Transition In Atomic Hydrogen Research Articles

Precision Spectroscopy of Atomic Hydrogen

Precise determinations of transition frequencies of simple atomic systems are required for a number of fundamental applications such as tests of quantum electrodynamics (QED), the determination of fundamental constants and nuclear charge radii. The sharpest transition in atomic hydrogen occurs between the metastable 2S state and the 1S ground state. Its transition frequency has now been measured with almost 15 digits accuracy using an optical frequency comb and a cesium atomic clock as a reference [1]. A recent measurement of the 2S – 2P3/2 transition frequency in muonic hydrogen is in significant contradiction to the hydrogen data if QED calculations are assumed to be correct [2, 3]. We hope to contribute to this so-called "proton size puzzle" by providing additional experimental input from hydrogen spectroscopy.

Precision metrology on the hydrogen atom in search for new physics

The Hydrogen atom has been the benchmark system throughout the history of atomic physics. This year we celebrate the centennial of the Bohr model [1], proposing the first quantum description of an atom and the rationale behind the Rydberg formula. This explanation of the spectrum of the H-atom ignited the quantum revolution. With the invention of the laser and the development of laser spectroscopic techniques the accuracy of spectroscopic measurements of the 1S-2S transition of hydrogen atom (natural linewidth 1.3 Hz) has improved by many orders of magnitude as shown in Figure 1, culminating now at an impressive 10 Hz or a relative accuracy of 4×10−15 [2]. Precision metrology of the Hatom is aimed towards testing fundamental theories in physics, in particular quantum electrodynamics (QED). At the basic level there are three ingredients involved in these tests: QED calculations for the H-atom, a value for the Rydberg constant R∞, and a value for the rms proton charge radius 〈rp〉rms [3]. The effect of the proton radius is small, only contributing some 1.2 MHz on the binding energy of the 1S ground state [3], but with respect to the present-day 10-Hz experimental accuracy, this contribution is significant. The uncertainties are however intertwined, e.g. the present uncertainty in the proton charge radius from electron scattering propagates Figure 1 Display of improvement of the relative accuracy achieved in spectroscopic studies of the 1S-2S transition in atomic hydrogen. (adapted and extended from Hansch, Rev. Mod. Phys. 78, 1297 (2006)).

Precision experiments and fundamental physics at low energies – Part I

Precision experiments and fundamental physics at low energies – Part I

Precision spectroscopy of the 2S‐4P transition in atomic hydrogen on a cryogenic beam of optically excited 2S atoms

Precision spectroscopy of the 2S − 4P1/2 and 2S − 4P3/2 transitions in atomic hydrogen is performed with a reproducibility of a few parts in 1012. A cryogenic beam of metastable 2S atoms is obtained by optical excitation, avoiding excessive heating of electron impact excitation used in all previous experiments of this kind. Despite the low temperature of 5.8 K, the first‐order Doppler effect is the dominating systematic shift, which is suppressed to a very high degree. The effectiveness of this suppression is verified by employing a time‐resolved detection scheme. This experiment should contribute to an improved determination of the Rydberg constant and the proton r.m.s. charge radius.

Precision measurement of the hydrogen 1S-2S frequency via a 920-km fiber link.

We have measured the frequency of the extremely narrow 1S-2S two-photon transition in atomic hydrogen using a remote cesium fountain clock with the help of a 920 km stabilized optical fiber. With an improved detection method we obtain f(1S-2S)=2466 061 413 187 018 (11) Hz with a relative uncertainty of 4.5×10(-15), confirming our previous measurement obtained with a local cesium clock [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011)]. Combining these results with older measurements, we constrain the linear combinations of Lorentz boost symmetry violation parameters c((TX))=(3.1±1.9)×10(-11) and 0.92c((TY))+0.40c((TZ))=(2.6±5.3)×10(-11) in the standard model extension framework [D. Colladay, V. A. Kostelecký, Phys. Rev. D. 58, 116002 (1998)].

