Atomic Level Shifts Research Articles

Mirror-mediated ultralong-range atomic dipole–dipole interactions

In three dimensions, dipole–dipole interactions which alter atomic level shifts and spontaneous decay rates only persist over distances comparable to the wavelength of the emitted light. In this paper we show that it is possible to significantly extend the range of these interactions with the help of a partially transparent asymmetric mirror interface. Suppose two two-level atoms are placed on opposite sides of the interface, each at the position of the mirror image of the other. In this case, their emitted light interferes almost exactly as it would when the atoms are right next to each other. Hence their dipole–dipole interaction assumes an additional maximum, even when the actual distance of the atoms is several orders of magnitude larger than the transition wavelength. Although the resulting ultralong-range interactions are in general relatively weak, we expect them to find applications in quantum technology, like non-invasive quantum sensing.

Isotope shifts in cadmium as a sensitive probe for physics beyond the standard model

Isotope shifts (ISs) of atomic energy levels are sensitive probes of nuclear structure and new physics beyond the standard model. We present an analysis of the ISs of the cadmium atom (Cd I) and singly charged cadmium ion (Cd II). ISs of the 229 nm, 326 nm, 361 nm and 480 nm lines of Cd I are measured with a variety of techniques; buffer–gas-cooled beam spectroscopy, capturing atoms in a magneto-optic-trap, and optical pumping. IS constants for the D1 and D2 lines of Cd II are calculated with high accuracy by employing analytical response relativistic coupled-cluster theory in the singles, doubles and triples approximations. Combining the calculations for Cd II with experiments, we infer IS constants for all low-lying transitions in Cd I. We benchmark existing calculations via different many-body methods against these constants. Our calculations for Cd II enable nuclear charge radii of Cd isotopes to be extracted with unprecedented accuracy. The combination of our precise calculations and measurements shows that King plots for Cd I can improve the state-of-the-art sensitivity to a new heavy boson by up to two orders of magnitude.

Hadronic vacuum polarization correction to atomic energy levels

The shift of atomic energy levels due to hadronic vacuum polarization is evaluated in a semiempirical way for hydrogenlike ions and for muonic hydrogen. A parametric hadronic polarization function obtained from experimental cross sections of $e^-e^+$ annihilation into hadrons is applied to derive an effective relativistic Uehling potential. The energy corrections originating from hadronic vacuum polarization are calculated for low-lying levels using analytical Dirac-Coulomb wave functions, as well as bound wave functions accounting for the finite nuclear size. Closed formulas for the hadronic Uehling potential of an extended nucleus as well as for the relativistic energy shift in case of a point-like nucleus are derived. These results are compared to existing analytic formulas from non-relativistic theory.

Optical magnetism and wavefront control by arrays of strontium atoms

By analyzing the parameters of electronic transitions, we show how bosonic Sr atoms in planar optical lattices can be engineered to exhibit optical magnetism and other higher-order electromagnetic multipoles that can be harnessed for wavefront control of incident light. Resonant $\lambda\simeq 2.6\mu$m light for the $^3D_1\rightarrow {^3}P_0$ transition mediates cooperative interactions between the atoms while the atoms are trapped in a deeply subwavelength optical lattice. The atoms then exhibit collective excitation eigenmodes, e.g., with a strong cooperative magnetic response at optical frequencies, despite individual atoms having negligible coupling to the magnetic component of light. We provide a detailed scheme to utilize excitations of such cooperative modes consisting of arrays of electromagnetic multipoles to form an atomic Huygens' surface, with complete $2\pi$ phase control of transmitted light and almost no reflection, allowing nearly arbitrary wavefront shaping. In the numerical examples, this is achieved by controlling the atomic level shifts of Sr with off-resonant ${^3P}_J\rightarrow {^3D}_1$ transitions, which results in a simultaneous excitation of arrays of electric dipoles and electric quadrupoles or magnetic dipoles. We demonstrate the wavefront engineering for a Sr array by realizing the steering of an incident beam and generation of a baby-Skyrmion texture in the transmitted light via a topologically nontrivial transition of a Gaussian beam to a Poincar\'{e} beam, which contains all possible polarizations in a single cross-section.

