Eric-Olivier Le Bigot, P. Indelicato, P. J. Mohr
We present numerical values for the self-energy shifts predicted by QED (Quantum Electrodynamics) for hydrogenlike ions (nuclear charge $60 \le Z \le 110$) with an electron in an $n=3$, 4 or 5 level with high angular momentum ($5/2\le j \le 9/2$). Applications include predictions of precision transition energies and studies of the outer-shell structure of atoms and ions.
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We present an introduction to the principles behind atomic energy level calculations with Quantum Electrodynamics (QED) and the two-time Green's function method; this method allows one to calculate an effective Hamiltonian that contains all QED effects and that can be used to predict QED Lamb shifts of degenerate, quasidegenerate and isolated atomic levels.
The FAC, GRASP2K, and MCDFGME codes are compared in three case study of radiative transitions occurring in tungsten ions: (i) Ni1 and Ni2 lines in Ni-like tungsten, (ii) $3p_{3/2}{-}3p_{1/2}$ fine splitting in Cl-like tungsten, and (iii) $Kα_{1}$ and $Kα_{2}$ lines in W VIII. Various approaches to including the Breit interaction term and QED corrections in atomic calculations are examined. Electron correlation effects are also investigated and compared to the Breit and QED contributions. The data presented here may be used to estimate theoretical uncertainties relevant to interpretation of hig…
QED calculations of intra-$L$-shell doubly excited states in Be-like ions
本研究采用严格QED方法计算宽核电荷数范围内类铍高电荷离子的L壳层内双激发态能级，解决近简并能级混合问题，所得结果是目前该体系最精确的理论描述，与实验数据吻合良好。
QED calculations of intra-$L$-shell singly excited states in Be-like ions
本研究针对类铍高电荷离子的L壳层内单激发态，结合准简并QED微扰理论等方法计算激发与跃迁能，考虑多种效应并分析不确定性，得到与实验高度吻合的高精度理论预测。
The quantum electrodynamic theory of the nuclear recoil effect on the atomic g factor to all orders in αZ and to first order in m/M is formulated. The complete αZ-dependence formula for the recoil correction to the bound-electron g factor in a hydrogenlike atom is derived. This formula is used to calculate the recoil correction to the bound-electron g factor in the order (αZ)^2 m/M for an arbitrary state of a hydrogenlike atom.
The Markovian approximation is widely applied in the field of quantum optics due to the weak frequency dependence of the vacuum field amplitude, and in consequence non-Markovian effects are typically regarded to play a minor role in the optical electron-photon interaction. Here, we give an example where non-Markovianity changes the qualitative behavior of a quantum optical system, rendering the Markovian approximation quantitatively and qualitatively insufficient. Namely, we study a multiple-emitter, multiple-excitation waveguide quantum-electrodynamic (waveguide-QED) system and include propag…
We propose simple analytic, non-orthogonal but selectively orthogonalizable, generalized Laguerre type atomic orbitals, providing clear physical interpretation and near equivalent accuracy with numerical multi-configuration self-consistent field, to atomic configuration interaction calculations. By analyzing the general Eckart theorem we use their simple interpretation, via a thorough investigation in orbital space, to estimate, for the first time (the exact value being, or considered, unknown), an ab-initio energy uncertainty, i.e. proximity to the exact energy, for several excited atomic sta…
An approach, based on the use of the quasiclassical Green's function, is developed for investigating high-energy quantum electrodynamical processes in combined strong laser and atomic fields. Employing an operator technique, we derive the Green's function of the Dirac equation in an arbitrary plane wave and a localized potential. Then, we calculate the total cross section of high-energy electron-positron photoproduction in an atomic field of arbitrary charge number (Bethe-Heitler process) in the presence of a strong laser field. It is shown that the laser field substantially modifies the cross…
We use the radiative potential method to perform a detailed study of quantum electrodynamics (QED) radiative corrections to electric dipole (E1) transition amplitudes in heavy alkali-metal atoms Rb, Cs, Fr, and alkali-metal-like ions Sr+, Ba+, and Ra+. The validity of the method is checked by comparing with the results of rigorous QED in simple atomic potentials. We study the effects of core relaxation, polarization of the core by the E1 field, and valence-core correlations on QED, which are shown to be important in some cases. We identify several transitions for which the QED contribution exc…
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine-structure constant $α$. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, $r_1$, $r_2$ and $r = |\vec{r}_1-\vec{r}_2|$. The choice of the exponential basis functions of the form $\exp(-αr_1 -βr_2 -γr)$ allows us to construct an accurate and c…
We report a clear evidence of atomic fractals in the nonlinear motion of a two-level atom in a standing-wave microcavity. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependencies of outgoing positions and momenta of scattered atoms on their ingoing values and in the dependence of exit times of cold atoms on their initial momenta in the generic semiclassical models of cavity QED (1) with atoms in a far-detuned amplitude (phase)-modulated standing wave and (2) with coupled atomic external and internal degrees of freedom. Tiny interplay between all the de…
The photon polarization operator in superstrong magnetic fields induces the dynamical photon "mass" which leads to screening of Coulomb potential at small distances $z\ll 1/m$, $m$ is the mass of an electron. We demonstrate that this behaviour is qualitatively different from the case of D=2 QED, where the same formula for a polarization operator leads to screening at large distances as well. Because of screening the ground state energy of the hydrogen atom at the magnetic fields $B \gg m^2/e^3$ has the finite value $E_0 = -me^4/2 \ln^2(1/e^6)$.
