Simulations of classical three-body thermalization in one dimension.

One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of pointlike particles, typically the dominant process for reaching thermal equilibrium in higher-dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential V_{ij}∝1/|x_{i}-x_{j}|^{n} or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature T toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low-density limit. For the inverse power-law potential, the rate of thermalization is proportional to ρ^{2}T^{1/2-1/n}, where ρ is the number density. The corresponding proportionality constant decreases with increasing n.

Simulations and theory of power spectral density functions for time-dependent and anharmonic Langevin oscillators.

Simulations and theory are presented for the power spectral density functions (PSDs) of particles in time-dependent and anharmonic potentials, including the effects of a thermal environment leading to damping and fluctuating forces. We investigate three one-dimensional perturbations to the harmonic oscillator of which two are time-dependent changes in the natural frequency of the oscillator, while the other is a time-independent extension of the quadratic potential to include a quartic term. We investigate the effect of these perturbations on two PSDs of the motion that are used in experiments on trapped nano-oscillators. We also derive and numerically test the PSDs for the motion of a spherical nanoparticle in a Paul trap. We found that the simple harmonic Langevin oscillator's PSDs are good approximations for the x and y coordinates' PSDs for small values of the parameter q of the Mathieu equation, but the difference can be more than a factor of two as "q" increases. We also numerically showed that the presence of a permanent electric dipole on the nanosphere can significantly affect the PSDs in the x and y coordinates.

Laser-Driven Superradiant Ensembles of Two-Level Atoms near Dicke Regime.

We report the experimental observation of a superradiant emission emanating from an elongated dense ensemble of laser cooled two-level atoms, with a radial extent smaller than the transition wavelength. In the presence of a strong driving laser, we observe that the system is superradiant along its symmmetry axis. This occurs even though the driving laser is orthogonal to the superradiance direction. This superradiance modifies the spontaneous emission, and, resultantly, the Rabi oscillations. We also investigate Dicke superradiance in the emission of an almost fully inverted system as a function of the atom number. The experimental results are in qualitative agreement with ab-initio, beyond-mean-field calculations.

Sympathetic cooling of positrons to cryogenic temperatures for antihydrogen production.

The positron, the antiparticle of the electron, predicted by Dirac in 1931 and discovered by Anderson in 1933, plays a key role in many scientific and everyday endeavours. Notably, the positron is a constituent of antihydrogen, the only long-lived neutral antimatter bound state that can currently be synthesized at low energy, presenting a prominent system for testing fundamental symmetries with high precision. Here, we report on the use of laser cooled Be+ ions to sympathetically cool a large and dense plasma of positrons to directly measured temperatures below 7 K in a Penning trap for antihydrogen synthesis. This will likely herald a significant increase in the amount of antihydrogen available for experimentation, thus facilitating further improvements in studies of fundamental symmetries.

Laser cooling of antihydrogen atoms.

The photon-the quantum excitation of the electromagnetic field-is massless but carries momentum. A photon can therefore exert a force on an object upon collision1. Slowing the translational motion of atoms and ions by application of such a force2,3, known as laser cooling, was first demonstrated 40 years ago4,5. It revolutionized atomic physics over the following decades6-8, and it is now a workhorse in many fields, including studies on quantum degenerate gases, quantum information, atomic clocks and tests of fundamental physics. However, this technique has not yet been applied to antimatter. Here we demonstrate laser cooling of antihydrogen9, the antimatter atom consisting of an antiproton and a positron. By exciting the 1S-2P transition in antihydrogen with pulsed, narrow-linewidth, Lyman-α laser radiation10,11, we Doppler-cool a sample of magnetically trapped antihydrogen. Although we apply laser cooling in only one dimension, the trap couples the longitudinal and transverse motions of the anti-atoms, leading to cooling in all three dimensions. We observe a reduction in the median transverse energy by more than an order of magnitude-with a substantial fraction of the anti-atoms attaining submicroelectronvolt transverse kinetic energies. We also report the observation of the laser-driven 1S-2S transition in samples of laser-cooled antihydrogen atoms. The observed spectral line is approximately four times narrower than that obtained without laser cooling. The demonstration of laser cooling and its immediate application has far-reaching implications for antimatter studies. A more localized, denser and colder sample of antihydrogen will drastically improve spectroscopic11-13 and gravitational14 studies of antihydrogen in ongoing experiments. Furthermore, the demonstrated ability to manipulate the motion of antimatter atoms by laser light will potentially provide ground-breaking opportunities for future experiments, such as anti-atomic fountains, anti-atom interferometry and the creation of antimatter molecules.

