Imaging-Assisted Single-Photon Doppler-Free Laser Spectroscopy and the Ionization Energy of Metastable Triplet Helium.

Skimmed supersonic beams provide intense, cold, collision-free samples of atoms and molecules and are one of the most widely used tools in atomic and molecular laser spectroscopy. High-resolution optical spectra are typically recorded in a perpendicular arrangement of laser and supersonic beams to minimize Doppler broadening. Typical Doppler widths are nevertheless limited to tens of MHz by the residual transverse-velocity distribution in the gas-expansion cones. We present an imaging method to overcome this limitation that exploits the correlation between the positions of the atoms and molecules in the supersonic expansion and their transverse velocities, and thus their Doppler shifts. With the example of spectra of (1s)(np) ^{3}P_{0-2}←(1s)(2s) ^{3}S_{1} transitions to high Rydberg states of metastable triplet He, we demonstrate the suppression of the residual Doppler broadening and a reduction of the full linewidths at half maximum to only about 1 MHz in the UV. Using a retroreflection arrangement for the laser beam and a cross-correlation method, we determine Doppler-free spectra without any signal loss from the selection, by imaging, of atoms within ultranarrow transverse-velocity classes. As an illustration, we determine the ionization energy of triplet metastable He and confirm the significant discrepancy between recent experimental [G. Clausen et al., Phys. Rev. Lett. 127, 093001 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.093001] and high-level theoretical [V. Patkós et al., Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] values of this quantity.

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.

Multipole-moment effects in ion-molecule reactions at low temperatures: part I - ion-dipole enhancement of the rate coefficients of the He+ + NH3 and He+ + ND3 reactions at collisional energies Ecoll/kB near 0 K.

The energy dependence of the rates of the reactions between He+ and ammonia (NY3, Y = {H,D}), forming NY2+, Y and He as well as NY+, Y2 and He, and the corresponding product branching ratios have been measured at low collision energies Ecoll between 0 and kB·40 K using a recently developed merged-beam technique [Allmendinger et al., ChemPhysChem, 2016, 17, 3596]. To avoid heating of the ions by stray electric fields, the reactions are observed within the large orbit of a highly excited Rydberg electron. A beam of He Rydberg atoms was merged with a supersonic beam of ammonia using a curved surface-electrode Rydberg-Stark deflector, which is also used for adjusting the final velocity of the He Rydberg atoms, and thus the collision energy. A collision-energy resolution of about 200 mK was reached at the lowest Ecoll values. The reaction rate coefficients exhibit a sharp increase at collision energies below ∼kB·5 K and pronounced deviations from Langevin-capture behaviour. The experimental results are interpreted in terms of an adiabatic capture model describing the rotational-state-dependent orientation of the ammonia molecules by the electric field of the He+ atom. The model faithfully describes the experimental observations and enables the identification of three classes of |JKMp〉 rotational states of the ammonia molecules showing different low-energy capture behaviour: (A) high-field-seeking states with |KM| ≥ 1 correlating to the lower component of the umbrella-motion tunnelling doublet at low fields. These states undergo a negative linear Stark shift, which leads to strongly enhanced rate coefficients; (B) high-field-seeking states subject to a quadratic Stark shift at low fields and which exhibit only weak rate enhancements; and (C) low-field-seeking states with |KM| ≥ 1. These states exhibit a positive Stark shift at low fields, which completely suppresses the reactions at low collision energies. Marked differences in the low-energy reactivity of NH3 and ND3-the rate enhancements in ND3 are more pronounced than in NH3-are quantitatively explained by the model. They result from the reduced magnitudes of the tunnelling splitting and rotational intervals in ND3 and the different occupations of the rotational levels in the supersonic beam caused by the different nuclear-spin statistical weights. Thermal capture rate constants are derived from the model for the temperature range between 0 and 10 K relevant for astrochemistry. Comparison of the calculated thermal capture rate coefficients with the absolute reaction rates measured above 27 K by Marquette et al. (Chem. Phys. Lett., 1985, 122, 431) suggests that only 40% of the close collisions are reactive.

