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A very precise ratio The value of the ratio of the masses of the proton and the electron has a bearing on the values of other physical constants. This ratio is known to a very high precision. Patra et al. improved this precision even further by measuring particular frequencies in the rovibrational spectrum of the hydrogen deuteride molecular ion (HD + ) (see the Perspective by Hori). To reach this high precision, the researchers placed the HD + molecules in an ion trap and surrounded them by beryllium ions. The cold beryllium ions then helped cool the HD + molecules, making the HD + spectral lines narrow enough that the proton-electron mass ratio could be extracted by comparison with theoretical predictions. Science , this issue p. 1238 ; see also p. 1160

International audience; We present a parts-per-million test of quantum electrodynamics (QED) in the HD+ molecular hydrogen ion, improving on previous tests based on vibrational and rotational transitions by factors of 76 and 1.4, respectively. The test is performed following a unified statistical approach that also produces improved constraints on physics beyond the standard model. We furthermore show how individual constraints derived from the various degrees of freedom in HD+ and antiprotonic helium can be combined to enhance the sensitivity, thus ruling out “fifth forces” on the Ångstrom scale that are 1011 times weaker than the electromagnetic interaction.

Contradictory values for the masses of atomic nuclei have cast doubt on the reliability of these widely used quantities. A new mass measurement of the deuteron, the second-simplest atomic nucleus, clarifies the situation. The mass of the second-simplest atomic nucleus.

A trans-national optical fiber time transfer link, based on the White Rabbit Precision Time Protocol has between established between the UTC timescale realizations of the Belgian Metrology Service (SMD) in Brussels, Belgium and the ESTEC Radio Navigation Laboratory in Noordwijk, The Netherlands. The link consists of a single fiber covering a span of approximately 260 km. For verification, the optical fiber time transfer is compared with GPS-based common view time transfer. The results of the two techniques agree well within the combined uncertainties. The estimated uncertainty for the optical fiber time transfer is 0.2 ns.

Spectroscopy of hydrogen can be used for a search into physics beyond the Standard Model. Differences between the absorption spectra of H$_2$ as observed at high redshift and those measured in the laboratory can be interpreted in terms of possible variations of the proton-electron mass ratio. Investigation of some ten of such absorbers in the redshift range $z= 2.0-4.2$ yields a constraint of $|\Delta\mu/\mu|< 5 \times 10^{-6}$ at 3$\sigma$. Observation of H$_2$ from the photospheres of white dwarf stars inside our Galaxy delivers a constraint of similar magnitude on a dependence of $\mu$ on a gravitational potential $10^4$ times as strong as on the Earth's surface. Laser-based precision measurements of dissociation energies, vibrational splittings and rotational level energies in H$_2$ molecules and their deuterated isotopomers HD and D$_2$ produce values for the rovibrational binding energies fully consistent with quantum ab initio calculations including relativistic and quantum electrodynamical (QED) effects. Similarly, precision measurements of high-overtone vibrational transitions of HD$^+$ ions, captured in ion traps and sympathetically cooled to mK temperatures, also result in transition frequencies fully consistent with calculations including QED corrections. Precision measurements of inter-Rydberg transitions in H$_2$ can be extrapolated to yield accurate values for level splittings in the H$_2^+$-ion. These comprehensive results of laboratory precision measurements on neutral and ionic hydrogen molecules can be interpreted to set bounds on the existence of possible fifth forces and of higher dimensions, phenomena describing physics beyond the Standard Model., Comment: Special Review Lecture. Journal of Molecular Spectroscopy

International audience; We present a new derivation of the proton-electron mass ratio from the hydrogen molecular ion, HD$^+$. The derivation entails the adjustment of the mass ratio in highly precise theory so as to reproduce accurately measured ro-vibrational frequencies. This work is motivated by recent improvements of the theory, as well as the more accurate value of the electron mass in the recently published CODATA-14 set of fundamental constants, which justifies using it as input data in the adjustment, rather than the proton mass value as done in previous works. This leads to significantly different sensitivity coefficients and, consequently, a different value and larger uncertainty margin of the proton-electron mass ratio as obtained from HD$^+$.

