Publications

Preserving quantum coherence with the increase of a system's size and complexity is a major challenge. Molecules, with their diverse sizes and complexities and many degrees of freedom, are an excellent platform for studying the transition from quantum to classical behavior. While most quantum-control studies of molecules focus on vibrations and rotations, we focus here on creating a quantum superposition between two nuclear-spin isomers of the same molecule. We present a scheme that exploits an avoided crossing in the spectrum to create strong coupling between two uncoupled nuclear-spin-isomer states, hence creating an isomeric qubit. We model our scheme using a four-level Hamiltonian and explore the coherent dynamics in the different regimes and parameters of our system. Our four-level model and approach can be applied to other systems with a similar energy-level structure.

Stray electric fields induce excess micromotion in ion traps, limiting experimental performance. We present a new micromotion-compensation technique that utilizes a dark ion in a bright-dark-bright linear ion crystal. Stray electric fields in the radial plane of the trap deform the crystal axially. We exploit the mode softening near the transition to the zig-zag configuration to increase our sensitivity dramatically. We corroborate our results with a modified ion-displacement compensation method using a single bright ion. Our modification allows us to compensate stray fields on the 2D radial plane from a 1D measurement of the ion position on the camera. Both methods require only a fixed imaging camera and continuous ion-fluorescence detection. As such, they can be readily implemented in virtually any ion-trapping experiment without additional hardware modifications.

The nature of dark matter (DM) and its interaction with the Standard Model (SM) is one of the biggest open questions in physics nowadays. The vast majority of theoretically motivated ultralight-DM (ULDM) models predict that ULDM couples dominantly to the SM strong/nuclear sector. This coupling leads to oscillations of nuclear parameters that are detectable by comparing clocks with different sensitivities to these nature's constants. Vibrational transitions of molecular clocks are more sensitive to a change in the nuclear parameters than the electronic transitions of atomic clocks. Here, we propose the iodine molecular ion, I2+, as a sensitive detector for such a class of ULDM models. The iodine's dense spectrum allows us to match its transition frequency to that of an optical atomic clock (Ca+) and perform correlation spectroscopy between the two clock species. With this technique, we project a few-orders-of-magnitude improvement over the most sensitive clock comparisons performed to date. We also briefly consider the robustness of the corresponding "Earth-bound"under modifications of the ZN-QCD axion model.

Frequency dissemination in phase-stabilized optical fiber networks for metrological frequency comparisons and precision measurements are promising candidates to overcome the limitations imposed by satellite techniques. However, in an architecture shared with telecommunication data traffic, network constraints restrict the availability of dedicated channels in the commonly-used C-band. Here, we demonstrate the dissemination of an SI-traceable ultrastable optical frequency in the L-band over a 456 km fiber network with ring topology, in which data traffic occupies the full C-band. We characterize the optical phase noise and evaluate a link instability of 4.7 × 10-16 at 1 s and 3.8 × 10-19 at 2000 s integration time, and a link accuracy of 2 × 10-18. We demonstrate the application of the disseminated frequency by establishing the SI-traceability of a laser in a remote laboratory. Finally, we show that our metrological frequency does not interfere with data traffic in the telecommunication channels. Our approach combines an unconventional spectral choice in the telecommunication L-band with established frequency-stabilization techniques, providing a novel, cost-effective solution for ultrastable frequency-comparison and dissemination, and may contribute to a foundation of a world-wide metrological network.

We review our recent experimental results on the non-destructive quantum-state detection and spectroscopy of single trapped molecules. At the heart of our scheme, a single atomic ion is used to probe the state of a single molecular ion without destroying the molecule or even perturbing its quantum state. This method opens up perspectives for new research directions in precision spectroscopy, for the development of new frequency standards, for tests of fundamental physical concepts and for the precise study of chemical reactions and molecular collisions with full control over the molecular quantum state.

