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arXiv2019

The Lamb shift of the $1s$ state in hydrogen: two-loop and three-loop contributions

We consider the $1s$ Lamb shift in hydrogen and helium ions, a quantity, required for an accurate determination of the Rydberg constant and the proton charge radius by means of hydrogen spectroscopy, as well as for precision tests of the bound-state QED. The dominant QED contribution to the uncertainty originates from $α^8m$ external-field contributions (i.e., the contributions at the non-recoil limit). We discuss the two- and three-loop cases and in particular, we revisit calculations of the coefficients $B_{61}, B_{60}, C_{50}$ in standard notation. We have found a missing logarithmic contribution of order $α^2(Zα)^6m$. We have also obtained leading pure self-energy logarithmic contributions of order $α^2(Zα)^8m$ and $α^2(Zα)^9m$ and estimated the subleading terms of order $α^2(Zα)^7m$, $α^2(Zα)^8m$, and $α^2(Zα)^9m$. The determination of those higher-order contributions enabled us to improve the overall accuracy of the evaluation of the two-loop self-energy of the electron. We investigated the asymptotic behavior of the integrand related to the next-to-leading three-loop term (order $α^3(Zα)^5m$, coefficient $C_{50}$ in standard notation) and applied it to approximate integration over the loop momentum. Our result for contributions to the $1s$ Lamb shift for the total three loop next-to-leading term is $(-3.3\pm10.5)(α^3/π^3)(Zα)^5m$. Altogether, we have completed the evaluation of the logarithmic contributions to the $1s$ Lamb shift of order $α^8m$ and reduced the overall $α^8m$ uncertainty by approximately a factor of three for H, D, and He$^+$ as compared with the most recent CODATA compilation.

physics.atom-ph↗

arXiv2019

One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures

In this review we provide a rigorous and self-contained presentation of one-body reduced density-matrix (1RDM) functional theory. We do so for the case of a finite basis set, where density-functional theory (DFT) implicitly becomes a 1RDM functional theory. To avoid non-uniqueness issues we consider the case of fermionic and bosonic systems at elevated temperature and variable particle number, i.e, a grand-canonical ensemble. For the fermionic case the Fock space is finite-dimensional due to the Pauli principle and we can provide a rigorous 1RDM functional theory relatively straightforwardly. For the bosonic case, where arbitrarily many particles can occupy a single state, the Fock space is infinite-dimensional and mathematical subtleties (not every hermitian Hamiltonian is self-adjoint, expectation values can become infinite, and not every self-adjoint Hamiltonian has a Gibbs state) make it necessary to impose restrictions on the allowed Hamiltonians and external non-local potentials. For simple conditions on the interaction of the bosons a rigorous 1RDM functional theory can be established, where we exploit the fact that due to the finite one-particle space all 1RDMs are finite-dimensional. We also discuss the problems arising from 1RDM functional theory as well as DFT formulated for an infinite-dimensional one-particle space.

math-ph↗

arXiv2018

High resolution spectroscopy on Te_2: new lines for reference

Ro-vibrational spectra of different electronic states of molecules are often used as absolute wavelength or frequency standards. These standards are also used to mitigate any slow drift of laser frequency during an experiment. In precision experiment, the two most commonly used molecular standards are iodine and tellurium, both are homo-nuclear diatomic molecules. The former is mostly used as standard for the long wavelength ($600-900$~nm) region, while the tellurium spectrum is widely used in short wavelength ($400-550$~nm) including near ultra violet. A comprehensive data on tellurium spectra can be obtained from the tellurium atlas~\cite{Te2atlas:80}. However near the $455~$nm range where a number of important atomic resonance line, the atlas provides no significant data. We have performed high resolution modulation transfer spectroscopy~(MTS) on tellurium molecule in a hot cell in the region close to $455~$nm wavelength thereby obtained more than $100$ new spectral lines which were not observed before. The resolution of each of these peaks is about few MHz, making them suitable for laser frequency locking.

physics.atom-ph↗

arXiv2010

Energetic driving force for preferential binding of self-interstitial atoms to Fe grain boundaries over vacancies