Recently we reported a high precision optical frequency measurement of the (v,L):(0,2)->(8,3) vibrational overtone transition in trapped deuterated molecular hydrogen (HD+) ions at 10 mK temperature. Achieving a resolution of 0.85 parts-per-billion (p.p.b.) we found the experimental value ($��_0= 383,407,177.38(41)$ MHz) to be in agreement with the value from molecular theory ($��_\text{th}=383,407,177.150(15)$ MHz) within 0.6(1.1) p.p.b. [Biesheuvel et al., Nat. Commun. 7, 10385 (2016)]. This enabled an improved test of molecular theory (including QED), new constraints on the size of possible effects due to 'new physics', and the first determination of the proton-electron mass ratio from a molecule. Here, we provide the details of the experimental procedure, spectral analysis, and the assessment of systematic frequency shifts. Our analysis focuses in particular on deviations of the HD+ velocity distribution from thermal (Gaussian) distributions under the influence of collisions with fast ions produced during (laser-induced) chemical reactions, as such deviations turn out to significantly shift the hyperfine-less vibrational frequency as inferred from the saturated and Doppler-broadened spectrum, which contains partly unresolved hyperfine structure., 22 pages, 20 figures

We present a new measurement principle to determine the absolute time delay of a waveform from an optical reference plane to an electrical reference plane and vice versa. We demonstrate a method based on this principle with 2 ps uncertainty. This method can be used to perform accurate time delay determinations of optical transceivers used in fiber-optic time-dissemination equipment. As a result the time scales in optical and electrical domain can be related to each other with the same uncertainty. We expect this method will be a new breakthrough in high-accuracy time transfer and absolute calibration of time-transfer equipment.

Narrow ro-vibrational transitions in ultracold molecules are excellent candidates for frequency references in the near-IR to visible spectral domain and interesting systems for fundamental tests of physics, in particular for a satellite test of the gravitational redshift of clocks. We have performed laser spectroscopy of several ro-vibrational overtone transitions υ = 0 → υ = 4 in HD + ions at around 1.4 μm. 1+1 REMPD was used as a detection method, followed by measurement of the number of remaining molecules. The molecular ions were stored in a linear radiofrequency trap and cooled to millikelvin temperatures, by sympathetic cooling using laser-cooled Be + ions simultaneously stored in the same trap.

We report a method to determine propagation delays of optical 10 Gb/s data traveling through a 75 km long amplified fiber link with an uncertainty of 4 ps. The one-way propagation delay is determined by two-way exchange and cross correlation of short (< 1 ms) bursts of 10 Gb/s data, with a single-shot time resolution better than 2.5 ps. We thus achieve a novel optical communications link suited for both long-haul high-capacity data transfer and time transfer with picosecond-range uncertainty. This opens up the perspective of synchronized optical telecommunication networks allowing picosecond-range time distribution and millimeter-range positioning., This paper was published in Opt.Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-21-26-32643 Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law

Doppler broadening plays an important role in laser rovibrational spectroscopy of trapped deuterated molecular hydrogen ions (HD$^+$), even at the millikelvin temperatures achieved through sympathetic cooling by laser-cooled beryllium ions. Recently, Biesheuvel \textit{et al.} \cite{Biesheuvel2016} presented a theoretical lineshape model for such transitions which not only considers linestrengths and Doppler broadening, but also the finite sample size and population redistribution by blackbody radiation, which are important in view of the long storage and probe times achievable in ion traps. Here, we employ the rate equation model developed by Biesheuvel \textit{et al.} to theoretically study the Doppler-broadened hyperfine structure of the $(v,L):(0,3)\rightarrow(4,2)$ rovibrational transition in HD$^+$ at 1442~nm. We observe prominent yet hitherto unrecognized ghost features in the simulated spectrum, whose positions depend on the Doppler width, transition rates, and saturation levels of the hyperfine components addressed by the laser. We explain the origin and behavior of such features, and we provide a simple quantitative guideline to assess whether ghost features may appear. As such ghost features may be common to saturated Doppler-broadened spectra of rotational and vibrational transitions in trapped ions composed of partly overlapping lines, our work illustrates the necessity to use lineshape models that take into account all the relevant physics., 9 figures