We theoretically explore manipulation of interactions between excited and ground state atoms at nanoscale separations by cavity quantum electrodynamics (CQED). We develop an adiabatic molecular dressed state formalism and show that it is possible to generate Fano-Feshbach resonances between ground and long-lived excited-state atoms inside a cavity. The resonances are shown to arise due to non-adiabatic coupling near a pseudo-crossing between the dressed state potentials. We illustrate our results with a model study using fermionic $^{171}$Yb atoms in a two-modal cavity. Our study is important …
Correlation Localization in Waveguide QED with Delayed Interactions
研究布拉格条件下有延迟非马尔可夫相互作用的原子阵列中原子间关联长度，从单个激发原子出发，利用其激发扩散达稳态，发现剩余激发定位于初始原子附近，关联长度随延迟幂律下降，揭示延迟对关联传输的影响。
This paper presents a setup capable of producing a high-flux continuous beam of cold rubidium atoms for cavity QED experiments in the regime of strong coupling. A 2 $D^+$ MOT, loaded by rubidium getters in a dry film coated vapor cell, fed a secondary moving-molasses MOT (MM-MOT) at a rate of 1.5 x $10^{10}$ atoms/sec. The MM-MOT provided a continuous beam with tunable velocity. This beam was then directed through the waist of a 280 $μ$m cavity resulting in a Rabi splitting of more than +/- 10 MHz. The presence of sufficient number of atoms in the cavity mode also enabled splitting in the pola…
The derivation of leading quantum electrodynamic corrections to the nuclear magnetic shielding in light hydrogen- and helium-like atomic systems is described in detail. The presented theoretical approach applies to any light atomic and molecular systems, enabling the determination of the magnetic moment of light nuclei with much higher precision than known presently.
Continuous cavity-QED with an atomic beam
该研究设计了一种产生连续原子束穿过光学腔的装置，实现集体强耦合并测量连续光学增益，为连续超辐射激光等集体现象的阈值条件研究奠定基础。
Energy levels and fine-structure intervals of the $1s2l2l'$ core-excited states are calculated for ions along the Li isoelectronic sequence from argon to uranium. The calculation is performed by the relativistic configuration-interaction method adapted for treatment of autoionizing core-excited states. The calculational approach includes the relativistic treatment of the nuclear recoil effect, the leading QED shifts as delivered by the model QED operator, and the frequency dependence of the Breit interaction. The $1s2l2l'-1s^22l$ transition energies are obtained by combining the present result…
We discuss how we formulate time evolution of physical quantities in the framework of the Rigged QED (Quantum Electrodynamics). The Rigged QED is a theory which has been proposed to treat dynamics of electrons, photons and atomic nuclei in atomic and molecular systems in a quantum field theoretic way. To solve the dynamics in the Rigged QED, we need different techniques from those developed for the conventional QED. As a first step toward this issue, we propose a procedure to expand the Dirac field operator, which represents electrons, by the electron annihilation/creation operators and soluti…
Probing "Continuous Spin" QED with Rare Atomic Transitions
提出路径积分方法计算非零自旋Casimir参数下标量QED原子跃迁，发现新衰变通道显著改变禁戒跃迁速率，为实验室检验QED提供新方向。
We study the reflection of two counter-propagating modes of the light field in a ring resonator by ultracold atoms either in the Mott insulator state or in the superfluid state of an optical lattice. We obtain exact numerical results for a simple two-well model and carry out statistical calculations appropriate for the full lattice case. We find that the dynamics of the reflected light strongly depends on both the lattice spacing and the state of the matter-wave field. Depending on the lattice spacing, the light field is sensitive to various density-density correlation functions of the atoms. …
A simple model based on QED is presented for the estimation of contribution of the excited level few-photon decays to the radiation escape from the matter in the epoch of the cosmological hydrogen recombination. It is shown that apart from the widely studied two-photon decays, some specific 3-photon decays can contribute on the level of 0.1% accuracy, required by the recent astrophysical observations.
