Atomic and Molecular Spectroscopy Group

Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps.

We study an excited atom-polar molecular ion chemical reaction (Ca$^*$ + BaCl$^+$) at low temperature by utilizing a hybrid atom-ion trapping system. The reaction rate and product branching fractions are measured and compared to model calculations as a function of both atomic quantum state and collision energy. At the lowest collision energy we find that the chemical dynamics dramatically differ from capture theory predictions and are primarily dictated by the radiative lifetime of the atomic quantum state instead of the underlying excited-state interaction potential. We provide a simple rule for calculating at what temperature this regime, where the collision complex lifetime is longer than the radiative lifetime of the quantum state, is reached. This effect, which greatly suppresses the reactivity of short-lived excited states, provides a means for directly probing reaction range. It also naturally suppresses unwanted chemical reactions in hybrid trapping experiments, allowing longer molecular ion coherence and interrogation times.

We present measurements of the charge-exchange reaction rate between neutral sodium (Na) and ionized calcium (\ce{Ca+}) in a hybrid atom-ion trap, which is comprised of a Na magneto-optical trap concentric with a linear Paul trap. Once the Na and \ce{Ca+} are co-trapped, the reaction rate is measured by continuously quenching the reaction product \ce{Na+} from the ion trap, and then destructively measuring the decay of the remaining ion population. The reactants' electronic state and temperature are experimentally controlled, allowing us to determine the four individual reaction-rates between $\text{Na}[\text{S~or~P}]$ and $\text{Ca}^+[\text{S~or~D}]$ at different collision energies. With the exception of the largest reaction-rate channel ($\text{Na}[\text{S}]+\text{Ca}^+[\text{D}]$), our rates agree with classical Langevin rate limit. We have also found evidence of reactant collision-energy thresholds associated with two of the four entrance-channels.

The Dicke model, which describes the coupling of an ensemble of spins to a harmonic oscillator, is known for its superradiant phase transition, which can both be observed in the ground state in a purely Hamiltonian setting, as well as in the steady state of an open-system Dicke model with dissipation. We demonstrate that, in addition, the dissipative Dicke model can undergo a second phase transition to a nonstationary phase, characterized by unlimited heating of the harmonic oscillator. Identifying the mechanism of the phase transition and deriving the scaling of the critical coupling with the system size we conclude that the novel phase transition can be understood as a cooperative breakdown of the oscillator blockade which otherwise prevents higher excitation of the system. We discuss an implementation with trapped ions and investigate the role of cooling, by which the breakdown can be suppressed.

We present model-independent measurements of the excited-state population of atoms in a sodium (Na) magneto-optical trap (MOT) using a hybrid ion-neutral trap composed of a MOT and a linear Paul trap (LPT). We photoionize excited Na atoms trapped in the MOT and use two independent methods to measure the resulting ions: directly by trapping them in our LPT, and indirectly by monitoring changes in MOT fluorescence. By measuring the ionization rate via these two independent methods, we have enough information to directly determine the population of MOT atoms in the excited-state. The resulting measurement reveals that there is a range of trapping-laser intensities where the excited-state population of atoms in our MOT follows the standard two-level model intensity-dependence. However, an experimentally determined effective saturation intensity must be used instead of the theoretically predicted value from the two-level model. We measured the effective saturation intensity to be $I_\mathrm{se}=22.9(3)\:\textrm{mW}/\textrm{cm}^2$ for the type-I Na MOT and $I_\mathrm{se}=48.9(7)\;\textrm{mW}/\textrm{cm}^2$ for the type-II Na MOT, approximately 1.7 and 3.6 times the theoretical estimate, respectively. Lastly, at large trapping-laser intensities, our experiment reveals a clear departure from the two-level model at a critical intensity that we believe is due to a state-mixing effect, whose critical intensity can be determined by a simple power broadening model.

Hypermetallic alkaline earth (M) oxides of formula MOM have been studied under plasma conditions that preclude insight into their formation mechanism. We present here the application of emerging techniques in ultracold physics to the synthesis of a mixed hypermetallic oxide, BaOCa$^+$. These methods, augmented by high-level electronic structure calculations, permit detailed investigation of the bonding and structure, as well as the mechanism of its formation via the barrierless reaction of Ca $(^3P_J)$ with BaOCH$_{3}^+$. Further investigations of the reaction kinetics as a function of collision energy over the range 0.005 K to 30 K and of individual Ca fine-structure levels compare favorably with calculations based on long-range capture theory.

