Tunable targeted single-photon routing in a waveguide-QED structure containing a time-modulated two-level atom

yang lan, Haozhen Li, Ran Zeng, Xiaopei Zhang, Miao Hu, mengmeng xu, xuefang zhou, and Qiliang Li

DOI: 10.1364/JOSAB.521931 Received 20 Feb 2024; Accepted 13 May 2024; Posted 13 May 2024  View: PDF

Abstract: Single-photon routing between two one-dimensional waveguides mediated by a single mode cavity embedded with a time-modulated two-level atom is investigated. Two configurations, where the single-photon incident from an infinite or semi-infinite waveguide, are considered. Using the analytical expressions of the single-photon scattering amplitudes, the transmission behaviors in the two waveguides are discussed. The results show that the time modulation of the atomic frequency enables a dynamically tunable quantum router. A single-photon with different frequencies can be routed dynamically from the incident waveguide to the other by properly manipulating the amplitude-to-frequency ratio of the atom. The routing efficiency can be improved to approach 100% by terminating the incident waveguide. In the semi-waveguide configuration, the routing behaviors controlled by the quantum coherent feedback is also investigated. The influence of the phase shifts introduced by the terminated waveguide on the routing capability and the conditions for perfect single-photon routing are discussed in detail. A frequency tunable targeted single-photon router can even be realized associated with the help of chiral coupling. These results may be beneficial to the photon control in quantum network based on time-modulated quantum nodes.

Deterministic preparation of optical qubits with coherent feedback control

Amy Rouillard, Tanita Permaul, Sandeep Goyal, and Thomas Konrad

DOI: 10.1364/JOSAB.523407 Received 08 Mar 2024; Accepted 12 May 2024; Posted 13 May 2024  View: PDF

Abstract: We propose a class of preparation schemes for orbital angular momentum and polarisation qubits carried by single photons or classical states of light based on coherent feedback control by an ancillary degree of freedom of light. The preparation methods use linear optics and include the transcription of an arbitrary polarisation state onto a two-level OAM system (swap) for arbitrary OAM values $\pm\ell$ within a light beam, i.e. without spatial interferometer. The preparations can be carried out with unit efficiency independent from the potentially unknown initial state of the system. The swap scheme also allows us to implement arbitrary unitary gates on OAM qubits ($\pm\ell$) by reducing them to polarisation gates. In addition, we show how to translate measurement-based qubit control channels into coherent feedback schemes for optical implementation.

Fractional squashed entanglement and its efficiency

Eman El-Hadidy, KHADIJA EL ANOUZ, and Nasser Metwally

DOI: 10.1364/JOSAB.519282 Received 17 Jan 2024; Accepted 11 May 2024; Posted 13 May 2024  View: PDF

Abstract: In this article we investigate the fractional quantum correlations via squashed entanglement and negativity, where an analytical solution of fractional Schr\"{o}dinger equation under an $XXX$ model of a spin-spin Hamiltonian has introduced. It has shown that, by starting with initially large entangled state, both quantifiers decrease during the interaction. This decay, increases as one increases the degree of the fractional order and the coupling constant between the two spins. However, the squashed entanglement and the negativity increase gradually if the initial state contains a small amount of quantum correlations. The sudden/gradually changes of these phenomena have observed at small/large values of the fractional order, respectively. The constantly behavior of these measures is observed at small values of the fractional orders. Our results show that, the fractional state can be used as a quantum channel with high efficiency to perform quantum teleportation. The long-lived constantly behavior of the teleportation inequality indicates that the efficiency of this channel will be a constant during the teleportation process.

The spectral continuum in the Rabi-Stark model

Daniel Braak, Lei Cong, Hans-Peter Eckle, Henrik Johannesson, and Elinor Twyeffort

DOI: 10.1364/JOSAB.524014 Received 15 Mar 2024; Accepted 08 May 2024; Posted 09 May 2024  View: PDF

Abstract: The Rabi-Stark model is a non-linear generalization of the quantum Rabi model including the dynamical Stark shift as a tunable term, which can be realized via quantum simulation on a cavity QED platform. When the Stark coupling becomes equal to the mode frequency, the spectrum changes drastically, a transition usually termed ``spectral collapse" because numerical studies indicate an infinitely degenerate ground state. We show that the spectrum extends continuously from a threshold value up to infinity. A set of normalizable states are embedded in the continuum which furnishes an unexpected analogy to the atomic Stark effect. Bound states and continuum can be obtained analytically through two equally justified, but different confluence processes of the associated differential equation in Bargmann space. Moreover, these results are obtained independently using a method based on adiabatic elimination of the spin degree of freedom and corroborated through large-scale numerical checks.

