Principal Quantum Number Research Articles

Few generalized entropic relations related to Rydberg atoms.

We calculate the analytical and numerical values of the position space Shannon entropy, momentum space Shannon entropy, and total Shannon entropy, S_rho, S_gamma, and S_T, respectively, of free and trapped Rydberg hydrogen-like atoms. The influence of atomic number Z, the principal quantum number n, and energy E on the Shannon entropy of the Rydberg atoms are illustrated. The scaling properties of Shannon entropy with energy of states E and the principal quantum number n have been reported for the first time to the best of our knowledge. Our work explains how Shannon entropy indicates localization-delocalization of the wavefunction. The total Shannon entropy as a measure of the number of nodes in the trapped Rydberg atom’s wavefunction is also discussed. We show why an uncertainty relation based on Shannon entropy is superior to Heisenberg uncertainty for Rydberg atoms.

The Rydberg atom-atom collisions: Chemi-ionization cross-sections and rate coefficients in alkali-metal astrophysical and low-temperature laboratory plasmas

In this manuscript, the chemi-ionization (CI) processes in atom - Rydberg atom collisions are examined. We obtained the cross-sections, as well as rate coefficients for CI processes in potassium and sodium collisions for principal quantum numbers 5⩽n⩽25 in the 500 K ⩽T⩽1500 K temperature region. The presented data could be useful for the improvement of analysis and modelling of weakly ionized layers of different atmospheres and cosmic objects where these and other CI processes could change excited state populations and the free electron density, consequently affecting the optical characteristics.

The mass spectrum and wave functions of the Bc system

The spectrum and relativistic wave functions of Bc system are investigated via solving the complete Salpeter equation. Emphases are put on the study of the partial waves of each JP state. Our study shows that there are three categories of JP states. The first category contains 0− and 0+ states, which are 1S0 dominant state with a small amount of P wave and 3P0 dominant state with a small amount of S wave, respectively. The second category includes the natural parity states, such as 1−, 2+, 3−, etc. Taking the 1− state as an example, we study it in two cases. One is the 3S1 dominant state with a small amount of P and D waves, and the other is the 3D1 dominant state but contains a large amount of S and P wave components. The third category includes the unnatural parity states, such as 1+, 2−, 3+, etc. For the 1+ spectrum, the states are grouped into pairs with different radial quantum numbers. Each pair contains two 1P1−3P1 mixing states, and the corresponding mixing angles are calculated by using the relativistic wave functions.

Rashba effect in a quantum dot subject to a parabolic confining potential and external fields

The Rashba effect has been investigated in a spherical quantum dot confined by a radial parabolic potential. Also, external parallel magnetic and electric fields have been applied. The solution of the Schrödinger equation in the presence of the Rashba interactions has been derived by applying an approach that differs from the one used in an earlier treatment. The wave function in the presence of these interactions has been expanded in terms of the eigenfunctions of the Hamiltonian in their absence. In our opinion, the form introduced for the wave function presents the exact solution in a more accurate manner. The coefficients of expansion have been chosen either to depend on the three quantum numbers involved or on the principal quantum number only. The results have shown that the Rashba interactions have a considerable effect on the electron energy levels and on their splitting. The variation of this effect with the applied fields and the Rashba coupling strength has been investigated.Graphical abstract

K-shell Emission from O vi Near 19 Å

Laboratory measurements of O vi K-shell emission lines are presented that are situated near the O viii Lyα line at 19 Å. The data provide additional rest-frame references for velocity determinations based on absorption features in the spectra of warm absorbers in active galactic nuclei and other astrophysical objects. They also provide benchmarks for testing atomic structure calculations of energy levels with electrons in a high principal quantum number (n = 3, 4). Excellent agreement is found with our calculations using the many-body perturbation theory method, and we provide a complete listing of the O vi energy levels calculated with this approach.

Angle-Dependent Magic Optical Trap for the 6S1/2↔nP3/2 Rydberg Transition of Cesium Atoms

The existence of an anisotropic tensor part of atomic states with an angular momentum greater than 1/2 causes their dynamic polarizabilities to be very sensitive to the polarization direction of the laser field. Therefore, the magic wavelength of the transition between two atomic states also depends on the polarization angle between the quantized axis and the polarization vector. We perform a calculation of the magic conditions of the 6S1/2↔nP3/2 (n = 50–90) Rydberg transition of cesium atoms by introducing an auxiliary electric diople transition connected to the target Rydberg state and a low-excited state. The magic condition is determined by the intersection of dynamic polarizabilities of the 6S1/2 ground state and the nP3/2 Rydberg state. The dynamic polarizability is calculated by using the sum-over-states method. Furthermore, we analyze the dependence of magic detuning on the polarization angle for a linearly polarized trapping laser and establish the relationship between magic detuning and a principal quantum number of the Rydberg state at the magic angle. The magic optical dipole trap can confine the ground-state and Rydberg-state atoms simultaneously, and the differential light shift in the 6S1/2↔nP3/2 transition can be canceled under the magic condition. It is of great significance for the application of long-lifetime high-repetition-rate accurate manipulation of Rydberg atoms on high-fidelity entanglement and quantum logic gate operation.