We present experimental measurements of the steady-state ion number in a linear Paul trap (LPT) as a function of the ion-loading rate. These measurements, taken with (a) constant Paul trap stability parameter $q$, (b) constant radio-frequency (rf) amplitude, or (c) constant rf frequency, show nonlinear behavior. At the loading rates achieved in this experiment, a plot of the steady-state ion number as a function of loading rate has two regions: a monotonic rise (region I) followed by a plateau (region II). Also described are simulations and analytical theory which match the experimental results. Region I is caused by rf heating and is fundamentally due to the time dependence of the rf Paul-trap forces. We show that the time-independent pseudopotential, frequently used in the analytical investigation of trapping experiments, cannot explain region I, but explains the plateau in region II and can be used to predict the steady-state ion number in that region. An important feature of our experimental LPT is the existence of a radial cut-off $\hat R_{\rm cut}$ that limits the ion capacity of our LPT and features prominently in the analytical and numerical analysis of our LPT-loading results. We explain the dynamical origin of $\hat R_{\rm cut}$ and relate it to the chaos border of the fractal of non-escaping trajectories in our LPT. We also present an improved model of LPT ion-loading as a function of time.

We investigate the prospects of controlling charge-exchange in ultracold collisions of heteroisotopic combinations of atoms and ions of the same element. The treatment, readily applicable to alkali or alkanine-earth metals, is illustrated in the process $^9$Be$^{+}$ + $^{10}$Be $\leftrightarrow$ $^{9}$Be + $^{10}$Be$^{+}$, which exhibits favorable electronic, nuclear, and hyperfine structure. Feshbach resonances are obtained from quantum scattering calculations in a standard coupled-channel formalism with non-BO terms originating from the nuclear kinetic operator. Near a narrow resonance predicted at 322 G, we find the charge-exchange rate coefficient to rise from practically zero to values larger than $10^{-12}$ cm$^3$/s. Our results suggest controllable charge-exchange reactions between different isotopes of suitable atom-ion pairs with potential applications to quantum systems engineered to study charge diffusion in trapped cold atom-ion mixtures and emulate many-body physics.

We present a theoretical analysis of optical pathways for formation of cold Ca($^1$S)Na$^+$($^1$S) molecular ions via an intermediate state. The formation schemes are based on ab initio potential energy curves and transition dipole moments calculated using effective-core-potential methods of quantum chemistry. In the proposed approach, starting from a mixture of cold trapped Ca$^+$ ions immersed into an ultracold gas of Na atoms, (NaCa)$^+$ molecular ions are photoassociated in the excited E$^{1}Σ^+$ electronic state and allowed to spontaneously decay either to the ground electronic state or an intermediate state from which the population is transferred to the ground state via an additional optical excitation. By analyzing all possible pathways, we find that the efficiency of a two-photon scheme, via either B$^{1}Σ^+$ or C$^{1}Σ^+$ potential, is sufficient to produce significant quantities of ground state (NaCa)$^+$ molecular ions. A single-step process results in lower formation rates that would require either a high density sample or a very intense photoassociation laser to be viable.

We predict that the steady-state ion number $N_s$ for radio-frequency (rf) traps, loaded at a rate of $λ$ particles per unit time, shows universal non-monotonic behavior as a function of loading rate $λ$. The shape of $N_s(λ)$, characterized by four dynamical regions, is universal in the sense that it is predicted to manifest itself in all rf traps independently of the details of their construction. For $λ\ll$ 1 particles / rf cycle (Region I), as expected, $N_s(λ)$ increases monotonically with $λ$. However, contrary to intuition, at intermediate $λ\sim 1$ particles / rf cycle (Region II), $N_s(λ)$ reaches a maximum, followed by a minimum of $N_s(λ)$ (Region III). For $λ\gg 1$ particles / rf cycle (Region IV), $N_s(λ)$ again rises monotonically. In Region IV numerical simulations, analytical calculations, and experiments show $N_s(λ)\sim λ^{2/3}$. We confirm this prediction experimentally with MOT-loaded Na$^+$ ions stored in a hybrid ion-neutral trap.