Simultaneous Multiphoton-Multiatom Processes in Atomic Gases under Laser Fields
本文研究激光场下原子气体中多原子同时吸收光子激发的集体QED过程，揭示其独立于原子间相互作用的特征长度尺度，并提出实验方案加以验证。
We describe a method to observe the dynamics of an excited-state transition in a room temperature atomic vapor using hyperfine quantum beats. Our experiment using cesium atoms consists of a pulsed excitation of the D2 transition, and continuous-wave driving of an excited-state transition from the 6P$_{3/2}$ state to the 7S$_{1/2}$ state. We observe quantum beats in the fluorescence from the 6P$_{3/2}$ state which are modified by the driving of the excited-state transition. The Fourier spectrum of the beat signal yields evidence of Autler-Townes splitting of the 6P$_{3/2}$, F = 5 hyperfine leve…
The emission of light from a multiply excited atomic ensemble is examined and it is shown how symmetric (spin-wave) and non-symmetric states of excitation radiate into spatially separate field modes. This observation has potential application to single photon generation and spin wave entanglement, since in the presence of atomic interactions it can result in isolated single photon emission into a phase-matched field mode.
We perform ab initio QED calculations of energy levels for the $n=1$ and $n=2$ states of He-like ions with the nuclear charge in the range $Z = 12$-100. The complete set of two-electron QED corrections is evaluated to all orders in the parameter $\aZ$. Uncalculated contributions to energy levels come through orders $α^3 (\aZ)^2$, $α^2 (\aZ)^7$, and higher. The calculation presented is the first treatment for excited states of He-like ions complete through order $α^2 (\aZ)^4$. A significant improvement in accuracy of theoretical predictions is achieved, especially in the high-$Z$ region.
Programmable cavity QED with a fiber-integrated atomic array
本研究结合12位点⁸⁷Rb光镊阵列与高协同度光纤法布里-珀罗微腔，实现单原子耦合强度的连续调控，测量集体增强真空拉比分裂并完成原子数非破坏性读出，为光纤集成量子网络节点提供可扩展架构。
A two-dimensional model atom is employed to study the ionization behavior of initially excited atomic states in highly-frequent intense laser pulses beyond the dipole approximation. An additional regime of ionization suppression is found at laser intensities where the stabilization effect is expected to break down. The appearance of this effect is due to a strong coupling of the initial wave function to the ground state of the cycle-averaged space-translated ionic potential, followed by a subsequent population transfer to the ground state during the laser pulse turn-off. Non-dipole effects are…
Results of a calculation valid to all orders in the nuclear-strength parameter Zαare presented for the two-loop Lamb shift, notably for the two-loop self-energy correction, for the ground and first excited states of ions with the nuclear charge numbers Z=60-100. A detailed comparison of the all-order calculation with earlier investigations based on an expansion in the parameter Zαis given. The calculation removes the largest theoretical uncertainty for the 2p_j-2s transition energies in heavy Li-like ions and is important for interpretation of experimental data.
Accurate calculations of phase lag associated with coherent control where an excited system decays into more than one product channel have recently been reported for atomic barium in PhysRevA.105.013113 (2022). The present study extends the calculations to make predictions of that observable for another alkaline earth atom, strontium, with a discussion of its spectrum and phase lag for energies between the $Sr^{+}$ $4d_{3/2}$ and $4d_{5/2}$ thresholds. We will explore the physics influenced by the electron correlations of strontium and the long-range Coulomb potential. The behavior of the phas…
We show that the highly excited rovibrational spectra of a diatomic molecule and the closely related slow atomic collision processes contain more systematics and require less parameters to characterize than the Rydberg spectrum of an atom. In the case of a single channel, for example, we show that a single short-range parameter gives a complete description of slow collisions for practically all angular momenta, and covers an energy range of hundreds of millikelvins. The same parameter also describes the highly excited rovibrational spectra in the threshold region, including states of different…
We measure inelastic collisional cross sections for the ground $^3$F$_2$ state and the excited $^3$P$_0$ state of atomic thorium in cold collisions with $^3$He. We determine for Th ($^3$F$_2$) at 800 mK the ratio $γ\approx 500$ of the momentum-transfer to Zeeman relaxation cross sections for collisions with $^3$He. For Th ($^3$P$_0$), we study electronic inelastic processes and find no quenching even after $10^6$ collisions. We also determine the radiative lifetime of Th ($^3$P$_0$) to be $τ> 130$ ms. This great stability of the metastable state opens up the possibility for further study, incl…
Subradiant excited states in finite chains of two-level quantum emitters coupled to a one-dimensional reservoir are a resource for superior photon storage and controlled photon manipulation. Typically, states storing multiple excitations exhibit fermionic correlations and are thus characterized by an anti-symmetric wavefunction, which makes them hard to prepare experimentally. Here we identify a class of quasi-localized dark states with up to half of the qubits excited, which appear for lattice constants that are an integer multiple of the guided-mode wavelength. They allow for a high-fidelity…
On the basis of general theoretical results developed previously in [I. M. Sokolov et al., J. Exp. Theor. Phys. 112, 246 (2011)], we analyze spontaneous decay of a single atom inside cold atomic clouds under conditions when the averaged interatomic separation is less or comparable with the wavelength of quasi resonant radiation. Beyond the decay dynamics we analyze shifts of resonance as well as distortion of the spectral shape of the atomic transition.