The possible use of high-resolution rovibrational spectroscopy of the hydrogen molecular ions H + 2 and HD + for an independent determination of several fundamental constants is analyzed. While these molecules had been proposed for metrology of nuclear-to-electron mass ratios, we show that they are also sensitive to the radii of the proton and deuteron and to the Rydberg constant at the level of the current discrepancies colloquially known as the proton size puzzle. The required level of accuracy, in the 10 --12 range, can be reached both by experiments, using Doppler-free two-photon spectroscopy schemes, and by theoretical predictions. It is shown how the measurement of several well-chosen rovibrational transitions may shed new light on the proton-radius puzzle, provide an alternative accurate determination of the Rydberg constant, and yield new values of the proton-to-electron and deuteron-to-proton mass ratios with one order of magnitude higher precision.

We revisit the mα^{6}(m/M) order corrections to the hyperfine splitting in the H_{2}^{+} ion and find a hitherto unrecognized second-order relativistic contribution associated with the vibrational motion of the nuclei. Inclusion of this correction term produces theoretical predictions which are in excellent agreement with experimental data [K. B. Jefferts, Phys. Rev. Lett. 23, 1476 (1969)], thereby concluding a nearly 50-year-long theoretical quest to explain the experimental results within their 1-ppm error. The agreement between the theory and experiment corroborates the proton structural properties as derived from the hyperfine structure of atomic hydrogen. Our work furthermore indicates that, for future improvements, a full three-body evaluation of the mα^{6}(m/M) correction term will be mandatory.

The simplest molecules in nature, molecular hydrogen ions in the form of H2+ and HD+, provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD+ by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws., Molecular hydrogen ions, the simplest molecules in nature, constitute a benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, the authors report on a laser spectroscopic frequency measurement of a transition in HD+ in agreement with theory within 0.6 (1.1) part-per-billion.

We study the feasibility of nearly-degenerate two-photon rovibrational spectroscopy in ensembles of trapped, sympathetically cooled hydrogen molecular ions using a resonance-enhanced multiphoton dissociation (REMPD) scheme. Taking advantage of quasi-coincidences in the rovibrational spectrum, the excitation lasers are tuned close to an intermediate level to resonantly enhance two-photon absorption. Realistic simulations of the REMPD signal are obtained using a four-level model that takes into account saturation effects, ion trajectories, laser frequency noise and redistribution of population by blackbody radiation. We show that the use of counterpropagating laser beams enables optical excitation in an effective Lamb-Dicke regime. Sub-Doppler lines having widths in the 100 Hz range can be observed with good signal-to-noise ratio for an optimal choice of laser detunings. Our results indicate the feasibility of molecular spectroscopy at the $10^{-14}$ accuracy level for improved tests of molecular QED, a new determination of the proton-to-electron mass ratio, and studies of the time (in)dependence of the latter., Comment: 16 pages, 17 figures

Highly accurate results from frequency measurements on neutral hydrogen molecules H_2, HD and D_2 as well as the HD^+ ion can be interpreted in terms of constraints on possible fifth-force interactions. Where the hydrogen atom is a probe for yet unknown lepton-hadron interactions, and the helium atom is sensitive for lepton-lepton interactions, molecules open the domain to search for additional long-range hadron-hadron forces. First principles calculations in the framework of quantum electrodynamics have now advanced to the level that hydrogen molecules and hydrogen molecular ions have become calculable systems, making them a search-ground for fifth forces. Following a phenomenological treatment of unknown hadron-hadron interactions written in terms of a Yukawa potential of the form V_5(r)=\beta exp(-r/\lambda)/r current precision measurements on hydrogenic molecules yield a constraint \beta < 1 \times 10^{-7} eV\AA for long-range hadron-hadron interactions at typical force ranges commensurate with separations of a chemical bond, i.e. \lambda ~1 \AA and beyond., Comment: 7 pages, 3 figures, 1 table