Relative strengths of sum and difference frequency generation in perturbative high harmonic wave mixing

Zhengyan Li, Zijuan Wei, Mingdong Yan, Fan Xia, Ting Men, Weiqi Tang, Weiwei Yan, and Shiyuan Liu

DOI: 10.1364/JOSAB.525386 Received 01 Apr 2024; Accepted 06 May 2024; Posted 09 May 2024  View: PDF

Abstract: High harmonic generation (HHG) modulated by a weak laser field allows the perturbative wave mixing process which involves sum and difference frequency generations (SFG and DFG). The relative strengths of SFG and DFG have been extensively discussed in the literature but are still ambiguous. Here we experimentally study the relative strengths between SFG and DFG channels by applying a frequency-offset second-harmonic perturbing laser field collinearly in a thin gaseous nonlinear medium. It shows that SFG is favored for low harmonic orders but DFG dominates for high energy photons, when only short trajectories of high harmonics are considered. A semi-classical model incorporating both modulations to the tunneling ionization and the electron propagation steps by the perturbing laser field for a train of attosecond pulses explains the experimental results.

Jaynes-Cummings atoms coupled to a structured environment: Leakage elimination operators and the Petz recovery maps

Dawei Luo and Ting Yu

DOI: 10.1364/JOSAB.522819 Received 04 Mar 2024; Accepted 06 May 2024; Posted 07 May 2024  View: PDF

Abstract: We consider the Jaynes-Cummings (JC) model embedded in a structured environment, where the atom inside an optical cavity would sense a hierarchical environment consisting of the cavity and its environment. We propose several effective strategies to control and suppress the decoherence effects to protect the quantum coherence of the JC atom. We study the non-perturbative control of the system dynamics by means of the leakage elimination operators. We have established a full quantum state reversal scheme by engineering the system and its coupling to the bath via the Petz recovery map. Our findings include that, with the Petz recovery map, the dynamics of the JC atom can be fully recovered regardless of Markov or non-Markovian noises. Finally, we show that our quantum control and recovery methods are effective at protecting different aspects of the system coherence.

Strong Raman enhancement in structured colloids

Jessica Dipold, Niklaus Wetter, Francisco Marques, Anderson Freitas, Aristide Dogariu, and Ernesto Jimenez Villar

DOI: 10.1364/JOSAB.523100 Received 07 Mar 2024; Accepted 06 May 2024; Posted 06 May 2024  View: PDF

Abstract: Raman spectroscopy is a powerful technique for studying the interaction between light and matter. Here we show a significant enhancement of Raman emission over a broad range of pumping wavelengths from strongly scattering media comprising spatially-correlated photonic structures of core-shell TiO2@Silica scatterers mixed with silica nanoparticles and suspended in ethanol. Long-range Coulomb interactions between nanoparticles inside these photonic colloidal structures induce a correlation in the scatterers’ positions (TiO2@Silica), affecting local and global photonic properties. The anomalous enhancement in Raman signal increases as the scattering strength is increased (either through scatterer concentration or pumping wavelength), however, the signal strength continues to behave linearly with excitation power, ruling out classical nonlinear and interferential phenomena. These observations may indicate strong photon correlation in strongly localized electromagnetic modes, inducing successive photon interactions with the atoms or molecules. Aside from the fundamental relevance to understanding measurable properties in this regime of strongly localized electromagnetic modes, our demonstration of strongly enhanced Raman emission over a broad range of pumping wavelength provides new opportunities for the development of advanced photonic materials and devices.

Generation of complex beams using flattening of binary gratings

Anil Ringne, Nirjhar Kumar, Subrata Karmakar, Pratyush Pushkar, and Ananth Krishnan

DOI: 10.1364/JOSAB.518682 Received 16 Jan 2024; Accepted 04 May 2024; Posted 06 May 2024  View: PDF

Abstract: The generation of complex beams, such as composite vortex beams, using the logical flattening of two or more co-oriented and registered gratings is demonstrated theoretically and experimentally. The geometrical aspects of such gratings were examined to generate composite vortex beams with the desired intensity and orientation. The proposed methodology was extended to produce other complex beams, such as Laguerre Gaussian transformed Hermite Gaussian and composite vortex transformed airy beams.

