetry-controlled collective dynamics.

Interacting many-particle systems can self-organize into a rich variety of crystalline structures. While symmetry provides a powerful framework for predicting whether transitions between crystal states are continuous or discontinuous, collective lattice dynamics offer complementary insights into the microscopic mechanisms that drive these transitions. Trapped laser-cooled ions present a pristine and highly controllable few-body system for studying this interplay of symmetry and dynamics. Here, we use real-time fluorescence imaging while deforming the trap potential to observe a variety of structural transitions in three-dimensional (3D), unit-cell-like ion clusters. We identify a set of transitions signaled by parity-odd octupole order parameters, and probe their distinct dynamical signatures. Our observations reveal the softening of a collective Higgs-like mode indicating spontaneous symmetry-breaking, hysteresis resulting from a catastrophe where a metastable state vanishes abruptly, and stochastic switching between metastable states of differing symmetries. We also uncover a remarkable coincidence of symmetry-breaking and discontinuous transitions, analogous to a thermodynamic triple point. Our results establish 3D trapped-ion clusters as a versatile platform to engineer complex potential energy landscapes, opening new avenues for studies of reaction kinetics, geometric frustration, and related phenomena in mesoscopic platforms.

The formation of Li$_2^+$ and subsequently Li$^+$ ions, during the excitation of $^7$Li atoms to the $3S_{1/2}$ state in a $^7$Li magneto optical trap (MOT), is probed in an ion-atom hybrid trap. Associative ionization occurs during the collision of Li($2P_{3/2}$) and Li($3S_{1/2}$) ultracold atoms, creating Li$_2^+$ ions. Photodissociation of Li$_2^+$ by the MOT lasers is an active channel for the conversion of Li$_2^+$ to Li$^+$. A fraction of the Li$_2^+$ ions is long lived even in the presence of MOT light. Additionally, rapid formation of Li$^+$ from Li$_2^+$ in the absence of MOT light is observed. Resonant excitation of ultracold atoms, resulting in intricate molecular dynamics, reveals important processes in ultracold dilute gases.

We report the measurement of collision rate coefficient for collisions between ultracold Cs atoms and low energy Cs+ ions. The experiments are performed in a hybrid trap consisting of a magneto-optical trap (MOT) for Cs atoms and a Paul trap for Cs+ ions. The ion-atom collisions impart kinetic energy to the ultracold Cs atoms resulting in their escape from the shallow MOT and, therefore, in a reduction in the number of Cs atoms in the MOT. By monitoring, using fluorescence measurements, the Cs atom number and the MOT loading dynamics and then fitting the data to a rate equation model, the ion-atom collision rate is derived. The Cs-Cs+ collision rate coefficient $9.3(\pm0.4)(\pm1.2)(\pm3.5) \times 10^{-14}$ m$^{3}$s$^{-1}$, measured for an ion distribution with most probable collision energy of 95 meV ($\approx k_{B}.1100$ K), is in fair agreement with theoretical calculations. As an intermediate step, we also determine the photoionization cross section of Cs $6P_{3/2}$ atoms at 473 nm wavelength to be $2.28 (\pm 0.33) \times 10^{-21}$ m$^{2}$.

The two most widely used ion cooling methods are laser cooling and sympathetic cooling by elastic collisions (ECs). Here we demonstrate another method of cooling ions that is based on resonant charge exchange (RCE) between the trapped ion and the ultracold parent atom. Specifically, trapped Cs$^{+}$ ions are cooled by collisions with co-trapped, ultracold Cs atoms and, separately, by collisions with co-trapped, ultracold Rb atoms. We observe that the cooling of Cs$^{+}$ ions by Cs atoms is more efficient than cooling of Cs$^{+}$ ions by Rb atoms. This signals the presence of a cooling mechanism apart from the elastic ion-atom collision channel for the Cs-Cs$^{+}$ case, which is cooling by RCE. The efficiency of cooling by RCE is experimentally determined and the per-collision cooling is found to be two orders of magnitude higher than cooling by EC. The result provides the experimental basis for future studies on charge transport by electron hopping in atom-ion hybrid systems.

We present a technique, based on atoms coupled to an optical cavity, for non-destructive detection of trapped ions. We demonstrate the vacuum-Rabi splitting (VRS), arising due to the collective strong coupling of ultracold Rb atoms to a cavity, to change in presence of trapped Rb+ ions. The Rb+ ions are optically dark and the Rb atoms are prepared in a dark magneto-optical trap (MOT). The VRS is measured on an optically open transition of the initially dark Rb atoms. The measurement itself is fast, non-destructive and has sufficient fidelity to permit the measurement of atomic-state selective ion-atom collision rate. This demonstration illustrates a method based on atom-cavity coupling to measure two particle interactions generically and non-destructively.