We report the observation of the hitherto unde- tected v � = 8 ← v = 0 vibrational overtone in trapped HD + molecular ions, sympathetically cooled by laser-cooled Be + ions. The overtone is excited using 782 nm laser radiation, after which HD + ions in v = 8 are photodissociated by the 313 nm laser used for Be + cooling. The concomitant loss of HD + is detected by the method of secular excitation (Roth et al. in Phys. Rev. A. 74:040501(R), 2006). We furthermore present details of the experimental setup, and we show that results from spectroscopy of v � = 8 ← v = 0 overtones in combination with accurate ab initio calculations may yield a new value for the proton-electron mass ratio with an accu- racy of order 1 ppb.

We demonstrate direct frequency-comb (FC) spectroscopy of the dipole-forbidden 4s(2)S(1/2)-3d(2)D(5/2) transition in trapped (40)Ca(+) ions using an unamplified FC laser. The excitation is detected with nearly 100% efficiency using a shelving scheme in combination with single-ion imaging. The method demonstrated here has the potential to reach hertz-level accuracy, if a hertz-level linewidth FC is used in combination with confinement in the Lamb-Dicke regime.

A calculation of dynamic polarizabilities of rovibrational states with vibrational quantum number $v=0-7$ and rotational quantum number $J=0,1$ in the 1s$\sigma_g$ ground-state potential of HD$^+$ is presented. Polarizability contributions by transitions involving other 1s$\sigma_g$ rovibrational states are explicitly calculated, whereas contributions by electronic transitions are treated quasi-statically and partially derived from existing data [R.E. Moss and L. Valenzano, \textit{Molec. Phys.}, 2002, \textbf{100}, 1527]. Our model is valid for wavelengths $>4~\mu$m and is used to to assess level shifts due to the blackbody radiation (BBR) electric field encountered in experimental high-resolution laser spectroscopy of trapped HD$^+$ ions. Polarizabilities of 1s$\sigma_g$ rovibrational states obtained here agree with available existing accurate \textit{ab initio} results. It is shown that the Stark effect due to BBR is dynamic and cannot be treated quasi-statically, as is often done in the case of atomic ions. Furthermore it is pointed out that the dynamic Stark shifts have tensorial character and depend strongly on the polarization state of the electric field. Numerical results of BBR-induced Stark shifts are presented, showing that Lamb-Dicke spectroscopy of narrow vibrational optical lines ($\sim 10$ Hz natural linewidth) in HD$^+$ will become affected by BBR shifts only at the $10^{-16}$ level.

Laser control of atomic ions through dipole-forbidden transitions has provided a way of probing quantum mechanics. These transitions have now been observed in molecular ions, opening the door to a new generation of spectroscopy experiments.

We have constructed an optical clock with a fractional frequency inaccuracy of 8.6e-18, based on quantum logic spectroscopy of an Al+ ion. A simultaneously trapped Mg+ ion serves to sympathetically laser-cool the Al+ ion and detect its quantum state. The frequency of the 1S0->3P0 clock transition is compared to that of a previously constructed Al+ optical clock with a statistical measurement uncertainty of 7.0e-18. The two clocks exhibit a relative stability of 2.8e-15/ sqrt(tau), and a fractional frequency difference of -1.8e-17, consistent with the accuracy limit of the older clock., 4 pages, 2 tables, 3 figures

Repeated measurements of the frequency ratio of 199Hg + and 27A1+ singleatom optical clocks over the course of a year yield a constraint on the possible present-era temporal variation of the fine-structure constant a. The time variation of the measured ratio corresponds to a time variation in the fine structure constant of ά/α = (-1.6 ± 2.3) × 10-17/year, consistent with no change. The frequency ratio of these clocks was measured with a fractional uncertainty of 5.2 × 10-17. Stability simulations for optical clocks whose probe period is limited by 1/f-noise in the laser local oscillator provide an estimate of the optimal probe period, as well as a modified expression for the theoretical clock stability.