Dressed Ion-Pair States of an Ultralong-Range Rydberg Molecule.

We predict the existence of a universal class of ultralong-range Rydberg molecular states whose vibrational spectra form trimmed Rydberg series. A dressed ion-pair model captures the physical origin of these exotic molecules, accurately predicts their properties, and reveals features of ultralong-range Rydberg molecules and heavy Rydberg states with a surprisingly small Rydberg constant. The latter is determined by the small effective charge of the dressed anion, which outweighs the contribution of the molecule's large reduced mass. This renders these molecules the only known few-body systems to have a Rydberg constant smaller than R_{∞}/2.

Propagating molecular rotational coherences through single-frequency pulses in the strong field regime.

In the weak-field limit in which microwave spectroscopy is typically carried out, an application of a single-frequency pulse that is resonant with a molecular transition will create a coherence between the pair of states involved in the rotational transition, producing a free-induction decay (FID) that, after Fourier transform, produces a molecular signal at that same resonance frequency. With the advent of chirped-pulse Fourier transform microwave methods, the high-powered amplifiers needed to produce broadband microwave spectra also open up other experiments that probe the molecular response in the high-field regime. This paper describes a series of experiments involving resonant frequency pulses interrogating jet-cooled molecules under conditions of sufficient power to Rabi oscillate the two-state system through many Rabi cycles. The Fourier-transformed FID shows coherent signal not only at the applied resonant frequency but also at a series of transitions initially connected to the original one by sharing an upper or lower level with it. As the duration of the single-frequency excitation is increased from 250 to 1500 ns, the number of observed off-resonant, but dipole-allowed, molecular coherences grow. The phenomenon is quite general, having been demonstrated in Z-phenylvinylnitrile, E-phenylvinylnitrile (E-PVN), benzonitrile, guaiacol, and 4-pentynenitrile. In E-PVN, the highest power/longest pulse duration, coherent signal is also present at energetically nearby but not directly connected transitions. Even in molecular samples containing more than one independent species, only transitions due to the single species responsible for the original resonant transition are present. We develop a time-dependent model of the molecular/photon system and use it in conjunction with the experiment to test possible sources of the phenomenon.

Observation of the 1S-2P Lyman-α transition in antihydrogen.

In 1906, Theodore Lyman discovered his eponymous series of transitions in the extreme-ultraviolet region of the atomic hydrogen spectrum1,2. The patterns in the hydrogen spectrum helped to establish the emerging theory of quantum mechanics, which we now know governs the world at the atomic scale. Since then, studies involving the Lyman-α line-the 1S-2P transition at a wavelength of 121.6 nanometres-have played an important part in physics and astronomy, as one of the most fundamental atomic transitions in the Universe. For example, this transition has long been used by astronomers studying the intergalactic medium and testing cosmological models via the so-called 'Lyman-α forest'3 of absorption lines at different redshifts. Here we report the observation of the Lyman-α transition in the antihydrogen atom, the antimatter counterpart of hydrogen. Using narrow-line-width, nanosecond-pulsed laser radiation, the 1S-2P transition was excited in magnetically trapped antihydrogen. The transition frequency at a field of 1.033 tesla was determined to be 2,466,051.7 ± 0.12 gigahertz (1σ uncertainty) and agrees with the prediction for hydrogen to a precision of 5 × 10-8. Comparisons of the properties of antihydrogen with those of its well-studied matter equivalent allow precision tests of fundamental symmetries between matter and antimatter. Alongside the ground-state hyperfine4,5 and 1S-2S transitions6,7 recently observed in antihydrogen, the Lyman-α transition will permit laser cooling of antihydrogen8,9, thus providing a cold and dense sample of anti-atoms for precision spectroscopy and gravity measurements10. In addition to the observation of this fundamental transition, this work represents both a decisive technological step towards laser cooling of antihydrogen, and the extension of antimatter spectroscopy to quantum states possessing orbital angular momentum.