We present systematic calculations of energy levels of the $1s^22l$ and $1s2l2l'$ states of ions along the lithium isoelectronic sequence from carbon till chlorine. The calculations are performed by using the relativistic-configuration-interaction method adapted to the treatment of autoionizing core-excited states. The relativistic energies are supplemented with the QED energy shifts calculated within the model QED operator approach. A systematic estimation of the theoretical uncertainties is performed for every electronic state and every nuclear charge. The results are in agreement with exist…
We propose a novel method that uses the oscillation of an atomic excited wave packet observed through a pump-probe technique to accurately determine the zero time delay between a pair of ultrashort laser pulses. This physically-based approach provides an easy fix for the intractable problem of synchronizing two different femtosecond laser pulses in a practical experimental environment, especially where an in situ time zero measurement with high accuracy is required.
We study the excitation redistribution from cesium $7\mathrm{P}_{1/2}$ or $7\mathrm{P}_{3/2}$ to neighboring energy levels by Black Body Radiation (BBR) and inter atomic collisions using pump-probe spectroscopy inside a vapor cell. At low vapor densities we measure redistribution of the initial, velocity-selected, atomic excitation by BBR. This preserves the selected atomic velocities allowing us to perform high resolution spectroscopy of the $\mathrm{6D\rightarrow 7F}$ transitions. This transfer mechanism could also be used to perform sub-Doppler spectroscopy of the cesium highly-excited $\ma…
Sub-part-per-trillion test of the Standard Model with atomic hydrogen
通过高精度测量氢原子2S-6P跃迁频率，验证了标准模型的预测，将QED修正测试精度提升至0.5 ppm，达到0.7 ppt水平。
In cavity quantum electrodynamics (QED), the interaction between an atomic transition and the cavity field is measured by the vacuum Rabi frequency $Ω_0$. The analogous term "circuit QED" has been introduced for Josephson junctions, because superconducting circuits behave as artificial atoms coupled to the bosonic field of a resonator. In the regime with $Ω_0$ comparable to the two-level transition frequency, "superradiant" quantum phase transitions for the cavity vacuum have been predicted, e.g. within the Dicke model. Here, we prove that if the time-independent light-matter Hamiltonian is co…
We consider the phase stability of a local oscillator (or laser) locked to a cavity QED system comprised of atoms with an ultra-narrow optical transition. The atoms are cooled to millikelvin temperatures and then released into the optical cavity. Although the atomic motion introduces Doppler broadening, the standing wave nature of the cavity causes saturated absorption features to appear, which are much narrower than the Doppler width. These features can be used to achieve an extremely high degree of phase stabilization, competitive with the current state-of-the-art. Furthermore, the inhomogen…
Testing strong-field QED to second-order in the highly correlated atomic system berylliumlike Pb78+ by electron-ion recombination spectroscopy
本研究通过测量类铍Pb$^{78+}$离子的电子-离子复合光谱，精确测定了其激发能，验证了二阶强场QED理论，并指出实验精度可进一步提升。
The current status of bound state quantum electrodynamics calculations of transition energies for few-electron ions is reviewed. Evaluation of one and two body QED correction is presented, as well as methods to evaluate many-body effects that cannot beevaluated with present-day QED calculations. Experimental methods, their evolution over time, as well as progress in accuracy are presented. A detailed, quantitative, comparison between theory and experiment is presented for transition energies in few-electron ions. In particular the impact of the nuclear size correction on the quality of QED tes…
Following detailed analysis of relativistic, QED and mass corrections for helium-like and lithium-like ions with static nuclei for $Z \leq 20$ the domain of applicability of Non-Relativistic QED (NRQED) is localized for ground state energy. It is demonstrated that for both helium-like and lithium-like ions with $Z \leq 20$ the finite nuclear mass effects do not change 4-5 significant digits (s.d.), and the leading relativistic and QED effects leave unchanged 3-4 s.d. in the ground state energy. It is shown that the non-relativistic ground state energy can be interpolated with accuracy not less…