The direct photodissociation of trapped $^{85}$Rb$_2^+$ (rubidium) molecular ions by the cooling light for the $^{85}$Rb magneto-optical trap (MOT) is studied, both experimentally and theoretically. Vibrationally excited Rb$_{2}^{+}$ ions are created by photoionization of Rb$_{2}$ molecules formed photoassociatively in the Rb MOT and are trapped in a modified spherical Paul trap. The decay rate of the trapped Rb$_{2}^{+}$ ion signal in the presence of the MOT cooling light is measured and agreement with our calculated rates for molecular ion photodissociation is observed. The photodissociation mechanism due to the MOT light is expected to be active and therefore universal for all homonuclear diatomic alkali metal molecular ions.

We experimentally demonstrate cooling of trapped ions by collisions with co-trapped, higher mass neutral atoms. It is shown that the lighter $^{39}$K$^{+}$ ions, created by ionizing $^{39}$K atoms in a magneto-optical trap (MOT), when trapped in an ion trap and subsequently allowed to cool by collisions with ultracold, heavier $^{85}$Rb atoms in a MOT, exhibit a longer trap lifetime than without the localized $^{85}$Rb MOT atoms. A similar cooling of trapped $^{85}$Rb$^{+}$ ions by ultracold $^{133}$Cs atoms in a MOT is also demonstrated in a different experimental configuration to validate this mechanism of ion cooling by localized and centered ultracold neutral atoms. Our results suggest that cooling of ions by localized cold atoms holds for any mass ratio, thereby enabling studies on a wider class of atom-ion systems irrespective of their masses.

We present an unique experimental arrangement which permits the simultaneous trapping and cooling of ions and neutral atoms, within a Fabry-Perot (FP) cavity. The versatility of this hybrid trap experiment enables a variety of studies with trapped mixtures. The motivations behind the production of such a hybrid trap system are explained, followed by details of how the experiment is put together. Several experiments that have been performed with this system are presented and some opportunities with this system are discussed. However the primary emphasis is focussed on the aspects that pertain to the trapped ions, in this hybrid system.

We measure the collision rate coefficient between laser cooled Rubidium (Rb) atoms in a magneto-optical trap (MOT) and optically dark Rb+ ions in an overlapping Paul trap. In such a mixture, the ions are created from the MOT atoms and allowed to accumulate in the ion trap, which results in a significant reduction in the number of steady state MOT atoms. A theoretical rate equation model is developed to describe the evolution of the MOT atom number, due to ionization and ion-atom collision, and derive an expression for the ion-atom collision rate coefficient. The loss of MOT atoms is studied systematically, by sequentially switching on the various mechanisms in the experiment. Combining the measurements with the model allows the direct determination of the ion-atom collision rate coefficient. Finally the scope of the experimental technique developed here is discussed.

A mixed system of cooled and trapped, ions and atoms, paves the way for ion assisted cold chemistry and novel many body studies. Due to the different individual trapping mechanisms, trapped atoms are significantly colder than trapped ions, therefore in the combined system, the strong binary ion$-$atom interaction results in heat flow from ions to atoms. Conversely, trapped ions can also get collisionally heated by the cold atoms, making the resulting equilibrium between ions and atoms intriguing. Here we experimentally demonstrate, Rubidium ions (Rb$^+$) cool in contact with magneto-optically trapped (MOT) Rb atoms, contrary to the general expectation of ion heating for equal ion and atom masses. The cooling mechanism is explained theoretically and substantiated with numerical simulations. The importance of resonant charge exchange (RCx) collisions, which allows swap cooling of ions with atoms, wherein a single glancing collision event brings a fast ion to rest, is discussed.

We report an experimental apparatus and technique which simultaneously traps ions and cold atoms with spatial overlap. Such an apparatus is motivated by the study of ion-atom processes at temperatures ranging from hot to ultra-cold. This area is a largely unexplored domain of physics with cold trapped atoms. In this article we discuss the general design considerations for combining these two traps and present our experimental setup. The ion trap and atom traps are characterized independently of each other. The simultaneous operation of both is then described and experimental signatures of the effect of the ions and cold-atoms on each other are presented. In conclusion the use of such an instrument for several problems in physics and chemistry is briefly discussed.

We propose an ion trap configuration such that individual traps can be stacked together in a three dimensional simple cubic arrangement. The isolated trap as well as the extended array of ion traps are characterized for different locations in the lattice, illustrating the robustness of the lattice of traps concept. Ease in the addressing of ions at each lattice site, individually or simultaneously, makes this system naturally suitable for a number of experiments. Application of this trap to precision spectroscopy, quantum information processing and the study of few particle interacting system are discussed.