Development of two-color laser system for high-resolution polarization spectroscopy measurements of atomic hydrogen

We have developed a high-spectral-resolution laser system for two-photon pump, polarization spectroscopy probe (TPP-PSP) measurements of atomic hydrogen in flames. In the TPP-PSP technique, a 243-nm laser beam excites the two-photon 1S-2S transition, and excited n=2 atoms are then detected by polarization spectroscopy of the n=2 to n=3 transition using 656-nm laser radiation. The single-frequency-mode 243 and 656-nm beams are produced using injection-seeded optical parametric generators coupled with pulsed dye amplifiers. The use of single-mode lasers allows accurate measurement of signal line shapes and intensities even with significant pulse-to-pulse fluctuations in pulse energies. Use of single-mode lasers and introduction of a scheme to select nearly constant laser energies enable repeatable extraction of important spectral features in atomic hydrogen transitions.

Ns → n′s transition of hydrogen atom by positron impact with screened Coulomb interactions

We have made an investigation on H(ns) → H(n′ s) transition processes by positron impact with screened Coulomb potentials (SCP) by employing a distorted-wave formalism in the momentum space. Making use of simple variational wave functions of the hydrogen atom interacting with SCP we have been able to obtain the partial-wave scattering amplitudes in closed analytical forms. We have then used these distorted-wave scattering amplitudes to make a detailed study on differential and total cross sections in the energy range 20–300 eV. This study reveals some hitherto unknown features of the differential and total cross section. To the best of our knowledge such a study on the differential and total cross sections for inelastic positron-hydrogen collisions with SCP is reported for the first time in the literature.

Development of pulsed UV lasers and their application in laser spectroscopy

The application of two-photon laser spectroscopy to plasma diagnostics requires tuneable UV-laser spectrometers providing: some mJ pulse energy at ns time scale with spectral quality close to Fourier Transform Limit, good pulse to pulse reproducibility and tuning linearity. We report about two different systems, a first laser specially optimized for the radiation at 243 nm, which is required for the 1S-2S two photon transition of atomic hydrogen, and a second one generating 205 nm suited for the transition 1S – 3S/3D.

Spectroscopy as a test of Coulomb’s law: A probe of the hidden sector

High precision spectroscopy can provide a sensitive tool to test Coulomb's law on atomic length scales. This can then be used to constrain particles such as extra ``hidden'' photons or minicharged particles that are predicted in many extensions of the standard model, and which cause small deviations from Coulomb's law. In this paper we use a variety of transitions in atomic hydrogen, hydrogenic ions, and exotic atoms to probe Coulomb's law. This extends the region of pure Coulomb's law tests to larger masses. For hidden photons and minicharged particles this region is already tested by other astrophysical and laboratory probes. However, future tests of true muonium and muonic atoms are likely to probe new parameter space and therefore have good discovery potential for new physics. Finally, we investigate whether the discrepancy between the theoretical calculation of the $2{s}_{1/2}^{F=1}\ensuremath{-}2{p}_{3/2}^{F=2}$ transition in muonic hydrogen and its recent experimental measurement at PSI can be explained by the existence of a hidden photon. This explanation is ruled out by measurements of the Lamb shift in ordinary hydrogen.

Determination of electric field strength and kinetic temperature in the cathode fall region of a hollow cathode discharge

In this work, we demonstrate the high potential of two-photon excitation of the 1S -2S transition of atomic hydrogen followed by optogalvanic detection, for measuring under identical experimental conditions, the kinetic temperature and the electric field strength in the cathode sheath region of a hollow cathode discharge. The first obtained results for both parameters are discussed in this paper.