We describe the current status of high-precision ab initio calculations of the spectra of molecular hydrogen ions (H2+ and HD+) and of two experiments for vibrational spectroscopy. The perspectives for a comparison between theory and experiment at a level of 1 part in 109 are considered.

We have used laser spectroscopy to measure the rotational level distribution of trapped molecular $\mathrm{H}{\mathrm{D}}^{+}$ ions at translational temperatures in the millikelvin range. The $\mathrm{H}{\mathrm{D}}^{+}$ ions are loaded into an ion trap by electron-impact ionization, and sympathetically cooled using laser-cooled ${\mathrm{Be}}^{+}$ ions which are already stored in the trap. Under our experimental conditions, the internal (rotational) degrees of freedom turn out to be independent of the translational degrees of freedom, and an effective rotational temperature close to room temperature is found. The near absence of background-gas collisions allows the rotational temperature to be related directly to the temperature of the ambient blackbody radiation (BBR). This feature suggests the use of molecular ions for BBR thermometry, which may help to improve the accuracy of frequency standards based on trapped atomic ions. For the spectroscopic measurement of the rotational populations, we propose a nondestructive technique.

We report, for the first time, laser spectroscopy of the {sup 1}S{sub 0}{yields}{sup 3}P{sub 0} clock transition in {sup 27}Al{sup +}. A single aluminum ion and a single beryllium ion are simultaneously confined in a linear Paul trap, coupled by their mutual Coulomb repulsion. This coupling allows the beryllium ion to sympathetically cool the aluminum ion and also enables transfer of the aluminum's electronic state to the beryllium's hyperfine state, which can be measured with high fidelity. These techniques are applied to measure the clock transition frequency {nu}=1 121 015 393 207 851(6) Hz. They are also used to measure the lifetime of the metastable clock state {tau}=20.6{+-}1.4 s, the ground state {sup 1}S{sub 0} g factor g{sub S}=-0.000 792 48(14), and the excited state {sup 3}P{sub 0} g factor g{sub P}=-0.001 976 86(21), in units of the Bohr magneton.

By measurement of the frequency of a vibrational overtone transition in the molecular hydrogen ion ${\mathrm{HD}}^{+}$, we demonstrate the first optical spectroscopy of trapped molecular ions with submegahertz accuracy. We use a diode laser, locked to a stable frequency comb, to perform resonance-enhanced multiphoton dissociation spectroscopy on sympathetically cooled ${\mathrm{HD}}^{+}$ ions at 50 mK. The achieved 2-ppb relative accuracy is a factor of 150 higher than previous results for ${\mathrm{HD}}^{+}$, and the measured transition frequency agrees well with recent high-accuracy ab initio calculations, which include high-order quantum electrodynamic effects. We also show that our method bears potential for achieving considerably higher accuracy and may, if combined with slightly improved theoretical calculations, lead to a new and improved determination of the electron-proton mass ratio.

We report a high-resolution spectroscopic study of molecular ions at millikelvin temperatures. We measured several rovibrational infrared transitions in HD{sup +} molecular ions, stored in a radio-frequency trap and sympathetically cooled to {approx_equal}20 mK by laser-cooled Be{sup +} ions. We observed hyperfine splitting of the lines, in good agreement with theoretical predictions. The transitions were detected by monitoring the decrease in ion number after selective photodissociation of HD{sup +} ions in the upper vibrational state. The method described here is expected to be generally applicable.