Energy shift of a uniformly moving two-level atom through a thermal reservoir

We investigate the implications of an atomic constant velocity in the energy shift of a two-level atom inside the thermal bath of a quantum scalar field, which is described by the Bose-Einstein distribution. The use of DDC formalism shows that the contribution of thermal fluctuations on the atomic level shifts depends on the atomic velocity and the temperature of the heat reservoir but the contribution of radiation reaction is totally insusceptible. The resulting energy shifts are analyzed and examined in detail under different circumstances. The atomic uniform linear motion always broadens the atomic level spacing in the limit of low temperature but narrows down it in the limit of high temperature. Our work clearly indicates that the moving heat reservoir shifts the atomic levels in a way quite different from that of the static one.

Observation of second- and higher-order electric quadrupole interactions with an atomic ion

The response of matter to fields underlies the physical sciences, from particle physics to astrophysics, and from chemistry to biophysics. We observe an atom's response to an electric quadrupole field to second- and higher orders; this arises from the atom's electric quadrupole polarizability and hyperpolarizabilities. We probe a single atomic ion which is excited to Rydberg states and confined in the electric fields of a Paul trap. The quadrupolar trapping fields cause atomic energy level shifts and give rise to spectral sidebands. The observed effects are described well by theory calculations.

Absorption imaging of trapped atoms in presence of AC-Stark shift

In this work, the effect of AC-Stark shift of atomic energy levels in an optical dipole trap (ODT) on in situ absorption imaging of the trapped atoms has been investigated. The Stark shift of various energy levels of 87Rb atoms relevant for trapping in the optical dipole trap (ODT) has been calculated. The spatially varying AC-Stark shift of energy levels due to ODT beam results in position dependent absorption cross-section of the atom at the absorption probe laser wavelength, which significantly modifies the measured optical density (OD) of the trapped atom cloud during the in situ absorption imaging. We have estimated the number of atoms trapped in the ODT taking AC-Stark shift into account. The estimated numbers are found to be higher at higher ODT beam power, making a qualitative agreement with larger trap depth at higher ODT beam power. This work can be particularly useful in estimating the in situ loss rate of atoms from the trap during the evaporative cooling of the trapped atom cloud.

Exact solution of the non-Hermitian eigenvalue problem for electron orbital excitations in a hydrogen atom

A new way of solving the spectral problem to describe electronic excitations is demonstrated for a hydrogen atom. The applied methodology is based formally on the idea of electronic excitation description without introducing boundary conditions to the eigenvalue problem for the square of the angular momentum operator. The eigenvalues of such an operator are considered as complex in general. As a result, the spectral problem for the Schrödinger equation becomes non-Hermitian with complex energy values. The imaginary part of the total energy helps to estimate the excitation lifetime within a unified scheme. The existence of the Stark shift of atomic energy levels and the collapse of the atomic spectra are confirmed.

Optical Magnetism and Huygens' Surfaces in Arrays of Atoms Induced by Cooperative Responses.

By utilizing strong optical resonant interactions in arrays of atoms with electric dipole transitions, we show how to synthesize collective optical responses that correspond to those formed by arrays of magnetic dipoles and other multipoles. Optically active magnetism with the strength comparable with that of electric dipole transitions is achieved in collective excitation eigenmodes of the array. By controlling the atomic level shifts, an array of spectrally overlapping, crossed electric and magnetic dipoles can be excited, providing a physical realization of a nearly reflectionless quantum Huygens' surface with the full 2π phase control of the transmitted light that allows for extreme wavefront engineering even at a single photon level. We illustrate this by creating a superposition of two different orbital angular momentum states of light from an ordinary input state that has no orbital angular momentum.