Ionization Energy of the Metastable 2

In a recent breakthrough in first-principles calculations of two-electron systems, Patkós, Yerokhin, and Pachucki [Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] have performed the first complete calculation of the Lamb shift of the helium 2 ^{3}S_{1} and 2 ^{3}P_{J} triplet states up to the term in α^{7}m. Whereas their theoretical result of the frequency of the 2 ^{3}P←2 ^{3}S transition perfectly agrees with the experimental value, a more than 10σ discrepancy was identified for the 3 ^{3}D←2 ^{3}S and 3 ^{3}D←2 ^{3}P transitions, which hinders the determination of the He^{2+} charge radius from atomic spectroscopy. We present here a new measurement of the ionization energy of the 2 ^{1}S_{0} state of He [960 332 040.491(32) MHz] which we use in combination with the 2 ^{3}S_{1}←2 ^{1}S_{0} interval measured by Rengelink et al. [Nat. Phys. 14, 1132 (2018).NPAHAX1745-247310.1038/s41567-018-0242-5] and the 2 ^{3}P←2 ^{3}S_{1} interval measured by Zheng et al. [Phys. Rev. Lett. 119, 263002 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.263002] and Cancio Pastor et al. [Phys. Rev. Lett. 92, 023001 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.023001] to derive experimental ionization energies of the 2 ^{3}S_{1} state [1152 842 742.640(32) MHz] and the 2 ^{3}P centroid energy [876 106 247.025(39) MHz]. These values reveal disagreements with the α^{7}m Lamb shift prediction by 6.5σ and 10σ, respectively, and support the suggestion by Patkós et al. of an unknown theoretical contribution to the Lamb shifts of the 2 ^{3}S and 2 ^{3}P states of He.

The H2+ + HD reaction at low collision energies: H3+/H2D+ branching ratio and product-kinetic-energy distributions.

The fully state-selected reactions between H2+ molecules in the X+ 2Σg+(v+ = 0, N+ = 0) state and HD molecules in the X 1Σg+(v = 0, J = 0) state forming H3+ + D and H2D+ + H have been studied at collision energies Ecoll between 0 and kB·30 K with a resolution of about 75 mK at the lowest energies. H2 molecules in a supersonic beam were prepared in Rydberg-Stark states with principal quantum number n = 27 and merged with a supersonic beam of ground-state HD molecules using a curved surface-electrode Rydberg-Stark decelerator and deflector. The reaction between H2+ and HD was studied within the orbit of the Rydberg electron to avoid heating of the ions by stray electric fields. The reaction was observed for well-defined and adjustable time intervals, called reaction-observation windows, between two electric-field pulses. The first pulse swept all ions away from the reaction volume and its falling edge defined the beginning of the reaction-observation window. The second pulse extracted the product ions toward a charged-particle detector located at the end of a time-of-flight tube and its rising edge defined the end of the reaction-observation window. Monitoring and analysing the time-of-flight distributions of the H3+ and H2D+ products in dependence of the duration of the reaction-observation window enabled us to obtain information on the kinetic-energy distribution of the product ions and determine branching ratios of the H3+ + D and H2D+ + H reaction channels. The mean product-kinetic-energy release is 0.46(5) eV, representing 27(3)% of the available energy, and the H3+ + D product branching ratio is 0.225(20). The relative reaction rates correspond closely to Langevin capture rates down to the lowest energies probed experimentally (≈kB·50 mK).

Precision Measurements in Few-Electron Molecules: The Ionization Energy of Metastable

Molecular helium represents a benchmark system for testing ab initio calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the a ^{3}Σ_{u}^{+} state of He_{2}, corresponding to the energy interval between the a ^{3}Σ_{u}^{+} (v^{''}=0, N^{''}=1) state of He_{2} and the X^{+} ^{2}Σ_{u}^{+} (v^{+}=0, N^{+}=1) state of He_{2}^{+}, and of the lowest rotational interval of He_{2}^{+}. These measurements rely on the excitation of metastable He_{2} molecules to high Rydberg states using frequency-comb-calibrated continuous-wave UV radiation in a counterpropagating laser-beam setup. The observed Rydberg states were extrapolated to their series limit using multichannel quantum-defect theory. The ionization energy of He_{2} (a ^{3}Σ_{u}^{+}) and the lowest rotational interval of He_{2}^{+} (X^{+} ^{2}Σ_{u}^{+}) are 34 301.207 002(23)±0.000 037_{syst} cm^{-1} and 70.937 589(23)±0.000 060_{syst} cm^{-1}, respectively.

Ion-Molecule Reactions below 1 K: Strong Enhancement of the Reaction Rate of the Ion-Dipole Reaction He

The reaction between He^{+} and CH_{3}F forming predominantly CH_{2}^{+} and CHF^{+} has been studied at collision energies E_{coll} between 0 and k_{B}·10 K in a merged-beam apparatus. To avoid heating of the ions by stray electric fields, the reaction was observed within the orbit of a highly excited Rydberg electron. Supersonic beams of CH_{3}F and He(n) Rydberg atoms with principal quantum number n=30 and 35 were merged and their relative velocity tuned using a Rydberg-Stark decelerator and deflector, allowing an energy resolution of 150 mK. A strong enhancement of the reaction rate was observed below E_{coll}/k_{B}=1 K. The experimental results are interpreted with an adiabatic capture model that accounts for the state-dependent orientation of the polar CH_{3}F molecules by the Stark effect as they approach the He^{+} ion. The enhancement of the reaction rate at low collision energies is primarily attributed to para-CH_{3}F molecules in the J=1, KM=1 high-field-seeking states, which represent about 8% of the population at the 6 K rotational temperature of the supersonic beam.