BLACK HOLE FORMATION IN PRIMORDIAL GALAXIES: CHEMICAL AND RADIATIVE CONDITIONS

In massive primordial galaxies, the gas may directly collapse and form a single central massive object if cooling is suppressed. Line cooling by molecular hydrogen can be suppressed in the presence of a strong soft-ultraviolet radiation field, but the role played by other cooling mechanisms is less clear. In optically thin gas, Lyman-Alpha cooling can be very effective, maintaining the gas temperature below 10^4 K over many orders of magnitude in density. However, the large neutral hydrogen column densities present in primordial galaxies render them highly optically thick to Lyman-Alpha photons. In this letter, we examine in detail the effects of the trapping of these Lyman-Alpha photons on the thermal and chemical evolution of the gas. We show that despite the high optical depth in the Lyman series lines, cooling is not strongly suppressed, and proceeds via other atomic hydrogen transitions, in particular the 2s-1s and the 3-2 transitions. At densities larger than 10^9 cm^{-3}, collisional dissociation of molecular hydrogen becomes the dominant cooling process and decreases the gas temperature to about 5000 K. The gas temperature evolves with density as $T \propto \rho^{\gamma_{\rm eff} - 1}$, with $\gamma_{\rm eff} = 0.97-0.98$. The evolution is thus very close to isothermal, and so fragmentation is possible, but unlikely to occur during the initial collapse. However, after the formation of a massive central object, we expect that later-infalling, higher angular momentum material will form an accretion disk that may be unstable to fragmentation, which may give rise to star formation with a top-heavy IMF.

Two-colour three-photon transitions in a hydrogen atom embedded in Debye plasmas

We sketch two-colour three-photon bound–bound transitions in hydrogen atoms embedded in weakly coupled plasmas. In the present context, analytical wavefunctions are used for initial and final states along with the pseudostate summation technique for intermediate states. The analytical wavefunctions are obtained from the modified wavefunctions for the screening Coulomb potential (Debye model) using the Ritz variation method. The resonance enhancement frequencies are varied with the Debye length. The results reveal plasma effects on the three-photon bound–bound transition amplitudes for the plasma-imbedded hydrogen atom.

Application of variational method for three-color three-photon transitions in hydrogen atom implanted in Debye plasmas

Multiphoton processes, where transparency appears, have long fascinated physicists. Plasma screening effects are investigated on three-color three-photon bound-bound transitions in hydrogen atom embedded in Debye plasmas; where photons are linearly and circularly polarized, two left circular and one right circular. All possible combinations of frequency and polarization are considered. Analytical wave functions are used for initial and final states along with the pseudostate wave functions for intermediate states. The analytical wave functions are obtained from the modified wave functions for screening Coulomb potential (Debye model) using Ritz variational method. Here, we have found three-photon transparency for lower values of Debye length. This type of phenomenon occurs due to energy level shifting in the presence of Debye plasma environments. The description of resonance enhancements and three-photon transparency is reported in the present context along with the region of resonance enhancements and three-photon transparency.

Three-photon transitions in the hydrogen atom immersed in Debye plasmas

Plasma-screening effects are investigated on three-photon bound-bound transitions in hydrogen atoms embedded in weakly coupled plasmas. In the present context, we discuss a set of basis functions for the pseudostate method. The basis functions are obtained from the modified wave functions for screening Coulomb potential (Debye model) using the Ritz variation method. The calculated energy eigenvalues for various Debye lengths agree well with the other theoretical results. Our calculated transition amplitudes for free-atom case agree excellently with the existing results in the literature. We have calculated the three-photon transition matrix elements for various Debye lengths, showing the strong plasma effects on the three-photon bound-bound transition amplitudes for the plasmas-embedded hydrogen atom.

Semiconductor laser with the subhertz linewidth

A semiconductor laser emitting at 972 nm is stabilised with respect to a vibrationally and thermally compensated reference Fabry—Perot resonator with the vertical axis. The supporting points lie in the horizontal symmetry plane of the resonator, the influence of vibrations in the vertical direction being substantially suppressed in this case. This configuration provides a low sensitivity of the laser emission frequency to vertical accelerations of the reference resonator. To reduce the influence of temperature fluctuations, the resonator is made of an ULE (ultra-low-expansion) glass and is kept at temperature at which the expansion coefficient of this glass is close to zero. The laser linewidth is smaller than 0.5 Hz and the frequency drift is ≈0.1 Hz s-1. The minimum of the Allan deviation achieved for 3 s is 2×10-15. The laser was used to record the spectra of the 1S—2S transition in atomic hydrogen.

Two-photon transitions in hydrogen atoms embedded in weakly coupled plasmas

The pseudostate method has been applied to calculate energy eigenvalues and corresponding eigenfunctions of the hydrogen atom in Debye plasma environments. Resonant two-photon transition rates from the ground state of atomic hydrogen to 2s and 3s excited states have been computed as a function of photon frequency in the length and velocity gauges for different Debye lengths. A two-photon transparency is found in correspondence to each resonance for 1s–3s. The transparency frequency and resonance enhancement frequency vary significantly with the Debye length.