Influence of Stark-shift on quantum coherence and non-classical correlations for two two-level atoms interacting with a single-mode cavity field

An exact analytic solution for two two-level atoms coupled with a multi-photon single-mode electromagnetic cavity field in the presence of the Stark shift is derived. We assume that the field is initially prepared in a coherent state and the two atoms are initially prepared in excited state. Considering the atomic level shifts generated by the Stark shift effect, the dynamical behavior of both quantum coherence (QC) measured using a quantum Jensen–Shannon divergence and of quantum correlations captured by quantum discord (QD) are investigated. It is shown that the intensity-dependent Stark-shift in the cavity and the number of coherent state photons plays a key role in enhancing or destroying both QC and QD during the process of intrinsic decoherence. We remarked that increasing the Stark-shift parameters, the frequencies of the transition for the mode of the cavity field, and photons number destroy both the amount of QC and QD and affected their periodicity. More importantly, QC and QD exhibit similar behavior and both show a revival phenomenon. We believe that the present work shows that the quantum information protocols based on physical resources in optical systems could be controlled by adjusting the Stark-shift parameters.

Conjoint influence of quantum interference and Freeman resonance on substructures of the photoelectron spectra in above-threshold ionization

Based on the numerical solution of the full-dimensional time-dependent Schr\odinger equation, we study the above-threshold ionization of atomic hydrogen by subpicosecond laser pulses at wavelengths ranging from 300 nm to 800 nm, in which regime substructures of the photoelectron energy spectra resulting from quantum interference are entangled with those induced by the Freeman resonance. By analyzing the time-dependent populations and ac Stark energy shifts of the relevant atomic levels, and observing the pulse intensity dependence and the pulse length evolution of the spectra, we clearly identify the origins of the substructures exhibited in the spectra.

Nuclear Size Corrections to the Energy Levels of Single-Electron Atoms

A study is made of nuclear size corrections to the energy levels of single-electron atoms for the ground state of hydrogen like atoms. We consider Fermi charge distribution to the nucleus and calculate atomic energy level shift due to the finite size of the nucleus in the context of perturbation theory. The exact relativistic correction based upon the available analytical calculations is compared to the result of first-order relativistic perturbation theory and the non-relativistic approximation. We find small discrepancies between our perturbative results and those obtained from exact relativistic calculation even for large nuclear charge number Z.

Eliminating light shifts for single atom trapping

Microscopically controlled neutral atoms in optical tweezers and lattices have led to exciting advances in the study of quantum information and quantum many-body systems. The light shifts of atomic levels from the trapping potential in these systems can result in detrimental effects such as fluctuating dipole force heating, inhomogeneous detunings, and inhibition of laser cooling, which limits the atomic species that can be manipulated. In particular, these light shifts can be large enough to prevent loading into optical tweezers directly from a magneto-optical trap. We implement a general solution to these limitations by loading, as well as cooling and imaging the atoms with temporally alternating beams, and present an analysis of the role of heating and required cooling for single atom tweezer loading. Because this technique does not depend on any specific spectral properties, it should enable the optical tweezer platform to be extended to nearly any atomic or molecular species that can be laser cooled and optically trapped.

Attosecond transient absorption of argon atoms in the vacuum ultraviolet region: line energy shifts versus coherent population transfer

Using attosecond transient absorption, the dipole response of an argon atom in the vacuum ultraviolet (VUV) region is studied when an external electromagnetic field is present. An isolated attosecond VUV pulse populates Rydberg states lying 15 eV above the argon ground state. A synchronized few-cycle near infrared (NIR) pulse modifies the oscillating dipoles of argon impulsively, leading to alterations in the VUV absorption spectra. As the NIR pulse is delayed with respect to the VUV pulse, multiple features in the absorption profile emerge simultaneously including line broadening, sideband structure, sub-cycle fast modulations, and 5–10 fs slow modulations. These features indicate the coexistence of two general processes of the light–matter interaction: the energy shift of individual atomic levels and coherent population transfer between atomic eigenstates, revealing coherent superpositions. An intuitive formula is derived to treat both effects in a unifying framework, allowing one to identify and quantify the two processes in a single absorption spectrogram.