Molecular dynamics simulations of 50 Fe grain boundaries were used to understand their interaction with vacancies and self-interstitial atoms at all atomic positions within 20 Angstroms of the boundary, which is important for designing radiation-resistant polycrystalline materials. Site-to-site variation within the boundary of both vacancy and self-interstitial formation energies is substantial, with the majority of sites having lower formation energies than in the bulk. Comparing the vacancy and self-interstitial atom binding energies for each site shows that there is an energetic driving force for interstitials to preferentially bind to grain boundary sites over vacancies. Furthermore, these results provide a valuable dataset for quantifying uncertainty bounds for various grain boundary types at the nanoscale, which can be propagated to higher scale simulations of microstructure evolution.

cond-mat.mes-hall↗

arXiv2001

Coherent Transport

We discuss the transport of matter waves in low-dimensional waveguides. Due to scattering from uncontrollable noise fields, the spatial coherence gets reduced and eventually lost. We develop a description of this decoherence process in terms of transport equations for the atomic Wigner function. We outline its derivation and discuss the special case of white noise where an analytical solution can be found.

physics.atom-ph↗

arXiv2019

Accurate Electron Affinities and Orbital Energies of Anions from a Non-Empirically Tuned Range-Separated Density Functional Theory Approach

The treatment of atomic anions with Kohn-Sham density functional theory (DFT) has long been controversial since the highest occupied molecular orbital (HOMO) energy, $E_{HOMO}$, is often calculated to be positive with most approximate density functionals. We assess the accuracy of orbital energies and electron affinities for all three rows of elements in the periodic table (H-Ar) using a variety of theoretical approaches and customized basis sets. Among all of the theoretical methods studied here, we find that a non-empirically tuned range-separated approach (constructed to satisfy DFT-Koopmans' theorem for the anionic electron system) provides the best accuracy for a variety of basis sets - even for small basis sets where most functionals typically fail. Previous approaches to solve this conundrum of positive $E_{HOMO}$ values have utilized non-self-consistent methods; however electronic properties, such as electronic couplings/gradients (which require a self-consistent potential and energy), become ill-defined with these approaches. In contrast, the non-empirically tuned range-separated procedure used here yields well-defined electronic couplings/gradients and correct $E_{HOMO}$ values since both the potential and resulting electronic energy are computed self-consistently. Orbital energies and electron affinities are further analyzed in the context of the electronic energy as a function of electronic number (including fractional numbers of electrons) to provide a stringent assessment of self-interaction errors for these complex anion systems.

physics.chem-ph↗

arXiv2018

New angles on standard force fields: towards a general approach for treating atomic-level anisotropy

Nearly all standard force fields employ the 'sum-of-spheres' approximation, which models intermolecular interactions purely in terms of interatomic distances. Nonetheless, atoms in molecules can have significantly non-spherical shapes, leading to interatomic interaction energies with strong orientation dependencies. Neglecting this 'atomic-level anisotropy' can lead to significant errors in predicting interaction energies. Herein we propose a simple, transferable, and computationally-efficient model (MASTIFF) whereby atomic-level orientation dependence can be incorporated into ab initio intermolecular force fields. MASTIFF includes anisotropic exchange-repulsion, charge penetration, and dispersion effects, in conjunction with a standard treatment of anisotropic long-range (multipolar) electrostatics. To validate our approach, we benchmark MASTIFF against various sum-of-spheres models over a large library of intermolecular interactions between small organic molecules. MASTIFF achieves quantitative accuracy with respect to both high-level electronic structure theory and experiment, thus showing promise as a basis for 'next-generation' force field development.

physics.atom-ph↗

arXiv2013

Two-photon laser spectroscopy of antiprotonic helium and the antiproton-to-electron mass ratio