Observation of the (3)He(n, tp) Reaction by Detection of Far-Ultraviolet Radiation.

We have detected Lyman alpha radiation, 121.6 nm light produced from the n = 2 to n = 1 transition in atomic hydrogen, as a product of the 3He(n, tp) nuclear reaction occurring in a cell of 3He gas. The predominant source of this radiation appears to be decay of the 2p state of tritium produced by charge transfer and excitation collisions with the background 3He gas. Under the experimental conditions reported here we find yields of tens of Lyman alpha photons for every neutron reaction. These results suggest a method of cold neutron detection that is complementary to existing technologies that use proportional counters. In particular, this approach may provide single neutron sensitivity with wide dynamic range capability, and a class of neutron detectors that are compact and operate at relatively low voltages.

Photon pairs with tailor-made entanglement obtained from the two-photon decay of atomic hydrogen

From the work by W. Perrie et al. [Phys. Rev. Lett. 54, 1790 (1985)], it is known that the photon pairs that are emitted in the $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ (two-photon) decay of atomic hydrogen are quantum mechanically correlated, i.e., entangled. However, less information is available about the degree of polarization entanglement between the two photons if an arbitrary geometry is considered for collecting the photons. In this paper, we study the effect of the decay geometry on the degree of polarization entanglement between the two emitted photons. Results are shown for the $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ and $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ two-photon transitions of atomic hydrogen. The outlined theory is general and can be applied also to heavier elements. To demonstrate the influence of relativistic and multipole effects, results are also shown for the $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transition of hydrogenlike uranium.

Collision frequency shift of hyperfine transitions in atomic hydrogen at a low temperature

The experimental results on the collision frequency shift of ESR in diluted two-and three-dimensional atomic hydrogen at ultralow temperature have been analyzed. The apparent contradiction between experiment and theory is resolved by taking into account the relation between the symmetry of the state of two atoms and their total electron spin S. For example, transitions between symmetric and antisymmetric states of a pair of atoms induced by a symmetric perturbation are forbidden. If symmetric and antisymmetric states are, respectively, pure electronic triplets (S= 1) and singlets (S = 0), this results in the cancellation of the singlet-triplet transitions. Thus, the collision frequency shift of b → c and b → a transitions vanishes in a completely electron and nuclear spin-polarized gas (hyperfine state b). The comparison is performed with experiments in ultracold alkali vapors.

Some properties of Stark states of hydrogenic atoms and ions

The motivation for this work is the problem of providing accurate values of the atomic transition matrix elements for the Stark components of Rydberg–Rydberg transitions in atomic hydrogen and hydrogenic ions, for use in spectral line broadening calculations applicable to cool, low-density plasmas, such as those found in H II regions. Since conventional methods of calculating these transition matrix elements cannot be used for the high principal quantum numbers now easily attained in radio astronomical spectra, we attempt to show that the recurrence relation (ladder operator) method recently employed by Watson (2006 J. Phys. B: At. Mol. Opt. Phys. 39 1889–97) and Hey (2006 J. Phys. B: At. Mol. Opt. Phys. 39 2641–64) can be taken over into the parabolic coordinate system used to describe the Stark states of the atomic (ionic) radiators. The present method is therefore suggested as potentially useful for extending the work of Griem (1967 Astrophys. J. 148 547–58, 2005 Astrophys. J. 620 L133–4), Watson (2006), Stambulchik et al (2007 Phys. Rev. E 75 016401(9 pp) on Stark broadening in transitions between states of high principal quantum number, to physical conditions where the binary, impact approximation is no longer strictly applicable to both electron and ion perturbers. Another possible field of application is the study of Stark mixing transitions in ‘ultracold’ Rydberg atoms perturbed by long-range interactions with slow atoms and ions. Preparatory to the derivation of recurrence relations for states of different principal quantum number, a number of properties and recurrence relations are also found for states of identical principal quantum number, including the analogue in parabolic coordinates to the relations of Pasternack (1937 Proc. Natl Acad. Sci. USA 23 91–4, 250) in spherical polar coordinates.