New Method to Study Ion-Molecule Reactions at Low Temperatures and Application to the H2++H2→H3++H Reaction.

Studies of ion-molecule reactions at low temperatures are difficult because stray electric fields in the reaction volume affect the kinetic energy of charged reaction partners. We describe a new experimental approach to study ion-molecule reactions at low temperatures and present, as example, a measurement of the H2++H2→H3++H reaction with the H2+ ion prepared in a single rovibrational state at collision energies in the range Ecol /kB =5-60 K. To reach such low-collision energies, we use a merged-beam approach and observe the reaction within the orbit of a Rydberg electron, which shields the ions from stray fields. The first beam is a supersonic beam of pure ground-state H2 molecules and the second is a supersonic beam of H2 molecules excited to Rydberg-Stark states of principal quantum number n selected in the range 20-40. Initially, the two beams propagate along axes separated by an angle of 10°. To merge the two beams, the Rydberg molecules in the latter beam are deflected using a surface-electrode Rydberg-Stark deflector. The collision energies of the merged beams are determined by measuring the velocity distributions of the two beams and they are adjusted by changing the temperature of the pulsed valve used to generate the ground-state H2 beam and by adapting the electric-potential functions applied to the electrodes of the deflector. The collision energy is varied down to below Ecol /kB =10 K, that is, below Ecol ≈1 meV, with an energy resolution of 100 µeV. We demonstrate that the Rydberg electron acts as a spectator and does not affect the cross sections, which are found to closely follow a classical Langevin-capture model in the collision energy range investigated. Because all neutral atoms and molecules can be excited to Rydberg states, this method of studying ion-molecule reactions is applicable to other reactions involving singly charged cations.

Precision Spectroscopy in Cold Molecules: The Lowest Rotational Interval of He_{2}

Multistage Zeeman deceleration was used to generate a slow, dense beam of translationally cold He_{2} molecules in the metastable a ^{3}Σ_{u}^{+} state. Precision measurements of the Rydberg spectrum of these molecules at high values of the principal quantum number n have been carried out. The spin-rotational state selectivity of the Zeeman-deceleration process was exploited to reduce the spectral congestion, minimize residual Doppler shifts, resolve the Rydberg series around n=200 and assign their fine structure. The ionization energy of metastable He_{2} and the lowest rotational interval of the X^{+} ^{2}Σ_{u}^{+} (ν^{+}=0) ground state of ^{4}He_{2}^{+} have been determined with unprecedented precision and accuracy by Rydberg-series extrapolation. Comparison with ab initio predictions of the rotational energy level structure of ^{4}He_{2}^{+} [W.-C. Tung, M. Pavanello, and L. Adamowicz, J. Chem. Phys. 136, 104309 (2012)] enabled us to quantify the magnitude of relativistic and quantum-electrodynamics contributions to the fundamental rotational interval of He_{2}^{+}.

Multistage Zeeman deceleration of metastable neon.

A supersonic beam of metastable neon atoms has been decelerated by exploiting the interaction between the magnetic moment of the atoms and time-dependent inhomogeneous magnetic fields in a multistage Zeeman decelerator. Using 91 deceleration solenoids, the atoms were decelerated from an initial velocity of 580 m/s to final velocities as low as 105 m/s, corresponding to a removal of more than 95% of their initial kinetic energy. The phase-space distribution of the cold, decelerated atoms was characterized by time-of-flight and imaging measurements, from which a temperature of 10 mK was obtained in the moving frame of the decelerated sample. In combination with particle-trajectory simulations, these measurements allowed the phase-space acceptance of the decelerator to be quantified. The degree of isotope separation that can be achieved by multistage Zeeman deceleration was also studied by performing experiments with pulse sequences generated for (20)Ne and (22)Ne.

Direct EPR detection of transient and continuous wave signals at 2.5 GHz.

Direct detection of free induction decays and electron spin echoes, and the recording of echo-detected EPR spectra and electron spin echo envelope modulation patterns at a microwave frequency of 2.5 GHz is demonstrated. This corresponds to the measurement of the transverse magnetization in the laboratory frame, rather than in the rotating frame as usually done by down-converting the signal (homodyne detection). An oscilloscope with a 6-GHz analog bandwidth, a sampling rate of 20 GigaSamples per second, and a trigger frequency of 5 GHz for the edge trigger and 750 MHz for the advanced trigger, is used in these experiments. For signal averaging a 3-GHz microwave clock divider has been developed to synchronize the oscilloscope with the frequency of the EPR signal. Moreover, direct detection of continuous wave EPR signals at 2.5 GHz is described.