Recently developed techniques for quantum computation using trapped ions allow precise coherent control of the internal and external states of single atoms. Here we report how these techniques can be employed to perform precision spectroscopy of atomic and molecular ions that lack accessible transitions for laser cooling and detection. Furthermore, we discuss how quantum logic can be used to laser‐cool molecules to near their rotational and vibrational ground state by avoiding detrimental spontaneous emission of photons from the molecule.

We have studied a cloud of cold metastable helium (He*) atoms interacting with near-resonant light at 1083 nm and 389 nm. The 1083 nm light allows for efficient loading of a large magneto-optical trap (MOT) and the 389 nm light is subsequently used to increase the density and reduce the temperature of the He* cloud during a brief compression stage. Cold collisions in the cloud yield ions and fast metastables which are monitored separately using calibrated microchannel plate (MCP) detectors. We thus measure absolute production rates of ions and fast metastables escaping from the MOT during the various stages of the experiment. We observe that 389 nm optical collisions, apart from Penning ionization, produce a relatively large flux of fast metastables, which we relate to the short-range behaviour of the molecular potentials involved. Furthermore, by rapidly switching between 389 nm and 1083 nm the ratio between the respective two-body loss rate constants is determined. Using these values, together with the observed time dependence of the cloud size, the temporal behaviour of the absolute ion production rate during the compression stage is well reproduced.

We describe a powerful scheme which combines laser cooling on two transitions of metastable helium to obtain a high phase-space density. By running a sequence of a large $1083\phantom{\rule{0.3em}{0ex}}\text{nm}$ magneto-optical trap (MOT) and a compressed $389\phantom{\rule{0.3em}{0ex}}\text{nm}$ MOT, a density increase of more than one order of magnitude is achieved within $5\phantom{\rule{0.3em}{0ex}}\text{ms}$. After compression, $8\ifmmode\times\else\texttimes\fi{}{10}^{8}$ atoms at a central density of $5\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}3}$ remain, while the temperature of the cloud has been reduced from $1\phantom{\rule{0.3em}{0ex}}\text{mK}$ to $0.4\phantom{\rule{0.3em}{0ex}}\text{mK}$. The resulting phase-space density $(4.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6})$ is more than one order of magnitude higher than what we achieved by $1083\phantom{\rule{0.3em}{0ex}}\text{nm}$ laser cooling only.

We have constructed a magneto-optical trap (MOT) for metastable triplet helium atoms utilizing the 2 3S1 -> 3 3P2 line at 389 nm as the trapping and cooling transition. The far-red-detuned MOT (detuning Delta = -41 MHz) typically contains few times 10^7 atoms at a relatively high (~10^9 cm^-3) density, which is a consequence of the large momentum transfer per photon at 389 nm and a small two-body loss rate coefficient (2 * 10^-10 cm^3/s < beta < 1.0 * 10^-9 cm^3/s). The two-body loss rate is more than five times smaller than in a MOT on the commonly used 2 3S1 -> 2 3P2 line at 1083 nm. Furthermore, we measure a temperature of 0.46(1) mK, a factor 2.5 lower as compared to the 1083 nm case. Decreasing the detuning to Delta= -9 MHz results in a cloud temperature as low as 0.25(1) mK, at small number of trapped atoms. The 389 nm MOT exhibits small losses due to two-photon ionization, which have been investigated as well., 11 pages

The basic requirements for quantum computing and quantum simulation (single‐ and multi‐qubit gates, long memory times, etc.) have been demonstrated in separate experiments on trapped ions. Construction of a large‐scale information processor will require synthesis of these elements and implementation of high‐fidelity operations on a very large number of qubits. This is still well in the future. NIST and other groups are addressing part of the scaling issue by trying to fabricate multi‐zone arrays of traps that would allow highly‐parallel and scalable processing. In the near term, some simple quantum processing protocols are being used to aid in quantum metrology, such as in atomic clocks. As the number of qubits increases, Schrodinger’s cat paradox and the measurement problem in quantum mechanics become more apparent; with luck, trapped ion systems might be able to shed light on these fundamental issues.