Stanislav Tereshchenko
The connection between the quantum frequency of radiation by the transition of the electron from orbit n to orbit k and frequencies of circling of electron in these orbits for the atom of hydrogen is determined.
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We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g-factor of the electron, which was previously the most accurate prediction of QED.
We reconsider the calculation of rovibrational transition frequencies in hydrogen molecular ions. Some previously neglected contributions, such as the deuteron polarizability, are included into consideration in comparison with our previous work. In particular, one-loop and two-loop QED corrections at $mα^7$ and $mα^8$ orders are recalculated in the framework of the adiabatic approximation, with systematic inclusion of corrections associated with vibrational motion. Improved theoretical transitions frequencies are obtained and found to be in very good agreement with recent high-precision spectr…
Is it possible that two different transitions in the non-relativistic quantum mechanical model of the hydrogen atom give the same frequency? That is, can different energy level transitions in a hydrogen atom have the same photon radiation frequency? This question, which was asked during a Ph.D. oral exam in 1997 at the University of Colorado Boulder, is well-known among physics graduate students. We show a general solution to this question, in which all equifrequency transition pairs can be obtained from the set of solutions of a Diophantine equation. This fun puzzle is a simple yet concrete e…
We consider the application of a basic principle of quantum theory, the tracelessness of a certain class of hamiltonians, to the precision spectroscopy of the molecular hydrogen ions. We show that it is possible to obtain the spin-averaged transition frequencies between states from a simple weighted sum of experimentally accessible spin-dependent transition frequencies. We discuss the cases ${\rm H}_{2}^{+}$ and ${\rm HD}^{+}$, which are distinct in the multipole character of their rovibrational transitions. Inclusion of additional frequencies permits canceling also the electric quadrupole shi…
The effect of the relative phase between the components of a bichromatic field of frequencies $ω$ and $3ω$ is discussed in the case of free-free transitions in laser-assisted electron-hydrogen scattering. For fast projectile and low field intensities, the role of target dressing is pointed out.
The 7 standard deviations between the proton rms charge radius from muonic hydrogen and the CODATA-10 value from hydrogen spectroscopy and electron-scattering has caused considerable discussions. Here, we review the theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen combining the published contributions and theoretical approaches. The prediction of these quantities is necessary for the determination of both proton charge and Zemach radii from the two 2S-2P transition frequencies measured in muonic hydrogen.
The electric dipole polarizabilities evaluated at imaginary frequencies for hydrogen, the alkali-metal atoms, the alkaline earth atoms, and the inert gases are tabulated along with the resulting values of the atomic static polarizabilities, the atom-surface interaction constants, and the dispersion (or van der Waals) constants for the homonuclear and the heteronuclear diatomic combinations of the atoms.
We calculate the DC Stark effect for three molecular hydrogen ions in the non-relativistic approximation. The effect is calculated both in dependence on the rovibrational state and in dependence on the hyperfine state. We discuss special cases and approximations. We also calculate the AC polarisabilities for several rovibrational levels, and therefrom evaluate accurately the black-body radiation shift, including the effects of excited electronic states. The results enable the detailed evaluation of certain systematic shifts of the transitions frequencies for the purpose of ultra-high-precision…
In the present paper, we consider nonresonant corrections to $ 2s-ns/nd $ transition frequencies in hydrogen for the experiments based on two-photon spectroscopy. A detailed study of angular correlations of quantum interference effects within the framework of rigorous quantum electrodynamics is given. Closed expressions for the resonant two-photon scattering cross sections on an atomic level with dependence on all atomic quantum numbers including fine and hyperfine structure are derived. These expressions are applied for the description of experiments based on two-photon spectroscopy with fixi…
The "proton radius puzzle" was recently solved by reducing the four-standard deviation discrepancy between the results for electronic hydrogen ($H$) and muonic hydrogen ($μH$) atoms to $3.3$ value. The value of the root-mean-square radius of the proton ($r_p$), extracted from experiments on measuring the one-photon $2s-4p$ transition and the Lamb shift in hydrogen, is now $0.8335(95)$ fm, that is in good agreement with the muonic hydrogen experiments, $0.84087(39)$ fm. Even so, these values deviate significantly from the CODATA value, which is determined as the average using the results for va…
We study a stiff quasi-periodic orbit of the electromagnetic two-body problem of Dirac's electrodynamics of point charges. We expand the delay equations of motion about circular orbits to obtain the variational equations up to nonlinear terms. We study the normal modes of the variational dynamics with period of the order of the time for light to travel the interparticle distance. In the atomic magnitude these are fast frequencies compared to the circular rotation. We construct a quasi-periodic orbit with three frequencies; the frequency of the unperturbed circular rotation (slow) and the two f…
Free-free transitions in laser-assisted electron-hydrogen scattering in a bichromatic field of frequencies $ω$ and $2ω$ are studied at moderate intensities for fast projectiles. A hybrid approach is used, in which the field-projectile interaction is described exactly but the field-target one is described by second order perturbation theory; the projectile-target interaction is treated in the first Born approximation. The adopted description of the target enables a consistent study of the leading process to each of the considered sidebands. Numerical results are presented for the angular distri…
We discuss here the effect of the photon helicity in laser induced and inverse bremstrahlung for {\it high energy scattering} of electrons by hydrogen atoms. We demonstrate that it is possible to find EDAD for high scattering energies of the electrons if the{\it \ dressing of the atomic target} by the laser field is taken into account. We consider higher optical frequencies of the laser field and we restrict ourselves to the use of moderate field intensities.