Effects of classical drivings on the power broadening of atomic lineshapes

Leonardi Hernández Sánchez, IVAN BOCANEGRA GARAY, Iran Ramos Prieto, Francisco Soto-Eguibar, and Hector Moya-Cessa

DOI: 10.1364/JOSAB.522587 Received 29 Feb 2024; Accepted 04 May 2024; Posted 06 May 2024  View: PDF

Abstract: In the framework of the Jaynes-Cummings model, we investigate how atomic lineshapes are affected by coherently driving the atom-field interaction. We pay particular attention to the two-level atom interaction with a thermal quantized field, when both are influenced by external classical fields. Adopting a density matrix formalism, we calculate the average atomic inversion and demonstrate how the corresponding lineshapes vary as a function of the average number of thermal photons, and the atom-field classical coupling. Furthermore, we compare these results with those obtained from the standard Jaynes-Cummings model and validate our findings through numerical simulations.

Cavity QED systems for steady-state sources of Wigner-negative light

Alexander Elliott and Andrew Scott Parkins

DOI: 10.1364/JOSAB.524030 Received 18 Mar 2024; Accepted 02 May 2024; Posted 03 May 2024  View: PDF

Abstract: We present a theoretical investigation of optical cavity QED systems, as described by the driven, open Jaynes-Cummings model and some of its variants, as potential sources of steady-state Wigner-negative light. We consider temporal modes in the continuous output field from the cavity and demonstrate pronounced negativity in their Wigner distributions for experimentally-relevant parameter regimes. We consider models of both single and collective atomic spin systems, and find a rich structure of Wigner-distribution negativity as the spin size is varied. We also demonstrate an effective realization of all of the models considered using just a single ${}^{87}$Rb atom and based upon combinations of laser- and laser-plus-cavity-driven Raman transitions between magnetic sublevels in a single ground hyperfine state.

Attack detection scheme for continuous-variable quantum key distribution based on graph neural network

Di Jin, Wenqi Jiang, ying guo, junkai hu, and Duan Huang

DOI: 10.1364/JOSAB.524779 Received 25 Mar 2024; Accepted 02 May 2024; Posted 03 May 2024  View: PDF

Abstract: The practical security of a continuous-variable quantum key distribution (CV-QKD) system is vulnerable to various attack strategies due to the significant difference between the idealized theoretical model and the practical physical system. The existing countermeasures against these attacks involve exploiting different real-time monitoring modules, which presents a challenge in effectively classifying attacks. We investigate a graph neural network (GNN)-based attack detection scheme for CV-QKD, which models data as a graph structure using three different methods for various conditions. Particularly, one of the proposed methods requires no additional devices and can detect attacks with over 99% accuracy. The algorithm can be expanded to different scenarios without additional training and can achieve a detection efficiency of more than 95%. Furthermore, our proposed scheme incorporates anomaly detection algorithms into the detection module, enabling 85% effective detection of partially unknown attacks with minimal security data.

First-order quantum phase transition in the two-qubit squeezed Rabi model

Xuantong Pei, zhicheng shi, Li-Tuo Shen, and Zhen Biao Yang

DOI: 10.1364/JOSAB.519312 Received 05 Feb 2024; Accepted 01 May 2024; Posted 02 May 2024  View: PDF

Abstract: We study the ground state of the two-qubit squeezed Rabi model. Two special transformations are found to diagonalize the system Hamiltonian when each qubit’s frequency is close to the field frequency, where both the squeezing and counterrotating-wave interactions are removed, leading to an effective integrable Hamiltonian. The analytical ground state is determined and matches with numerical solutions well for a range of squeezing strengths and qubit-field detunings in the ultrastrong-coupling regime. We demonstrate that the ground state exhibits a first-order quantum phase transition at a phase boundary linearly induced by the squeezed light. We characterize the two-qubit negativity analytically and find that its two-qubit entanglement increases with the increasing of squeezing strength nonlinearly. Average photon number of field mode and variances of position and momentum quadratures are also analyzed to have a nonlinear relation with the squeezing strength.