Electromagnetically-induced-transparency spectroscopy of high-lying Rydberg states in K39

We present a study of the Rydberg spectrum in $^{39}K$ for $nS$ and $nD_{3/2}$ series connected to $5^2P_{1/2}$ using two-photon spectroscopy based on EIT in a heated vapor cell. We observed some 80 transitions from $5P_{1/2}$ to Rydberg states with principal quantum numbers $n\sim50-90$, and determined their transition frequencies and state energies with sub-GHz precision. Our spectroscopy results lay the groundwork for using Rydberg atoms as sensitive microwave photon detectors in searches for dark matter axions in the $\sim40-200$ $\mu$eV mass range, which is a prime range for future axion searches suggested by theory studies.

Rydberg exciton-polaritons in a Cu2O microcavity.

Giant Rydberg excitons with principal quantum numbers as high as n = 25 have been observed in cuprous oxide (Cu2O), a semiconductor in which the exciton diameter can become as large as ∼1 μm. The giant dimension of these excitons results in excitonic interaction enhancements of orders of magnitude. Rydberg exciton-polaritons, formed by the strong coupling of Rydberg excitons to cavity photons, are a promising route to exploit these interactions and achieve a scalable, strongly correlated solid-state platform. However, the strong coupling of these excitons to cavity photons has remained elusive. Here, by embedding a thin Cu2O crystal into a Fabry-Pérot microcavity, we achieve strong coupling of light to Cu2O Rydberg excitons up to n = 6 and demonstrate the formation of Cu2O Rydberg exciton-polaritons. These results pave the way towards realizing strongly interacting exciton-polaritons and exploring strongly correlated phases of matter using light on a chip.

Collision-induced radiative quenching and other disintegration modes of the 2s state of muonic hydrogen and deuterium atoms

The formation and various disintegration modes of $2s$ states for muonic hydrogen and deuterium atoms at kinetic energies both above and below the $2s-2p$ threshold are studied. The cross sections of the collision-induced radiative quenching, elastic scattering, and Coulomb deexcitation of $(\mu^- p)_{2s}$ and $(\mu^- d)_{2s}$ atoms in collisions with ordinary hydrogen and deuterium atoms at collision energies below the $2s-2p$ threshold are calculated in the framework of the close-coupling approach. The basis set includes all open and closed channels corresponding to exotic-atom states with principal quantum number $n$ from 1 up to 30. Results of these numerical quantum-mechanical calculations of cross sections are used as input data for detailed cascade calculations. The kinetics of atomic cascade for $\mu^- p$ and $\mu^-d$ atoms is studied in the wide range of the relative target densities, $\varphi = 10^{-8} -1$ applying the improved version of the cascade model. It is shown that the collision-induced radiative quenching gives a significant contribution to the total disintegration of the $2s$ state of muonic atoms at energies below the $2s-2p$ threshold. The initial population of the $2s$ state for both muonic hydrogen and deuterium atoms, absolute intensities and probabilities of the different disintegration modes as well as their lifetimes are calculated for the fractions with kinetic energies above and below the $2s-2p$ threshold. The obtained results are compared with the known experimental data.

Angstrom-precise fabrication of surface nanoscale axial photonics (SNAP) microresonators with a flame

We demonstrate the fabrication of surface nanoscale axial photonics bottle microresonators with angstrom precision using a flame. We observe strongly unscalable behavior of the whispering gallery mode cutoff wavelengths with different radial quantum numbers along the fibre length.

Energy Spectra of Some Dimers Confined by the Deformed-Type Coulomb Interaction Potential

The eigensolutions of the Schrödinger equation containing a deformed-type Coulomb interaction via parametric NU approach. The eigenvalues and its eigenfunctions are presented. Using molecular constants data, the energy spectra for a set of dimers (I_2, H_2, N_2, O_2) for any n and l quantum numbers are computed using MATLAB R2020a. The results show a monotonic dependence of the energy spectra on both principal and angular momentum quantum numbers. The spectra generated is more sensitive to both n and l quantum numbers than the inverse length of an approximation scheme and the masses of the dimers selected.