Characterization of the 1S-2S transition in antihydrogen.

In 1928, Dirac published an equation 1 that combined quantum mechanics and special relativity. Negative-energy solutions to this equation, rather than being unphysical as initially thought, represented a class of hitherto unobserved and unimagined particles-antimatter. The existence of particles of antimatter was confirmed with the discovery of the positron 2 (or anti-electron) by Anderson in 1932, but it is still unknown why matter, rather than antimatter, survived after the Big Bang. As a result, experimental studies of antimatter3-7, including tests of fundamental symmetries such as charge-parity and charge-parity-time, and searches for evidence of primordial antimatter, such as antihelium nuclei, have high priority in contemporary physics research. The fundamental role of the hydrogen atom in the evolution of the Universe and in the historical development of our understanding of quantum physics makes its antimatter counterpart-the antihydrogen atom-of particular interest. Current standard-model physics requires that hydrogen and antihydrogen have the same energy levels and spectral lines. The laser-driven 1S-2S transition was recently observed 8 in antihydrogen. Here we characterize one of the hyperfine components of this transition using magnetically trapped atoms of antihydrogen and compare it to model calculations for hydrogen in our apparatus. We find that the shape of the spectral line agrees very well with that expected for hydrogen and that the resonance frequency agrees with that in hydrogen to about 5 kilohertz out of 2.5 × 1015 hertz. This is consistent with charge-parity-time invariance at a relative precision of 2 × 10-12-two orders of magnitude more precise than the previous determination 8 -corresponding to an absolute energy sensitivity of 2 × 10-20 GeV.

Enhanced Control and Reproducibility of Non-Neutral Plasmas.

The simultaneous control of the density and particle number of non-neutral plasmas confined in Penning-Malmberg traps is demonstrated. Control is achieved by setting the plasma's density by applying a rotating electric field while simultaneously fixing its axial potential via evaporative cooling. This novel method is particularly useful for stabilizing positron plasmas, as the procedures used to collect positrons from radioactive sources typically yield plasmas with variable densities and particle numbers; it also simplifies optimization studies that require plasma parameter scans. The reproducibility achieved by applying this technique to the positron and electron plasmas used by the ALPHA antihydrogen experiment at CERN, combined with other developments, contributed to a 10-fold increase in the antiatom trapping rate.

Erratum: Observation of the hyperfine spectrum of antihydrogen.

This corrects the article DOI: 10.1038/nature23446.

Antihydrogen accumulation for fundamental symmetry tests.

Antihydrogen, a positron bound to an antiproton, is the simplest anti-atom. Its structure and properties are expected to mirror those of the hydrogen atom. Prospects for precision comparisons of the two, as tests of fundamental symmetries, are driving a vibrant programme of research. In this regard, a limiting factor in most experiments is the availability of large numbers of cold ground state antihydrogen atoms. Here, we describe how an improved synthesis process results in a maximum rate of 10.5 ± 0.6 atoms trapped and detected per cycle, corresponding to more than an order of magnitude improvement over previous work. Additionally, we demonstrate how detailed control of electron, positron and antiproton plasmas enables repeated formation and trapping of antihydrogen atoms, with the simultaneous retention of atoms produced in previous cycles. We report a record of 54 detected annihilation events from a single release of the trapped anti-atoms accumulated from five consecutive cycles.Antihydrogen studies are important in testing the fundamental principles of physics but producing antihydrogen in large amounts is challenging. Here the authors demonstrate an efficient and high-precision method for trapping and stacking antihydrogen by using controlled plasma.