Compact Blackbody Radiation Atomic Sensor: Measuring Temperature using Optically Excited Atoms in Vapor Cells
本文提出一种基于蒸汽池中光激发铷原子的紧凑型黑体辐射温度计，实现快速高精度测温，并展示自校准方案向基准温度计迈进。
Coherence relaxation in Na vapor was studied utilizing a pump-probe method with femtosecond pulses. The coherence was created by the pump pulse, which excited the Na atoms to the 4S state. The atoms were further excited to the 7P state by the probe pulse. As a result a coherent UV radiation was emitted by the atoms. This emission was used to study the relaxation of both the 4S-3S and 7P-3S coherent superpositions. The relaxation is mainly due to collisions with the Ar atoms serving as a buffer gas. Coherence relaxation times and collisional cross-sections for the Na-Ar collision pairs were ext…
The leading quantum electrodynamic corrections to the nuclear magnetic shielding in one- and two-electron atomic systems are obtained in a complete form, and the shielding constants of $^1$H, $^3$He$^+$, and $^3$He are calculated to be $17.735\,436(3) \cdot 10^{-6}$, $35.507\,434(9)\cdot 10^{-6}$, and $59.967\,029(23)\cdot 10^{-6}$, respectively. These results are orders of magnitude more accurate than previous ones, and, with the ongoing measurement of the nuclear magnetic moment of $^3$He$^+$ and planned $^3$He$^{2+}$, they open the window for high-precision absolute magnetometry using $^3$H…
We report the implementation of equation-of-motion coupled-cluster (EOMCC) method in the four-component relativistic framework with the spherical atomic potential to generate the excited states from a closed-shell atomic configuration. This theoretical development will be very useful to carry out high precision calculations of varieties of atomic properties in many atomic systems. We employ this method to calculate excitation energies of many low-lying states in a few Ne-like highly charged ions, such as Cr XV, Fe XVII, Co XVIII and Ni XIX ions, and compare them against their corresponding exp…
Classical variable stars called RR Lyrae stars have pulsating outer envelopes comprised of excited atoms. Here we demonstrate that the qualitative and quantitative properties of RR Lyrae variables and one subclass of their atomic scale constituents: singly-excited helium atoms undergoing transitions between Rydberg states, share a remarkable degree of self-similarity. In terms of masses, radii, oscillation periods, morphologies and kinematics the stellar and atomic analogues obey a simple set of discrete self-similar scaling equations. The concept of stellar/atomic self-similarity may prove us…
Two-photon decay rates in simple atoms such as hydrogenlike systems represent rather interesting fundamental problems in atomic physics. The sum of the energies of the two emitted photons has to fulfill an energy conservation condition, the decay takes place via intermediate virtual states, and the total decay rate is obtained after an integration over the energy of one of the emitted photons. Here, we investigate cases with a virtual state having an energy intermediate between the initial and the final state of the decay process, and we show that due to non-uniform convergence, only a careful…
Studies of ultracold atoms in optical lattices link various disciplines, providing a playground where fundamental quantum many-body concepts, formulated in condensed-matter physics, can be tested in much better controllable atomic systems, e.g., strongly correlated phases, quantum information processing. Standard methods to measure quantum properties of Bose-Einstein condensates (BECs) are based on matter-wave interference between atoms released from traps which destroys the system. Here we propose a nondestructive method based on optical measurements, and prove that atomic statistics can be m…
Interaction between Rydberg atoms can significantly modify Rydberg excitation dynamics. Under a resonant driving field the Rydberg-Rydberg interaction in high-lying states can induce shifts in the atomic resonance such that a secondary Rydberg excitation becomes unlikely leading to the Rydberg blockade effect. In a related effect, off-resonant coupling of light to Rydberg states of atoms contributes to the Rydberg anti-blockade effect where the Rydberg interaction creates a resonant condition that promotes a secondary excitation in a Rydberg atomic gas. Here, we study the light-matter interact…
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