Finite-element assembly approach of optical quantum walk networks

Christopher Schwarze, David Simon, Anthony Manni, Abdoulaye Ndao, and Alexander Sergienko

DOI: 10.1364/JOSAB.522588 Received 29 Feb 2024; Accepted 01 May 2024; Posted 02 May 2024  View: PDF

Abstract: We present a finite-element approach for computing the aggregate scattering matrix of a general network of linear coherent scatterers. These might be optical scatterers or more general scattering coins studied in quantum walk theory. With this method, a global unitary is assembled corresponding to one time step of the quantum walk on the network. After applying the relevant boundary conditions to this global matrix, the problem becomes non-unitary, and possesses a steady-state solution which is the output scattering state. We provide an algorithm to obtain this steady-state solution exactly using a matrix inversion, yielding the scattering state without requiring a direct calculation of the eigenspectrum. The approach is then numerically validated on a coupled-cavity interferometer example that possesses a known, closed-form solution. Finally, the method is shown to be a generalization of the Redheffer star product, which describes scatterers on one-dimensional lattices (2-regular graphs) and is often applied to the design of thin-film optics, making the current approach an invaluable tool for the design of higher-dimensional phase-reprogrammable optical devices and study of quantum walks on arbitrary graphs.

The enduring relevance of the Jaynes-Cummings model: a personal perspective

Peter Knight, Christopher Gerry, Richard Birrittella Jr., and Paul Alsing

DOI: 10.1364/JOSAB.524015 Received 15 Mar 2024; Accepted 01 May 2024; Posted 03 May 2024  View: PDF

Abstract: In this short perspective article we present our personal highlights on how the Jaynes-Cummings model has become a central model to describe spin-boson couplings underpinning much of modernquantum optics. To the current authors, the key contribution is a demonstration of a measurableeffect that showed the discreteness of the quantized radiation field.

A Comparison of the Jaynes-Cummings and Pauli-Fierz Hamiltonians for Light-Induced Electron Dynamics of Molecules in Cavities

Benjamin Peyton, Jared Weidman, and Angela Wilson

DOI: 10.1364/JOSAB.523931 Received 18 Mar 2024; Accepted 01 May 2024; Posted 09 May 2024  View: PDF

Abstract: The rapidly expanding field of polaritonic chemistry requires accurate theoretical simulations to understand new phenomena at the atomic scale. Computing the optoelectronic properties of molecules using established electronic structure methods is a careful balance of accuracy and computational expense, and expanding these methods to quantum electrodynamics to describe coupled cavity-molecule systems is an active topic of development. Key to these methods are the Hamiltonian operators representing the photon cavity modes, namely, the Jaynes-Cummings and Pauli-Fierz model Hamiltonians. The recently introduced QED-RTCI method allows for the combination of electron dynamics simulations with quantum electrodynamics, enabling the simulation of time-dependent optoelectronic properties of cavity-molecule systems. Using this method, a comparison of the Jaynes-Cummings and Pauli-Fierz model Hamiltonians is presented, with a particular focus on time-dependent properties in applied electric fields.

Directional switching of surface plasmons in PT-symmetric IMI structure

PRIYANKA CHAUDHARY and Akhilesh Mishra

DOI: 10.1364/JOSAB.523185 Received 05 Mar 2024; Accepted 30 Apr 2024; Posted 30 Apr 2024  View: PDF

Abstract: In the present work, we study the generation and propagation of surface plasmon polaritons (SPPs) in geometrically flat insulatormetal-insulator (IMI) structure with parity-time (PT) symmetric modulation on the dielectric layers. Unidirectional SPPs aregenerated by PT-symmetric modulation. Moreover, magnetic field switching is obtained between two metal-dielectric interfaces. Ithas been noticed that the metal thickness affects the oscillation frequency of excited SPPs along the direction of propagation. Also,we report that the field at the upper interface is manipulated by solely maneuvering the permittivity of the bottom dielectric. Themagnetic field distribution of the present structure is studied using COMSOL Multiphysics® Software. To ensure the accuracy andreliability of the simulation results, comprehensive analytical investigations have also been conducted.

Nonlinear propagation of chirped laser pulses through dispersive and turbulent atmosphere

Joshua Isaacs, B. Hafizi, Joseph Penano, and John Palastro

DOI: 10.1364/JOSAB.515777 Received 12 Dec 2023; Accepted 29 Apr 2024; Posted 30 Apr 2024  View: PDF

Abstract: The evolution of ultrashort laser pulses in dispersive, turbulent, nonlinear, and dissipative media is discussed in connection with nonlinear self-focusing collapse and the onset of laser filamentation. In quiescent air, a laser pulse propagating with a peak power greater than a critical power for self-focusing will undergo a catastrophic, transverse collapse until the intensity is large enough for photoionization. At this point, self-focusing is arrested and balanced by plasma refraction, forming a laser filament. By applying an appropriate chirp, the dispersive properties of the medium can be used to enhance this process and control its onset, and to counter dissipative effects such as molecular absorption and atmospheric scattering. This paper presents an analysis of the effect of atmospheric turbulence on the propagation of nonlinear pulses with dispersion compensation (chirp). The analytical results are compared with wave optics simulations and found to be in reasonable agreement as long as the pulse maintains a near-gaussian spatiotemporal profile.