Observation of the hyperfine spectrum of antihydrogen.

The observation of hyperfine structure in atomic hydrogen by Rabi and co-workers and the measurement of the zero-field ground-state splitting at the level of seven parts in 1013 are important achievements of mid-twentieth-century physics. The work that led to these achievements also provided the first evidence for the anomalous magnetic moment of the electron, inspired Schwinger's relativistic theory of quantum electrodynamics and gave rise to the hydrogen maser, which is a critical component of modern navigation, geo-positioning and very-long-baseline interferometry systems. Research at the Antiproton Decelerator at CERN by the ALPHA collaboration extends these enquiries into the antimatter sector. Recently, tools have been developed that enable studies of the hyperfine structure of antihydrogen-the antimatter counterpart of hydrogen. The goal of such studies is to search for any differences that might exist between this archetypal pair of atoms, and thereby to test the fundamental principles on which quantum field theory is constructed. Magnetic trapping of antihydrogen atoms provides a means of studying them by combining electromagnetic interaction with detection techniques that are unique to antimatter. Here we report the results of a microwave spectroscopy experiment in which we probe the response of antihydrogen over a controlled range of frequencies. The data reveal clear and distinct signatures of two allowed transitions, from which we obtain a direct, magnetic-field-independent measurement of the hyperfine splitting. From a set of trials involving 194 detected atoms, we determine a splitting of 1,420.4 ± 0.5 megahertz, consistent with expectations for atomic hydrogen at the level of four parts in 104. This observation of the detailed behaviour of a quantum transition in an atom of antihydrogen exemplifies tests of fundamental symmetries such as charge-parity-time in antimatter, and the techniques developed here will enable more-precise such tests.

Classical Fractals and Quantum Chaos in Ultracold Dipolar Collisions.

We examine a dipolar-gas model to address fundamental issues regarding the correspondence between classical chaos and quantum observations in ultracold dipolar collisions. The theoretical model consists of a short-range Lennard-Jones potential well with an anisotropic, long-range dipole-dipole interaction between two atoms. Both the classical and quantum dynamics are explored for the same Hamiltonian of the system. The classical chaotic scattering is revealed by the fractals developed in the scattering function (defined as the final atom separation as a function of initial conditions), while the quantum chaotic features lead to the repulsion of the eigenphases from the corresponding quantum S matrix. The nearest-eigenphase-spacing statistics have an intermediate behavior between the Poisson and the Wigner-Dyson distributions. The character of the distribution can be controlled by changing an effective Planck constant or the dipole moment. The degree of quantum chaos shows a good correspondence with the overall average of the classical scattering function. The results presented here also provide helpful insights for understanding the role of the inherent dipole-dipole interaction in the currently ongoing experiments on ultracold collisions of highly magnetic atoms.

Observation of the 1S-2S transition in trapped antihydrogen.

The spectrum of the hydrogen atom has played a central part in fundamental physics over the past 200 years. Historical examples of its importance include the wavelength measurements of absorption lines in the solar spectrum by Fraunhofer, the identification of transition lines by Balmer, Lyman and others, the empirical description of allowed wavelengths by Rydberg, the quantum model of Bohr, the capability of quantum electrodynamics to precisely predict transition frequencies, and modern measurements of the 1S-2S transition by Hänsch to a precision of a few parts in 1015. Recent technological advances have allowed us to focus on antihydrogen-the antimatter equivalent of hydrogen. The Standard Model predicts that there should have been equal amounts of matter and antimatter in the primordial Universe after the Big Bang, but today's Universe is observed to consist almost entirely of ordinary matter. This motivates the study of antimatter, to see if there is a small asymmetry in the laws of physics that govern the two types of matter. In particular, the CPT (charge conjugation, parity reversal and time reversal) theorem, a cornerstone of the Standard Model, requires that hydrogen and antihydrogen have the same spectrum. Here we report the observation of the 1S-2S transition in magnetically trapped atoms of antihydrogen. We determine that the frequency of the transition, which is driven by two photons from a laser at 243 nanometres, is consistent with that expected for hydrogen in the same environment. This laser excitation of a quantum state of an atom of antimatter represents the most precise measurement performed on an anti-atom. Our result is consistent with CPT invariance at a relative precision of about 2 × 10-10.