This article reports the first optical frequency measurement of the $1\mathrm{S}-3\mathrm{S}$ transition in hydrogen. The excitation of this transition occurs at a wavelength of 205 nm which is obtained with two frequency doubling stages of a titanium sapphire laser at 820 nm. Its frequency is measured with an optical frequency comb. The second-order Doppler effect is evaluated from the observation of the motional Stark effect due to a transverse magnetic field perpendicular to the atomic beam. The measured value of the $1\mathrm{S}_{1/2}(F=1)-3\mathrm{S}_{1/2}(F=1)$ frequency splitting is $2 …
The systematic shifts of the transition frequencies in the molecular hydrogen ions are of relevance to ultra-high-resolution radio-frequency, microwave and optical spectroscopy of these systems, performed in ion traps. We develop the ab-initio description of the interaction of the electric quadrupole moment of this class of molecules with the static electric field gradients present in ion traps. In good approximation, it is described in terms of an effective perturbation hamiltonian. An approximate treatment is then performed in the Born-Oppenheimer approximation. We give an expression of the …
Metrology of Rydberg states of the hydrogen atom
提出一种测量氢原子高-$n$里德堡态跃迁频率的方法，通过记录Stark光谱校准电场并修正能级能量，在10kHz不确定度内验证了Bohr公式，并确定了2s态的超精细分裂。
We studied the orbit of an electron revolving around an infinitely massive nucleus of a large classical Hydrogen atom subject to an AC electric field oscillating perpendicular to the electron's circular orbit. Using perturbation theory in geometric algebra, we show that the equation of motion of the electron perpendicular to the unperturbed orbital plane satisfies a forced simple harmonic oscillator equation found in Lorentz dispersion law in Optics. We show that even though we did not introduce a damping term, the initial orbital position and velocity of the electron results to a solution who…
This paper concerns the most intriguing question of modern atomic physics: determination of the proton root-mean-square (rms) charge radius ($r_p$). This problem was announced by the difference in $r_p$ values extracted from the experiments on measurement of transition frequencies in hydrogen ($H$) atom and measurement of Lamb shift in muonic hydrogen ($μH$) atom. The both experiments give the possibility for the very accurate comparison of values evaluated theoretically and experimentally. As a result of this analysis the value of proton charge radius extracted from the $μH$ experiment was fo…
We consider the most accurate tests of bound state QED theory of the hyperfine splitting in two-body atoms related to the HFS interval of the 1s state in muonium and positronium and the 2s state in hydrogen, deuterium and the helium-3 ion. We summarize their QED theory and pay special attention to involved effects of strong interactions and to recent optical measurements of the 2s HFS interval in hydrogen and deuterium. We present results for specific ratios of the 1s-2s frequencies in hydrogen and deuterium which happen to be among the most accurately measured and calculated quantities.
We present improved theoretical calculations of transition frequencies for the fundamental transitions $(L\!=\!0,v\!=\!1)\to(L'\!=\!0,v'\!=\!0)$ in the hydrogen molecular ions H$_2^+$ and HD$^+$ with a relative uncertainty $4\cdot10^{-11}$ and for the two-photon transitions in the antiprotonic helium atom with a relative uncertainty $10^{-10}$. To do that, the one-loop self-energy correction of order $α(Zα)^6$ is derived in the two Coulomb center approximation, and numerically evaluated in the case of the aforementioned transitions. The final results also include a complete set of other spin-i…
We propose a new laser cooling method for atomic species whose level structure makes traditional laser cooling difficult. For instance, laser cooling of hydrogen requires single-frequency vacuum-ultraviolet light, while multielectron atoms need single-frequency light at many widely separated frequencies. These restrictions can be eased by laser cooling on two-photon transitions with ultrafast pulse trains. Laser cooling of hydrogen, antihydrogen, and many other species appears feasible, and extension of the technique to molecules may be possible.