Environment dependence of magnetic moment and atomic level shifts within tight-binding approximation: An illustration in the case of cobalt

Most of tight-binding studies of transition metal based systems deviating from perfect bulk (surfaces, nanoparticles, alloys) are based on local charge neutrality rules per site, per valence orbital and per element. Unfortunately, such rules do not hold per spin when interested in magnetic elements. We present here a simple way to characterize the variation of the magnetic moment with the environment and to generalize the tight-binding expression of the energy to account for magnetism. This is illustrated in the particular case of cobalt, going from perfect pure bulk to surface, nanoparticles and then CoPt alloy.

Parity-time-antisymmetric atomic lattices without gain

Lossy atomic photonic crystals can be suitably tailored so that the real and imaginary parts of the susceptibility are, respectively, an odd and an even function of position. Such a parity-time $(PT)$ space antisymmetry in the susceptibility requires neither optical gain nor negative refraction, but is rather attained by a combined control of the spatial modulation of both the atomic density and their dynamic level shift. These passive photonic crystals made of dressed atoms are characterized by a tunable unidirectional reflectionlessness accompanied by an appreciable degree of transmission. Interestingly, such peculiar properties are associated with non-Hermitian degeneracies of the crystal scattering matrix, which can then be directly observed through reflectivity measurements via a straightforward phase modulation of the atomic dynamic level shift and even off resonance.

Erratum: Multipolar theory of blackbody radiation shift of atomic energy levels and its implications for optical lattice clocks [Phys. Rev. A74, 020502(R) (2006)

Erratum: Multipolar theory of blackbody radiation shift of atomic energy levels and its implications for optical lattice clocks [Phys. Rev. A<b>74</b>, 020502(R) (2006)

Ionization cross sections and contributions of continuum to optical characteristics of Rydberg states

Simple analytical properties of ionization cross sections allow high-precision evaluations of contributions from integrals over continuum to sum rules for oscillator-strength moments and to the blackbody-radiation-induced shifts of atomic levels. The contributions from continuum and from infinite sums over discrete states are presented in terms of the cross section for the threshold photoionization. General properties of the indicated contributions are determined for bound states with small angular momenta (l ⩽ 3) in hydrogen atoms. Asymptotic presentations for the contributions from continuum to the sums of oscillator-strength moments are proposed for highly excited Rydberg states. The estimate is given to the accuracy of determining the infinite sum over discrete states by a sum of a finite number of terms.

Lamb shift for static atoms outside a Schwarzschild black hole

We study, by separately calculating the contributions of vacuum fluctuations and radiation reaction to the atomic energy level shift, the Lamb shift of a static two-level atom interacting with real massless scalar fields in the Boulware, Unruh and Hartle-Hawking vacuums outside a Schwarzschild black hole. We find that in the Boulware vacuum, the Lamb shift gets a correction arising as a result of the backscattering of vacuum field modes off the space-time curvature, which is reminiscent of the correction to the Lamb shift induced by the presence of cavities. However, when the Unruh and Hartle-Hawking vacua are concerned, our results show that the Lamb shift behaves as if the atom were irradiated by a thermal radiation or immersed in a thermal bath at the Hawking temperature, depending on whether the scalar field is in the Unruh or the Hartle-Hawking vacuum. Remarkably, the thermal radiation is always backscattered by the space-time geometry.

Position-dependent energy-level shifts of an accelerated atom in the presence of a boundary

We consider a uniformly accelerated atom interacting with a vacuum electromagnetic field in the presence of an infinite conducting plane boundary and calculate separately the contributions of vacuum fluctuations and radiation reaction to the atomic energy level shift. We analyze in detail the behavior of the total energy shift in three different regimes of the distance in both the low acceleration and high acceleration limits. Our results show that, in general, an accelerated atom does not behave as if immersed in a thermal bath at the Unruh temperature in terms of the atomic energy level shifts, and the effect of the acceleration on the atomic energy level shifts may in principle become appreciable in certain circumstances, although it may not be realistic for actual experimental measurements. We also examine the effects of the acceleration on the level shifts when the acceleration is of the order of the transition frequency of the atom and we find some features differ from what was obtained in the existing literature.