High-resolution nanosecond spectroscopy of even-parity Rydberg excitons in Cu2O

We present a study of even parity Rydberg exciton states in cuprous oxide using time-resolved second harmonic generation (SHG). Excitonic states with principal quantum number n = 5 - 12 were excited by nanosecond pulses around 1143 nm. Using time-resolved single-photon counting, the coherently generated second harmonic was isolated both temporally and spectroscopically from inelastic emission due to lower-lying free and bound excitonic states, which included narrow resonances at 1.99 eV associated with an exceptional lifetime of 641 $\pm$ 7 $\mu$s. The near transform-limited excitation bandwidth enabled detailed measurements of the exciton lineshape and position, from which we obtained values for the quantum defects of the S and D excitonic states associated with the appropriate crystal symmetries. Odd parity P and F excitonic states were also observed, in accordance with predicted quadrupole-allowed two-photon excitation processes. We compared our measurements to conventional one-photon spectroscopy in the same sample, and find that the SHG spectrum is cut off at a lower principal quantum number (n = 12 vs n = 15). We attribute this effect to a combination of spatial inhomogeneities and local heating, and discuss the prospects for observing higher principal quantum number even parity states in future experiments.

He atom in a quantum dot: Structural, entanglement, and information-theoretical measures

Energy eigenvalues of ground and singly excited $1sns$ ($^{1,3}S$) ($n=2\ensuremath{-}5$, being the principal quantum number) states of a He atom in a quantum dot have been investigated in detail by incorporating explicitly correlated Hylleraas-type wave functions in the framework of the Ritz variational method. The quantum dot environment is simulated by considering the influence of the finite oscillator (FO) potential. We have examined the behavior of different energy components contributing to the total energy. In this regard, the Hund's spin multiplicity rule for $1sns$ ($^{1,3}S$) ($n=2\ensuremath{-}5$) states of a He atom has been examined in depth in terms of observed unusual ordering of the electron repulsion and total energy. The energy contribution due to the total correlation (in the presence of both radial and angular correlation) effect, the radial correlation limit and angular correlation limit of a He atom under different strengths of the FO potential have been studied. As a quantitative replication of our results, we have introduced and verified the Hellmann-Feynman theorem and virial theorem for both a He atom and its first ionization threshold, i.e., ${\mathrm{He}}^{+}$ ($1s,\phantom{\rule{0.16em}{0ex}}^{2}S$) ion under the influence of the FO potential. The expectation value of different radial quantities ${r}_{1}, {r}_{1}^{2}, {r}_{12},\phantom{\rule{0.16em}{0ex}}{r}_{12}^{2}, {r}_{<}=min({r}_{1},{r}_{2}),\phantom{\rule{0.16em}{0ex}}{r}_{>}=max({r}_{1},{r}_{2})$, angular quantities, e.g., interparticle angles ${\ensuremath{\theta}}_{1}, {\ensuremath{\theta}}_{12}$, one-electron delta function $\ensuremath{\delta}({\stackrel{P\vec}{r}}_{1})$, and two-electron delta function $\ensuremath{\delta}({\stackrel{P\vec}{r}}_{12})$ have been determined for different strengths of the FO potential. The effect of the FO potential on the quantum similarity index and dissimilarity between the ${\mathrm{He}}^{+}$ ($1s,\phantom{\rule{0.16em}{0ex}}^{2}S$) and He ($1{s}^{2},^{1}S$ and $1s2s,^{1,3}S$) as well as between He ($1s2s,^{1}S$) and He ($1s2s,^{3}S$) has been examined. The von Neumann, linear, and Shannon information entropy for the ground state He atom have been computed to ascertain the characteristic features of the electronic entanglement and the charge distribution under the FO potential.

Nondipole Coulomb sub-barrier ionization dynamics and photon momentum sharing

The nondipole under-the-barrier dynamics of the electron during strong-field tunneling ionization is investigated, examining the role of the Coulomb field of the atomic core. The common analysis in the strong-field approximation is consequently generalized to include the leading light-front nondipole Coulomb corrections and demonstrates the counterintuitive impact of the sub-barrier Coulomb field. Despite its attractive nature, the sub-barrier Coulomb field increases the photoelectron nondipole momentum shift along the laser propagation direction, involving a strong dependence on the laser field. The scaling of the effect with respect to the principal quantum number and angular momentum of the bound state is found. We demonstrate that the signature of Coulomb induced sub-barrier effects can be identified in the asymptotic photoelectron momentum distribution via a comparative study of the field-dependent longitudinal momentum shift for different atomic species with state-of-the-art experimental techniques of midinfrared lasers.