The cross section of a given process fundamentally quantifies the probability for that process to occur. In the quantum regime of low energies, the cross section can greatly vary with collision energy due to quantum effects. Here, we report on a method to directly measure the atom-ion collisional cross section in the energy range of 0.2-12mK×kB, by shuttling ultracold atoms trapped in an optical-lattice across a radio-frequency trapped ion. Using this method, the average number of atom-ion collisions per experiment is below one, such that the energy resolution is not limited by the broad (power-law) steady-state atom-ion energy distribution. Here, we estimate that the energy resolution is below 200μK×kB, limited by drifts in the ion's excess micromotion compensation and can be reduced to the tens of μK×kB regime. This resolution is one order-of-magnitude better than previous experiments measuring cold atom-ion collisional cross-section energy dependence. We used our method to measure the energy dependence of the inelastic collision cross sections of a nonadiabatic electronic-excitation-exchange (EEE) and spin-orbit change (SOC) processes. We found that, in the measured energy range, the EEE and SOC cross sections statistically agree with the classical Langevin cross section. This method allows for measuring the cross sections of various inelastic processes and opens the possibility to search for atom-ion quantum signatures such as shape resonances.

Quantum-logic techniques used to manipulate quantum systems are now increasingly being applied to molecules. Previous experiments on single trapped diatomic species have enabled state detection with excellent fidelities and highly precise spectroscopic measurements. However, for complex molecules with a dense energy-level structure improved methods are necessary. Here, we demonstrate an enhanced quantum protocol for molecular state detection using state-dependent forces. Our approach is based on interfering a reference and a signal force applied to a single atomic and molecular ion. By changing the relative phase of the forces, we identify states embedded in a dense molecular energy-level structure and monitor state-to-state inelastic scattering processes. This method can also be used to exclude a large number of states in a single measurement when the initial state preparation is imperfect and information on the molecular properties is incomplete. While the present experiments focus on N2+, the method is general and is expected to be of particular benefit for polyatomic systems.

Recent advances in quantum technologies have enabled the precise control of single trapped molecules on the quantum level. Exploring the scope of these new technologies, we studied theoretically the implementation of qubits and clock transitions in the spin, rotational, and vibrational degrees of freedom of molecular nitrogen ions including the effects of magnetic fields. The relevant spectroscopic transitions span six orders of magnitude in frequency, illustrating the versatility of the molecular spectrum for encoding quantum information. We identified two types of magnetically insensitive qubits with very low ("stretched"-state qubits) or even zero ("magic" magnetic-field qubits) linear Zeeman shifts. The corresponding spectroscopic transitions are predicted to shift by as little as a few mHz for an amplitude of magnetic-field fluctuations on the order of a few mG, translating into Zeeman-limited coherence times of tens of minutes encoded in the rotations and vibrations of the molecule. We also found that the Q(0) line of the fundamental vibrational transition is magnetic-dipole allowed by interaction with the first excited electronic state of the molecule. The Q(0) transitions, which benefit from small systematic shifts for clock operation and is thus well suited for testing a possible variation in the proton-to-electron mass ratio, were so far not considered in single-photon spectra. Finally, we explored possibilities to coherently control the nuclear-spin configuration of N2+ through the magnetically enhanced mixing of nuclear-spin states.Theoretical study of the implementation of qubits and clock transitions in the spin, rotational, and vibrational degrees of freedom of molecular nitrogen ions including the effect of magnetic fields.

Ultracold atom-ion collisions are an emerging field of research that can ultimately lead to their precise quantum control. In collisions in which the ion is prepared in an excited state, previous studies showed that the dominant reaction pathway was charge exchange. Here, we explored the outcome products and the energy released from a single ultracold collision between a single Sr+88 ion and a single Rb87 atom prepared in excited metastable and ground electronic states, respectively, with control over their relative spins. We found that the ion's long-lived D5/2 and D3/2 states quench after roughly three collisions, acquiring immense kinetic energy in the process. By performing single-shot thermometry on the ion after the collision, we identified two dominant reaction pathways: electronic excitation exchange and spin-orbit change. In contrast to previous experiments, we observed no charge-exchange events. These processes are theoretically understood to occur through Landau-Zener avoided crossings leading to the observed reaction pathways. We also found that spin orientation has almost no effect on the reaction pathways, due to strong Coriolis-spin mixing. Our results provide a deeper understanding of ultracold atom-ion inelastic collisions and offer additional quantum control tools for the cold chemistry field.