We consider high energy electron scattering by hydrogen atoms in the presence of a laser field of moderate power and higher frequencies. If the field is a superposition of a linearly and a circularly polarized laser beam in a particular configuration, then we can show that circular dichroism in two photon transitions can be observed not only for the differential but also for the integrated cross sections, provided the laser-dressing of the atomic target is treated in second order perturbation theory and the coupling between hydrogenic bound and continuum states is involved.
Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions III -- rovibrational spectrum and the non-minimal SME
通过研究氢和反氢分子离子H₂⁺和H₂⁻的转动振动跃迁，探讨洛伦兹和CPT对称性破坏，利用SME理论分析其光谱特性，扩展非最小SME结果，探讨转动和洛伦兹加速对跃迁频率的影响。
Dynamic stabilization of atomic hydrogen against ionization in high-frequency single- and two-color, circularly polarized laser pulses is observed by numerically solving the three-dimensional, time-dependent Schrödinger equation. The single-color case is revisited and numerically determined ionization rates are compared with both, exact and approximate high-frequency Floquet rates. The position of the peaks in the photoelectron spectra can be explained with the help of dressed initial states. In two-color laser fields of opposite circular polarization the stabilized probability density may be …
We introduce an ad-hoc electrodynamics with advanced and retarded Lienard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem, i.e., the hydrogen atom. We perform the linear stability analysis of circular orbits for oscillations perpendicular to the orbital plane. In particular we study the normal modes of the linearized dynamics that have an arbitrarily large imaginary eigenvalue. These large eigenvalues are fast frequencies that introduce a fast (stiff) timescale into the dynamics. As…
Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions I -- rovibrational states
通过分析氢分子离子的转动振动谱，研究洛伦兹和CPT不变性在低能有效理论中的表现，利用氢和反氢的高精度跃迁频率提高对基本对称性的测试。
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 $|Δμ/μ|< 5 \times 10^{-6}$ at 3$σ$. Observation of H$_2$ from the photospheres of white dwarf stars inside our Galaxy delivers a constraint of similar magnitude on a dependence of $μ$ on a gravitational p…
Prospects for the determination of fundamental constants with beyond-state-of-the-art uncertainty using molecular hydrogen ion spectroscopy
本文提出利用更大量子数能级及 D$_2^+$ 跃迁的分子氢离子光谱联合分析，解除质量比与高阶 QED 贡献的灵敏度关联，有望将质量比不确定度较 CODATA 2018 降低约三个数量级。
Simulation of STIRAP from the 1S to the 2S states of the Hydrogen/Antihydrogen atoms
研究氢/反氢原子从1S到2S态的转移，提出用STIRAP过程，利用圆偏振Ly-α脉冲和微波脉冲耦合相关能级，计算转移效率与实验参数关系，分析热系综情况及磁场影响，得出低温下效率增加等结论。
Extraction of spin-averaged rovibrational transition frequencies in HD$^+$ for the determination of fundamental constants
该研究通过全局最小二乘调整提取HD$^+$的三个自旋平均跃迁频率，并结合理论表达式与彭宁阱数据，显著改进了电子相对原子质量和质子-电子质量比的测定。
Reassessment of line profile asymmetry in measurements of the 1s-2s energy interval in hydrogen
该研究重新评估氢原子1s-2s能量间隔测量中线轮廓不对称性，结合近年理论成果修正相关理论分析，发现观测轮廓不对称会致跃迁频率偏移，与线形模型贡献一致，可依标准不对称轮廓调整。
Measurement of transition frequencies and hyperfine constants of molecular iodine at 520.2 nm
本文利用 PPLN 波导产生 520.2 nm 激光，测量了分子碘四条谱线的超精细跃迁频率，并以 1*10-11 的相对不确定度确定了 a1 分量频率，进而计算出超精细常数及其转动依赖关系。
We consider a hydrogen atom confined in a thick brane embedded in a higher-dimensional space. Due to effects of the extra dimensions, the gravitational potential is amplified in distances smaller than the size of the supplementary space, in comparison with the Newtonian potential. Studying the influence of the gravitational interaction modified by the extra dimensions on the energy levels of the hydrogen atom, we find independent constraints for the higher-dimensional Planck mass in terms of the thickness of the brane by using accurate measurements of atomic transition frequencies. The constra…
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