Physical laws are believed to be invariant under the combined transformations of charge, parity and time reversal (CPT symmetry). This implies that an antimatter particle has exactly the same mass and absolute value of charge as its particle counterpart. Metastable antiprotonic helium ($\bar{p}{\rm He}^+$) is a three-body atom consisting of a normal helium nucleus, an electron in its ground state and an antiproton ($\bar{p}$) occupying a Rydberg state with high principal and angular momentum quantum numbers, respectively $n$ and $\ell$, such that $n\sim\ell\sim 38$. These atoms are amenable to precision laser spectroscopy, the results of which can in principle be used to determine the antiproton-to-electron mass ratio and to constrain the equality between the antiproton and proton charges and masses. Here we report two-photon spectroscopy of antiprotonic helium, in which $\bar{p}{\rm ^3He^+}$ and $\bar{p}{\rm ^4He^+}$ isotopes are irradiated by two counter-propagating laser beams. This excites nonlinear, two-photon transitions of the antiproton of the type $(n,\ell)\rightarrow (n-2,\ell-2)$ at deep-ultraviolet wavelengths ($λ$=139.8, 193.0 and 197.0nm), which partly cancel the Doppler broadening of the laser resonance caused by the thermal motion of the atoms. The resulting narrow spectral lines allowed us to measure three transition frequencies with fractional precisions of 2.3-5 parts in $10^9$. By comparing the results with three-body quantum electrodynamics calculations, we derived an antiproton-to-electron mass ratio of 1,836.1526736(23), where the parenthetical error represents one standard deviation. This agrees with the proton-to-electron value known to a similar precision.

physics.atom-ph↗

arXiv2013

Suppression of the radiative decay of atomic coherence in squeezed vacuum

Quantum fluctuations of the electromagnetic vacuum are responsible for physical effects such as the Casimir force and the radiative decay of atoms, and set fundamental limits on the sensitivity of measurements. Entanglement between photons can produce correlations that result in a reduction of these fluctuations below the vacuum level allowing measurements that surpass the standard quantum limit in sensitivity. Here we demonstrate that the radiative decay rate of an atom that is coupled to quadrature squeezed electromagnetic vacuum can be reduced below its natural linewidth. We observe a two-fold reduction of the transverse radiative decay rate of a superconducting artificial atom coupled to continuum squeezed vacuum generated by a Josephson parametric amplifier, allowing the transverse coherence time T_2 to exceed the vacuum decay limit of 2T_1. We demonstrate that the measured radiative decay dynamics can be used to tomographically reconstruct the Wigner distribution of the the itinerant squeezed state. Our results are the first confirmation of a canonical prediction of quantum optics and open the door to new studies of the quantum light-matter interaction.

quant-ph↗

arXiv2013

Coupling a single electron to a Bose-Einstein condensate

The coupling of electrons to matter is at the heart of our understanding of material properties such as electrical conductivity. One of the most intriguing effects is that electron-phonon coupling can lead to the formation of a Cooper pair out of two repelling electrons, the basis for BCS superconductivity. Here we study the interaction of a single localized electron with a Bose-Einstein condensate (BEC) and show that it can excite phonons and eventually set the whole condensate into a collective oscillation. We find that the coupling is surprisingly strong as compared to ionic impurities due to the more favorable mass ratio. The electron is held in place by a single charged ionic core forming a Rydberg bound state. This Rydberg electron is described by a wavefunction extending to a size comparable to the dimensions of the BEC, namely up to 8 micrometers. In such a state, corresponding to a principal quantum number of n=202, the Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We observe surprisingly long lifetimes and finite size effects due to the electron exploring the wings of the BEC. Based on our results we anticipate future experiments on electron wavefunction imaging, investigation of phonon mediated coupling of single electrons, and applications in quantum optics.