Bloch Gauge symmetry of the semiconductor Bloch equations

Andrew Parks, Thomas Brabec, and Jerome Moloney

DOI: 10.1364/JOSAB.520221 Received 29 Jan 2024; Accepted 29 Apr 2024; Posted 07 May 2024  View: PDF

Abstract: The semiconductor Bloch equations (SBEs) are a well-established model for optical interactions in condensed matter. In particular, the SBEs in length gauge preserve the band picture of periodic crystals. As such, they provide an intuitive and numerically efficient model of high harmonic generation (HHG) in solids. The length gauge SBEs involve complex, gauge dependent transition dipole moments (TDMs) for materials with broken inversion or time-reversal symmetry. The numerical and conceptual complications resulting from gauge freedom have impeded interpretation and key applications of HHG, such as the tomographic reconstruction of crystal band structure. We derive gauge invariant SBEs (GI-SBEs) that contain only gauge invariant structural quantities: the absolute value of TDMs, the shift vector, and for more than two bands a triple product of TDM phases. The GI-SBEs provide insight into the physics of HHG in solids with broken inversion symmetry, which we demonstrate in gapped graphene.

Faraday rotation stimulated optical rotation quasi-phase-matching technique to radiate highly efficient elliptically polarized second harmonic

MOUMITA SAHA and SUMITA DEB

DOI: 10.1364/JOSAB.522790 Received 04 Mar 2024; Accepted 29 Apr 2024; Posted 30 Apr 2024  View: PDF

Abstract: Faraday rotation has been employed to ensure efficient frequency conversion in the ultraviolet regime. The reported 36% efficiency of the radiated 372 nm, continuous-wave second harmonic of this paper has been numerically analyzed in the presence of a magnetic field in a thin-film-coated magneto-optic crystal using the total-internal-reflection-based optical-rotation-quasi-phase-matching approach, considering the influence of surface roughness, absorption loss, and the nonlinear law of reflection.

Anisotropic atmospheric turbulence and partially coherent self-focusing vortex beams for wireless optical communication

Zhizhong Kang, Yun Zhu, Jicheng Wang, Mengmeng Li, Sergei Khakhomov, and Zhengda Hu

DOI: 10.1364/JOSAB.523505 Received 11 Mar 2024; Accepted 26 Apr 2024; Posted 29 Apr 2024  View: PDF

Abstract: It is generally believed that employing partially coherent light for wireless optical communication can improve the communication performance. In this paper, we show that whether the partial coherence contributes positively or negatively depends on the turbulence strength of the link. For illustration, partially coherent self-focusing vortex (PCSFV) beams propagating via anisotropic atmospheric turbulence at different altitudes are investigated. It is shown that lower coherence improves focusing and helps the signal receiving only for low-altitude links. There exists a critical altitude at which the communication performance is almost independent on the initial coherence of the beam. Besides, we focus on the channel capacity as well as the bit error rate (BER) for a high-altitude link. The results show that stronger anisotropy and larger inner scale parameters lead to higher average channel capacity with lower BER. By adjusting the beam waist or receiving aperture size, the communication performance can be further maximized. Our study represents the pioneering effort to assess the different impacts of the initial partial coherence on the receiving probability and validate the potential applications of PCSFV beams in wireless optical communications.

Peregrine soliton emits dispersive waves within graded-index multimode fibers without higher-order dispersion

YueLei Shuai, Zhixiang Deng, Haozhe Li, Yanxia Gao, Dianyuan Fan, and LIFU ZHANG

DOI: 10.1364/JOSAB.521634 Received 16 Feb 2024; Accepted 25 Apr 2024; Posted 26 Apr 2024  View: PDF

Abstract: We investigate the propagation dynamics of the Peregrine soliton, a significant prototype of rogue waves, within the graded-index multimode fibers, in the absence of higher-order dispersion. The Peregrine soliton keeps the approximate evolution trend when propagating within the graded-index multimode fibers to replace the single-mode fibers when preserving the equivalent nonlinear effect. In addition, a series of dispersive waves (also called resonant radiation) can be emitted by the Peregrine soliton, perturbated by the periodic beam oscillation caused by the spatial self-imaging effect within the graded-index multimode fibers. To be more exact, the location of the multiple resonant frequencies can be predicted using the modified quasi-phase-matching conditions, which are verified by the numerically calculated results. We can also manipulate the locations of spectral sidebands and the peak power of dispersive waves by changing the self-imaging parameter of the graded-index multimode fibers. Our findings can provide a deeper comprehension of the propagation characteristic of Peregrine soliton within the graded-index multimode fibers and provide valuable instruction for further rich nonlinear experiments.