Trapped atoms and ions, which are among the best-controlled quantum systems, find widespread applications in quantum science. For molecules, a similar degree of control is currently lacking owing to their complex energy-level structure. Quantum-logic protocols in which atomic ions serve as probes for molecular ions are a promising route for achieving this level of control, especially for homonuclear species that decouple from blackbody radiation. Here, a quantum-nondemolition protocol on single trapped N+2 molecules is demonstrated. The spin-rovibronic state of the molecule is detected with >99% fidelity, and a spectroscopic transition is measured without destroying the quantum state. This method lays the foundations for new approaches to molecular spectroscopy, state-to-state chemistry, and the implementation of molecular qubits.

Experiments in which ultra-cold neutral atoms and charged ions are overlapped, constitute a new field in atomic and molecular physics, with applications ranging from studying out-of-equilibrium dynamics to simulating quantum many-body systems. The holy grail of ion-neutral systems is reaching the quantum low-energy scattering regime, known as the s-wave scattering. However, in most atom-ion systems, there is a fundamental limit that prohibits reaching this regime. This limit arises from the time-dependent trapping potential of the ion, the Paul trap, which sets a lower collision energy limit which is higher than the s-wave energy. In this work, we studied both theoretically and experimentally, the way the Paul trap parameters affect the energy distribution of an ion that is immersed in a bath of ultra-cold atoms. Heating rates and energy distributions of the ion are calculated for various trap parameters by a molecular dynamics (MD) simulation that takes into account the attractive atom-ion potential. The deviation of the energy distribution from a thermal one is discussed. Using the MD simulation, the heating dynamics for different atom-ion combinations is also investigated. In addition, we performed measurements of the heating rates of a ground-state cooled Sr-88(+) ion that is immersed in an ultra-cold cloud of Rb-87 atoms, over a wide range of trap parameters, and compare our results to the MD simulation. Both the simulation and the experiment reveal no significant change in the heating for different parameters of the trap. However, in the experiment a slightly higher global heating is observed, relative to the simulation.

We report a precise determination of the lifetime of the (4p)2P3/2 state of 40Ca+, τP3/2=6.639(42)ns, using a combination of measurements of the induced light shift and scattering rate on a single trapped ion. Good agreement with the result of a recent high-level theoretical calculation, 6.69(6) ns [M. S. Safronova et al., Phys. Rev. A 83, 012503 (2011)], but a 6-σ discrepancy with the most precise previous experimental value, 6.924(19) ns [J. Jin et al., Phys. Rev. Lett. 70, 3213 (1993)], is found. To corroborate the consistency and accuracy of the new measurements, relativistically corrected ratios of reduced-dipole-matrix elements are used to directly compare our result with a recent result for the P1/2 state, yielding a good agreement. The application of the present method to precise determinations of radiative quantities of molecular systems is discussed.

We present theoretical and experimental progress towards a new approach for the precision spectroscopy, coherent manipulation and state-to-state chemistry of single isolated molecular ions in the gas phase. Our method uses a molecular beam for creating packets of rotationally cold neutrals from which a single molecule is state-selectively ionized and trapped inside a radiofrequency ion trap. In addition to the molecular ion, a single co-trapped atomic ion is used to cool the molecular external degrees of freedom to the ground state of the trap and to detect the molecular state using state-selective coherent motional excitation from a modulated optical-dipole force acting on the molecule. We present a detailed discussion and theoretical characterization of the present approach. We simulate the molecular signal experimentally using a single atomic ion, indicating that different rovibronic molecular states can be resolved and individually detected with our method. The present approach for the coherent control and non-destructive detection of the quantum state of a single molecular ion opens up new perspectives for precision spectroscopies relevant for, e.g., tests of fundamental physical theories and the development of new types of clocks based on molecular vibrational transitions. It will also enable the observation and control of chemical reactions of single particles on the quantum level. While focusing on N2+ as a prototypical example in the present work, our method is applicable to a wide range of diatomic and polyatomic molecules.