Electron Plasmas Cooled by Cyclotron-Cavity Resonance.

We observe that high-Q electromagnetic cavity resonances increase the cyclotron cooling rate of pure electron plasmas held in a Penning-Malmberg trap when the electron cyclotron frequency, controlled by tuning the magnetic field, matches the frequency of standing wave modes in the cavity. For certain modes and trapping configurations, this can increase the cooling rate by factors of 10 or more. In this Letter, we investigate the variation of the cooling rate and equilibrium plasma temperatures over a wide range of parameters, including the plasma density, plasma position, electron number, and magnetic field.

Torsional Optomechanics of a Levitated Nonspherical Nanoparticle.

An optically levitated nanoparticle in vacuum is a paradigm optomechanical system for sensing and studying macroscopic quantum mechanics. While its center-of-mass motion has been investigated intensively, its torsional vibration has only been studied theoretically in limited cases. Here we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the coupling between the spin angular momentum of photons and the torsional vibration of a nonspherical nanoparticle whose polarizability is a tensor. The torsional vibration frequency can be 1 order of magnitude higher than its center-of-mass motion frequency, which is promising for ground state cooling. We propose a simple yet novel scheme to achieve ground state cooling of its torsional vibration with a linearly polarized Gaussian cavity mode. A levitated nonspherical nanoparticle in vacuum will also be an ultrasensitive nanoscale torsion balance with a torque detection sensitivity on the order of 10^{-29} N m/sqrt[Hz] under realistic conditions.

An improved limit on the charge of antihydrogen from stochastic acceleration.

Antimatter continues to intrigue physicists because of its apparent absence in the observable Universe. Current theory requires that matter and antimatter appeared in equal quantities after the Big Bang, but the Standard Model of particle physics offers no quantitative explanation for the apparent disappearance of half the Universe. It has recently become possible to study trapped atoms of antihydrogen to search for possible, as yet unobserved, differences in the physical behaviour of matter and antimatter. Here we consider the charge neutrality of the antihydrogen atom. By applying stochastic acceleration to trapped antihydrogen atoms, we determine an experimental bound on the antihydrogen charge, Qe, of |Q| < 0.71 parts per billion (one standard deviation), in which e is the elementary charge. This bound is a factor of 20 less than that determined from the best previous measurement of the antihydrogen charge. The electrical charge of atoms and molecules of normal matter is known to be no greater than about 10(-21)e for a diverse range of species including H2, He and SF6. Charge-parity-time symmetry and quantum anomaly cancellation demand that the charge of antihydrogen be similarly small. Thus, our measurement constitutes an improved limit and a test of fundamental aspects of the Standard Model. If we assume charge superposition and use the best measured value of the antiproton charge, then we can place a new limit on the positron charge anomaly (the relative difference between the positron and elementary charge) of about one part per billion (one standard deviation), a 25-fold reduction compared to the current best measurement.

Visualizing the coupling between red and blue stark states using photoionization microscopy.

In nonhydrogenic atoms in a dc electric field, the finite size of the ionic core introduces a coupling between quasibound Stark states that leads to avoided crossings between states that would otherwise cross. Near an avoided crossing, the interacting states may have decay amplitudes that cancel each other, decoupling one of the states from the ionization continuum. This well-known interference narrowing effect, observed as a strongly electric field-dependent decrease in the ionization rate, was previously observed in several atoms. Here we use photoionization microscopy to visualize interference narrowing in helium atoms, thereby explicitly revealing the mechanism by which Stark states decay. The interference narrowing allows measurements of the nodal patterns of red Stark states, which are otherwise not observable due to their intrinsic short lifetime.