physics.atom-ph↗

arXiv2014

Hysteresis in a quantized, superfluid atomtronic circuit

Atomtronics is an emerging interdisciplinary field that seeks new functionality by creating devices and circuits where ultra-cold atoms, often superfluids, play a role analogous to the electrons in electronics. Hysteresis is widely used in electronic circuits, e.g., it is routinely observed in superconducting circuits and is essential in rf-superconducting quantum interference devices [SQUIDs]. Furthermore, hysteresis is as fundamental to superfluidity (and superconductivity) as quantized persistent currents, critical velocity, and Josephson effects. Nevertheless, in spite of multiple theoretical predictions, hysteresis has not been previously observed in any superfluid, atomic-gas Bose-Einstein condensate (BEC). Here we demonstrate hysteresis in a quantized atomtronic circuit: a ring of superfluid BEC obstructed by a rotating weak link. We directly detect hysteresis between quantized circulation states, in contrast to superfluid liquid helium experiments that observed hysteresis directly in systems where the quantization of flow could not be observed and indirectly in systems that showed quantized flow. Our techniques allow us to tune the size of the hysteresis loop and to consider the fundamental excitations that accompany hysteresis. The results suggest that the relevant excitations involved in hysteresis are vortices and indicate that dissipation plays an important role in the dynamics. Controlled hysteresis in atomtronic circuits may prove to be a crucial feature for the development of practical devices, just as it has in electronic circuits like memory, digital noise filters (e.g., Schmitt triggers), and magnetometers (e.g., SQUIDs).

cond-mat.quant-gas↗

arXiv2014

Direct high-precision measurement of the magnetic moment of the proton

The spin-magnetic moment of the proton $μ_p$ is a fundamental property of this particle. So far $μ_p$ has only been measured indirectly, analysing the spectrum of an atomic hydrogen maser in a magnetic field. Here, we report the direct high-precision measurement of the magnetic moment of a single proton using the double Penning-trap technique. We drive proton-spin quantum jumps by a magnetic radio-frequency field in a Penning trap with a homogeneous magnetic field. The induced spin-transitions are detected in a second trap with a strong superimposed magnetic inhomogeneity. This enables the measurement of the spin-flip probability as a function of the drive frequency. In each measurement the proton's cyclotron frequency is used to determine the magnetic field of the trap. From the normalized resonance curve, we extract the particle's magnetic moment in units of the nuclear magneton $μ_p=2.792847350(9)μ_N$. This measurement outperforms previous Penning trap measurements in terms of precision by a factor of about 760. It improves the precision of the forty year old indirect measurement, in which significant theoretical bound state corrections were required to obtain $μ_p$, by a factor of 3. By application of this method to the antiproton magnetic moment $μ_{\bar{p}}$ the fractional precision of the recently reported value can be improved by a factor of at least 1000. Combined with the present result, this will provide a stringent test of matter/antimatter symmetry with baryons.

physics.atom-ph↗

arXiv2014

Magneto-optical trapping of a diatomic molecule

Laser cooling and trapping are central to modern atomic physics. The workhorse technique in cold-atom physics is the magneto-optical trap (MOT), which combines laser cooling with a restoring force from radiation pressure. For a variety of atomic species, MOTs can capture and cool large numbers of particles to ultracold temperatures (<1 mK); this has enabled the study of a wide range of phenomena from optical clocks to ultracold collisions whilst also serving as the ubiquitous starting point for further cooling into the regime of quantum degeneracy. Magneto-optical trapping of molecules could provide a similarly powerful starting point for the study and manipulation of ultracold molecular gases. Here, we demonstrate three-dimensional magneto-optical trapping of a diatomic molecule, strontium monofluoride (SrF), at a temperature of approximately 2.5 mK. This method is expected to be viable for a significant number of diatomic species. Such chemical diversity is desired for the wide array of existing and proposed experiments which employ molecules for applications ranging from precision measurement, to quantum simulation and quantum information, to ultracold chemistry.

physics.atom-ph↗

arXiv2019

Fast quantum logic gates with trapped-ion qubits

Quantum bits based on individual trapped atomic ions constitute a promising technology for building a quantum computer, with all the elementary operations having been achieved with the necessary precision for some error-correction schemes. However, the essential two-qubit logic gate used for generating quantum entanglement has hitherto always been performed in an adiabatic regime, where the gate is slow compared with the characteristic motional frequencies of ions in the trap, giving logic speeds of order 10kHz. There have been numerous proposals for performing gates faster than this natural "speed limit" of the trap. We implement the method of Steane et al., which uses tailored laser pulses: these are shaped on 10 ns timescales to drive the ions' motion along trajectories designed such that the gate operation is insensitive to optical phase fluctuations. This permits fast (MHz-rate) quantum logic which is robust to this important source of experimental error. We demonstrate entanglement generation for gate times as short as 480ns; this is less than a single oscillation period of an ion in the trap, and 8 orders of magnitude shorter than the memory coherence time measured in similar calcium-43 hyperfine qubits. The method's power is most evident at intermediate timescales, where it yields a gate error more than ten times lower than conventional techniques; for example, we achieve a 1.6 us gate with fidelity 99.8%. Still faster gates are possible at the price of higher laser intensity. The method requires only a single amplitude-shaped pulse and one pair of beams derived from a continuous-wave laser, and offers the prospect of combining the unrivalled coherence properties, operation fidelities and optical connectivity of trapped-ion qubits with the sub-microsecond logic speeds usually associated with solid state devices.

