SI-traceable frequency dissemination at 1572.06 nm in a stabilized fiber network with ring topology.

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.

Non-destructive State Detection and Spectroscopy of Single Molecules.

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.

From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N2.

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.

Identification of molecular quantum states using phase-sensitive forces.

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 N[Formula: see text], the method is general and is expected to be of particular benefit for polyatomic systems.

Quantum-nondemolition state detection and spectroscopy of single trapped molecules.

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 [Formula: see text] 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.

State-selective coherent motional excitation as a new approach for the manipulation, spectroscopy and state-to-state chemistry of single molecular ions.

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.

Phase Locking between Different Partial Waves in Atom-Ion Spin-Exchange Collisions.

We present a joint experimental and theoretical study of spin dynamics of a single ^{88}Sr^{+} 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.

Direct Observation of Atom-Ion Nonequilibrium Sympathetic Cooling.

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 ∼200 K, and the bath is an ultracold cloud of atoms at µK 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.

Publisher Correction: Spin-controlled atom-ion chemistry.

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.

Spin-controlled atom-ion chemistry.

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 atom-ion inelastic (spin-exchange) processes and chemical (charge-exchange) reactions in an ultracold Rb-Sr+ mixture. The ion's spin state is controlled by the atomic hyperfine spin state via spin-exchange collisions, which polarize the ion's 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.

Dynamics of a Ground-State Cooled Ion Colliding with Ultracold Atoms.

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 atom-ion 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.