We present a joint experimental and theoretical study of spin dynamics of a single Sr-88(+) ion colliding with an ultracold cloud of Rb atoms in various hyperfine states. While spin exchange between the two species occurs after 9.1(6) Langevin collisions on average, spin relaxation of the Sr+ ion Zeeman qubit occurs after 48(7) Langevin collisions, which is significantly slower than in previously studied systems due to a small second-order spin-orbit coupling. Furthermore, a reduction of the endothermic spin-exchange rate is observed as the magnetic field is increased. Interestingly, we find that while the phases acquired when colliding on the spin singlet and triplet potentials vary largely between different partial waves, the singlet-triplet phase difference, which determines the spin-exchange cross section, remains locked to a single value over a wide range of partial waves, which leads to quantum interference effects.

Sympathetic cooling is the process of energy exchange between a system and a colder bath. We investigate this fundamental process in an atom-ion experiment where the system is composed of a single ion trapped in a radio-frequency Paul trap and prepared in a classical oscillatory motion with total energy of similar to 200 K, and the bath is an ultracold cloud of atoms at mu K temperature. We directly observe the sympathetic cooling dynamics with single-shot energy measurements during one to several collisions in two distinct regimes. In one, collisions predominantly cool the system with very efficient momentum transfer leading to cooling in only a few collisions. In the other, collisions can both cool and heat the system due to nonequilibrium dynamics in the presence of the ion trap's oscillating electric fields. While the bulk of our observations agree well with a molecular-dynamics simulation of hard-sphere (Langevin) collisions, a measurement of the scattering angle distribution reveals forward-scattering (glancing) collisions which are beyond the Langevin model. This work paves the way for further nonequilibrium and collision dynamics studies using the well-controlled atom-ion system.

The original version of this Article contained an error in the third sentence of the first paragraph of the 'Spin polarizing the Sr ⁺ ion with ultracold atoms' section of the Results, which incorrectly read 'The Langevin collision rate is 1.' The correct version adds 'kHz' after '1.' The fifth sentence of this same paragraph originally read as "Although ⁸⁷Rb has a I = 3/2 nuclear spin and a hyperfine-split ground-state manifold, ⁸⁸Sr has no nuclear spin and a Zeeman split two-fold ground state", which is incorrect. The correct version states " ⁸⁸Sr+" instead of " ⁸⁸Sr". The first sentence of the fourth paragraph of this same section originally read as "As the collisional energies are on the mK energy scale, spin exchange between Sr ⁺ and Rb prepared in the F = 1 state is allowed only as long as it does not require Rb to change its hyperfine state and climb the 330 m hyperfine energy gap", which is incorrect. The correct version states "330 mK" instead of "330 m".In the Discussion section, the text was originally incorrectly repeated.This has been corrected in both the PDF and HTML versions of the Article.

Experimental realizations of charged ions and neutral atoms in overlapping traps are gaining increasing interest due to their wide research application ranging from chemistry at the quantum level to quantum simulations of solid state systems. In this paper, we describe our experimental system in which we overlap a single ground-state cooled ion trapped in a linear Paul trap with a cloud of ultracold atoms such that both constituents are in the µK regime. Excess micromotion (EMM) currently limits atomion interaction energy to the mK energy scale and above. We demonstrate spectroscopy methods and compensation techniques which characterize and reduce the ions parasitic EMM energy to the µK regime even for ion crystals of several ions. We further give a substantial review on the non-equilibrium dynamics which governs atomion systems. The non-equilibrium dynamics is manifested by a power law distribution of the ions energy. We also give an overview on the coherent and non-coherent thermometry tools which can be used to characterize the ions energy distribution after single to many atomion collisions.

Quantum control of chemical reactions is an important goal in chemistry and physics. Ultracold chemical reactions are often controlled by preparing the reactants in specific quantum states. Here we demonstrate spin-controlled atomion inelastic (spin-exchange) processes and chemical (charge-exchange) reactions in an ultracold Rb-Sr+ mixture. The ions spin state is controlled by the atomic hyperfine spin state via spin-exchange collisions, which polarize the ions spin parallel to the atomic spin. We achieve ~90% spin polarization due to the absence of strong spin-relaxation channel. Charge-exchange collisions involving electron transfer are only allowed for (RbSr)+ colliding in the singlet manifold. Initializing the atoms in various spin states affects the overlap of the collision wave function with the singlet molecular manifold and therefore also the reaction rate. Our observations agree with theoretical predictions.