We present measurements of the total elastic and resonant charge-exchange ion-atom collision rate coefficient $k_\mathrm{ia}$ of cold sodium (\ce{Na}) with optically-dark low energy \ce{Na+} ions in a hybrid ion-neutral trap. To determine $k_\mathrm{ia}$, we measured the trap loading and loss from both a \ce{Na} magneto-optical trap (MOT) and a linear radio frequency quadrupole Paul trap. We found the total rate coefficient to be $7.4 \pm 1.9 \times 10^{-8}$ cm$^3$/s for the type I \ce{Na} MOT immersed within an $\approx 140$ K ion cloud and $1.10 \pm 0.25 \times 10^{-7}$ cm$^3$/s for the type II \ce{Na} MOT within an $\approx 1070$ K ion cloud. Our measurements show excellent agreement with previously reported theoretical fully quantal \textit{ab initio} calculations. In the process of determining the total rate coefficient, we demonstrate that a MOT can be used to probe an optically dark ion cloud's spatial distribution within a hybrid trap.

We study the XY model with infinite-range interactions (Lipkin-Meshkov-Glick model) in the presence of dissipation from spontaneous decay. We show that independent and collective decay lead to qualitatively different phase transitions of the steady state, even though the phase boundary is the same. Independent decay leads to a second-order phase transition to a ferromagnet, while collective decay leads to a first-order transition to a time-dependent oscillatory phase. Then we show that the addition of a drive leads to infinite spin squeezing for collective decay in the thermodynamic limit. Our results can be experimentally seen in trapped-ion and cavity-QED experiments.

Linear Paul r.f. ion traps (LPT) are used in many experimental studies such as mass spectrometry, atom-ion collisions and ion-molecule reactions. Mass selective resonant quenching (MSRQ) is implemented in LPT either to identify a charged particle's mass or to remove unwanted ions from a controlled experimental environment. In the latter case, MSRQ can introduce undesired heating to co-trapped ions of different mass, whose secular motion is off resonance with the quenching ac field, which we call off-resonance energy absorption (OREA). We present simulations and experimental evidence that show that the OREA increases exponentially with the number of ions loaded into the trap and with the amplitude of the off-resonance external ac field.

A hybrid ion-neutral trap provides an ideal system to study collisional dynamics between ions and neutrals. This system provides a general cooling method that can be applied to optically inaccessible species and can also potentially cool internal degrees of freedom. The long range polarization potentials ($V\propto-α/r^4$) between ions and neutrals result in large scattering cross sections at cold temperatures, making the hybrid trap a favorable system for efficient sympathetic cooling of ions by collisions with neutral atoms. We present experimental evidence of sympathetic cooling in a hybrid trap of \ce{Na+} ions, which are closed shell and therefore do not have a laser induced atomic transition, by equal mass cold Na atoms in a magneto-optical trap (MOT).

Long range polarization forces between ions and neutral atoms result in large elastic scattering cross sections, e.g., 10^6 a.u. for Na+ on Na or Ca+ on Na at cold and ultracold temperatures. This suggests that a hybrid ion-neutral trap should offer a general means for significant sympathetic cooling of atomic or molecular ions. We present SIMION 7.0 simulation results concerning the advantages and limitations of sympathetic cooling within a hybrid trap apparatus, consisting of a linear rf Paul trap concentric with a Na magneto-optical trap (MOT). This paper explores the impact of various heating mechanisms on the hybrid system and how parameters related to the MOT, Paul trap, number of ions, and ion species affect the efficiency of the sympathetic cooling.

New experiments were proposed recently to investigate the regime of cold atomic and molecular ion-atom collision processes in a special hybrid neutral-atom--ion trap under high vacuum conditions. The collisional cooling of laser pre-cooled Ca$^+$ ions by ultracold Na atoms is being studied. Modeling this process requires knowledge of the radiative lifetime of the excited singlet A$^1Σ^+$ state of the (NaCa)$^+$ molecular system. We calculate the rate coefficient for radiative charge transfer using a semiclassical approach. The dipole radial matrix elements between the ground and the excited states, and the potential curves were calculated using Complete Active Space Self-Consistent field and Möller-Plesset second order perturbation theory (CASSCF/MP2) with an extended Gaussian basis, 6-311+G(3df). The semiclassical charge transfer rate coefficient was averaged over a thermal Maxwellian distribution. In addition we also present elastic collision cross sections and the spin-exchange cross section. The rate coefficient for charge transfer was found to be $2.3\times 10^{-16}$ cm$^3$/sec, while those for the elastic and spin-exchange cross sections were found to be several orders of magnitude higher ($1.1\times 10^{-8}$ cm$^3$/sec and $2.3\times 10^{-9}$ cm$^3$/sec, respectively). This confirms our assumption that the milli-Kelvin regime of collisional cooling of calcium ions by sodium atoms is favorable with the respect to low loss of calcium ions due to the charge transfer.