quant-ph↗

arXiv2012

Symmetry Breaking and Topological Defect Formation in Ion Coulomb Crystals

Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, defects will form with densities predicted to follow a power law scaling in the rate of the transition. The importance of this Kibble-Zurek mechanism (KZM) ranges from cosmology to condensed matter [1-4]. In previous tests in homogeneous systems, defect formation was seen, but weak dependence on the transition rate and limited control of external parameters so far prevented tests of KZM scaling. As recently predicted [5-9], in inhomogeneous systems propagation of the critical front enhances the role of causality and steepens scaling of defect density with the transition rate. We use ion Coulomb crystals in a harmonic trap to demonstrate, for the first time, scaling of the number of topological defects with the transition rate - the central prediction of KZM - in a well-controlled environment.

physics.atom-ph↗

arXiv2014

Experimental realization of quantum zeno dynamics

It is generally impossible to probe a quantum system without disturbing it. However, it is possible to exploit the back-action of quantum measurements and strong couplings to tailor and protect the coherent evolution of a quantum system. This is a profound and counterintuitive phenomenon known as quantum Zeno dynamics (QZD). Here we demonstrate QZD with a rubidium Bose-Einstein condensate in a five-level Hilbert space. We harness measurements and strong couplings to dynamically disconnect different groups of quantum states and constrain the atoms to coherently evolve inside a two-level subregion. In parallel to the foundational importance due to the realization of a dynamical superselection rule and the theory of quantum measurements, this is an important step forward in protecting and controlling quantum dynamics and, broadly speaking, quantum information processing.

quant-ph↗

arXiv2014

Veselago lensing with ultracold atoms in an optical lattice

Veselago pointed out that electromagnetic wave theory allows for materials with a negative index of refraction, in which most known optical phenomena would be reversed. A slab of such a material can focus light by negative refraction, an imaging technique strikingly different from conventional positive refractive index optics, where curved surfaces bend the rays to form an image of an object. Here we demonstrate Veselago lensing for matter waves, using ultracold atoms in an optical lattice. A relativistic, i.e. photon-like, dispersion relation for rubidium atoms is realized with a bichromatic optical lattice potential. We rely on a Raman $π$-pulse technique to transfer atoms between two different branches of the dispersion relation, resulting in a focusing completely analogous to the effect described by Veselago for light waves. Future prospects of the demonstrated effects include novel sub-de Broglie wave imaging applications.

physics.optics↗

arXiv2014

Proposal for demonstrating the Hong-Ou-Mandel effect with matter waves

The Hong-Ou-Mandel (HOM) effect is a striking demonstration of destructive quantum interference between pairs of indistinguishable bosons, realised so far only with massless photons. Here we propose an experiment which can realise this effect in the matter-wave regime using pair-correlated atoms produced via a collision of two Bose-Einstein condensates and subjected to two laser induced Bragg pulses. We formulate a novel measurement protocol appropriate for the multimode matter-wave field, which---unlike the typical two-mode optical case---bypasses the need for repeated measurements under different displacement settings of the beam-splitter, thus dramatically reducing the number of experimental runs required to map out the interference visibility. The protocol can be utilised in related matter-wave schemes; here we focus on condensate collisions and by simulating the entire experiment we predict a HOM-dip visibility of ~69%. By being larger than 50%, such a visibility highlights strong quantum correlations between the atoms and paves the way for a possible demonstration of a Bell inequality violation with massive particles in a related Rarity-Tapster setup.

quant-ph↗