The control of the ultracold collisions between neutral atoms is an extensive and successful field of study. The tools developed allow for ultracold chemical reactions to be managed using magnetic fields, light fields and spin-state manipulation of the colliding particles among other methods. The control of chemical reactions in ultracold atom-ion collisions is a young and growing field of research. Recently, the collision energy and the ion electronic state were used to control atom-ion interactions. Here, we demonstrate spin-controlled atom-ion inelastic processes. In our experiment, both spin-exchange and charge-exchange reactions are controlled in an ultracold Rb-Sr⁺ mixture by the atomic spin state. We prepare a cloud of atoms in a single hyperfine spin-state. Spin-exchange collisions between atoms and ion subsequently polarize the ion spin. Electron transfer is only allowed for (RbSr)⁺ colliding in the singlet manifold. Initializing the atoms in various spin states affects the overlap of the collision wavefunction with the singlet molecular manifold and therefore also the reaction rate. We experimentally show that by preparing the atoms in different spin states one can vary the charge-exchange rate in agreement with theoretical predictions.

An ensemble of atoms in a steady state, whether or not in thermal equilibrium, has a well-defined energy distribution. Since the energy of single atoms within the ensemble cannot be individually measured, energy distributions are typically inferred from statistical averages. Here, we show how to measure the energy of a single atom in a single experimental realization (single shot). The energy distribution of the atom over many experimental realizations can thus be readily and directly obtained. We apply this method to a single ion trapped in a linear Paul trap for which the energy measurement in a single shot is applicable from 10 K×kB and above. Our energy measurement agrees within 5% to a different thermometry method which requires extensive averaging. Apart from the total energy, we also show that the motion of the ion in different trap modes can be distinguished. We believe that this method will have profound implications on single-particle chemistry and collision experiments.

We study the time-dependent fluorescence of an initially hot, multilevel, single atomic ion trapped in a radio-frequency Paul trap during Doppler cooling. We have developed an analytical model that describes the fluorescence dynamics during Doppler cooling which is used to extract the initial energy of the ion. While previous models of Doppler cooling thermometry were limited to atoms with a two-level energy structure and neglected the effect of the trap oscillating electric fields, our model applies to atoms with multilevel energy structure and takes into account the influence of micromotion on the cooling dynamics. This thermometry applies to any initial energy distribution. We experimentally test our model with an ion prepared in coherent, thermal, and Tsallis energy distributions.

Ultracold atom-ion mixtures are gaining increasing interest due to their potential applications in ultracold and state-controlled chemistry, quantum computing, and many-body physics. Here, we studied the dynamics of a single ground-state cooled ion during few, to many, Langevin (spiraling) collisions with ultracold atoms. We measured the ion's energy distribution and observed a clear deviation from the Maxwell-Boltzmann distribution, characterized by an exponential tail, to a power-law distribution best described by a Tsallis function. Unlike previous experiments, the energy scale of atom-ion interactions is not determined by either the atomic cloud temperature or the ion's trap residual excess-micromotion energy. Instead, it is determined by the force the atom exerts on the ion during a collision which is then amplified by the trap dynamics. This effect is intrinsic to ion Paul traps and sets the lower bound of atomion steady-state interaction energy in these systems. Despite the fact that our system is eventually driven out of the ultracold regime, we are capable of studying quantum effects by limiting the interaction to the first collision when the ion is initialized in the ground state of the trap.

According to quantum electrodynamics, the exchange of virtual photons in a system of identical quantum emitters causes a shift of its energy levels. Such shifts, known as cooperative Lamb shifts, have been studied mostly in the near-field regime. However, the resonant electromagnetic interaction persists also at large distances, providing coherent coupling between distant atoms. Here, we report a direct spectroscopic observation of the cooperative Lamb shift of an optical electric-dipole transition in an array of Sr+ ions suspended in a Paul trap at inter-ion separations much larger than the resonance wavelength. By controlling the precise positions of the ions, we studied the far-field resonant coupling in chains of up to eight ions, extending to a length of 40 mu m. This method provides a novel tool for experimental exploration of cooperative emission phenomena in extended mesoscopic atomic arrays.