Super-resolution and super-sensitivity of quantum LiDAR with multi-photonic state and binary outcome photon counting measurement

Priyanka Sharma, Manoj Mishra, and Devendra Mishra

DOI: 10.1364/JOSAB.507405 Received 03 Oct 2023; Accepted 25 Apr 2024; Posted 29 Apr 2024  View: PDF

Abstract: Here we are investigating the enhancement in phase sensitivity and resolution in Mach-Zehnder interferometer (MZI) based quantum LiDAR. We are using multi-photonic state (MPS), superposition of four coherent states, as the input state and binary outcome parity photon countingmeasurement and binary outcome zero-nonzero photon counting measurement as the measurement schemes. We thoroughly investigate the results in lossless as well as in lossy cases. We found enhancementin resolution and phase sensitivity in comparison to the coherent state and even coherent superposition state (ECSS) based quantum LiDAR. Our analysis shows that MPS may be an alternative nonclassical resource in the field of quantum imaging and quantum sensing technologies, likein quantum LiDAR.

A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model

Anuar Kafuri, Felix Humberto Maldonado-Villamizar, Alexander Moroz, and Blas Rodriguez-Lara

DOI: 10.1364/JOSAB.522504 Received 29 Feb 2024; Accepted 24 Apr 2024; Posted 24 Apr 2024  View: PDF

Abstract: We revisit the Jaynes--Cummings and anti-Jaynes--Cummings model through the lens of the Lie theory, aiming to highlight the efficacy of operator-based approach for an explicit diagonalization.We focus on explicitly delineating the steps to go from an underlying abstract supersymmetry, provided by the $u(1 \vert 1)$ superalgebra, into concrete proper states and energies in the laboratory frame. Additionally, we explore the anisotropic Rabi model possessing an underlying supersymmetry, provided by the $ops(2 \vert 2)$ superalgebra, in a squeezed reference frame where it is possible to approximate its spectral characteristics by an effective Jaynes--Cummings model. Finally, we identify a regime for a factorizable anisotropic Rabi model, exhibiting an equally spaced, double degenerate energy spectrum with a unique ground state energy. Our work aims to merge mathematical physics with practical quantum optics, underscoring the critical role of the Lie theory.

Diagonalizing the Jaynes-Cummings Hamiltonian and Jaynes-Cummings coherent states

Stephen Barnett and Bryan Dalton

DOI: 10.1364/JOSAB.521046 Received 07 Feb 2024; Accepted 19 Apr 2024; Posted 24 Apr 2024  View: PDF

Abstract: We determine the form of the unitary transformation that diagonalizes the Jaynes-Cummings Hamiltonian.This leads to operators the action of which has a simple interpretation in terms of the dressed states,the energy eigenstates. This suggests a set of coherent states and spin coherent states based on the dressed states.

Ionization energies of Cu- and Ni-like ions with Z≤92. Applications to X-ray laser modeling II.

Elena Ivanova

DOI: 10.1364/JOSAB.520092 Received 29 Jan 2024; Accepted 17 Apr 2024; Posted 29 Apr 2024  View: PDF

Abstract: New methodologies are proposed for the determination of high-precision spectroscopic data for isoelectronic sequences. In this paper the ionization energies of Cu- and Ni- like ions are refined in order to achieve accuracy to the fifth significant digit. Two-stage technique is developed to interpolate and extrapolate the ionization energies along Z. I) Scaling the known ionization energies (IE) along Z that brings the function IE(Z) to a quasi-straight line. The scaled function IE(Z) changes in the fourth significant digit on a segment 0-15 Z-points, what allows to confidently perform interpolation with accuracy to the fifth significant digit. Scaling on successive segments allows a confident extrapolation to the region Z=92. II) The verification of the obtained results in stage I can be performed using the parameter of the relativistic model potential, which is used only to extrapolate IE(Z). The parameters b(4s1/2|Z) and b(3d5/2|Z) of the relativistic model potential as functions of Z turned to be practically straight lines for Z>75, which allows their accurate extrapolation in the region Z=92. The results of techniques I and II agree well up to Z~92.