Topological Effects of a Spiral Dislocation on Quantum Revivals

We analyse the influence of spiral dislocation topology on the revival time for the harmonic oscillator, for a particle confined to one-dimensional quantum ring, and a two-dimensional quantum ring. We first investigate the effects of a cut-off point that stems from the topology of this defect on the harmonic oscillator. Then, we show that the influence of spiral dislocation topology on the harmonic oscillator gives rise to a non-null revival time related to the radial quantum number. In the case of the two-dimensional quantum ring, we show that the revival times related to the radial quantum number and the angular momentum quantum number are influenced by the spiral dislocation topology.

Bound-state effects on dark matter coannihilation: Pushing the boundaries of conversion-driven freeze-out

Bound-state formation can have a large impact on the dynamics of dark matter freeze-out in the early Universe, in particular for colored coannihilators. We present a general formalism to include an arbitrary number of excited bound states in terms of an effective annihilation cross section, taking bound-state formation, decay and transitions into account, and derive analytic approximations in the limiting cases of no or efficient transitions. Furthermore, we provide explicit expressions for radiative bound-state formation rates for states with arbitrary principal and angular quantum numbers $n,\ell$ for a mediator in the fundamental representation of $SU(3)_c$, as well as electromagnetic transition rates among them in the Coulomb approximation. We then assess the impact of bound states within a model with Majorana dark matter and a colored scalar $t$-channel mediator. We consider the regime of coannihilation as well as conversion-driven freeze-out (or coscattering), where the relic abundance is set by the freeze-out of conversion processes. We find that the region in parameter space where the latter occurs is considerably enhanced into the multi-TeV regime. For conversion-driven freeze-out, dark matter is very weakly coupled, evading direct and indirect detection constraints but leading to prominent signatures of long-lived particles that provide great prospects to be probed by dedicated searches at the upcoming LHC runs.

Mode-resolved analysis of pump and Stokes beams in LD-pumped GRIN fiber Raman lasers.

All-fiber Raman lasers have demonstrated their potential for efficient conversion of highly multimode pump beams into high-quality Stokes beams. However, the modal content of these beams has not yet been investigated. In this work, based on a mode decomposition technique, we are able to reveal the details of intermodal interactions in the different operation regimes of continuous wave multimode graded-index fiber Raman lasers. We observed that, above the laser threshold, the residual pump beam is strongly depleted in its transverse modes with principal quantum number below 10. However, the generated Stokes signal beam mainly consists of the fundamental mode, but higher-order modes are also present, albeit with exponentially decreasing population.

Scrutinizing the Debye plasma model: Rydberg excitons unravel the properties of low-density plasmas in semiconductors

For low-density plasmas, the classical limit described by the Debye-H\"uckel theory is still considered as an appropriate description even though a clear experimental proof of this paradigm is lacking due to the problems in determining the plasma-induced shift of single-particle energies in atomic systems. We show that Rydberg excitons in states with a high principal quantum number are highly sensitive probes for their surrounding making it possible to unravel accurately the basic properties of low-density nondegenerate electron-hole plasmas. To this end, we accurately measure the parameters of Rydberg excitons such as energies and linewidths in absorption spectra of bulk cuprous oxide crystals in which a tailored electron-hole plasma has been generated optically. Since from the absorption spectra exciton energies, as well as the shift of the single-particle energies given by the band edge, can be directly derived, the measurements allow us to determine the plasma density and temperature independently, which has been a notoriously hard problem in semiconductor physics. Our analysis shows unambiguously that the impact of the plasma cannot be described by the classical Debye model, but requires a quantum many-body theory, not only for the semiconductor plasma investigated here, but in general. Furthermore, it reveals an exciton scattering mechanism with coupled plasmon-phonon modes becoming important even at very low plasma densities.

Non-local thermodynamic equilibrium spectral analysis of five hot, hydrogen-deficient pre-white dwarfs

Hot, compact, hydrogen-deficient pre-white dwarfs (pre-WDs) with effective temperatures ofTeff> 70 000 K and a surface gravity of 5.0 < logg< 7.0 are rather rare objects despite recent and ongoing surveys. It is believed that they are the outcome of either single star evolution (late helium-shell flash or late helium-core flash) or binary star evolution (double WD merger). Their study is interesting because the surface elemental abundances reflect the physics of thermonuclear flashes and merger events. Spectroscopically they are divided in three different classes, namely PG1159, O(He), or He-sdO. We present a spectroscopic analysis of five such stars that turned out to have atmospheric parameters in the rangeTeff= 70 000–80 000 K and logg= 5.2–6.3. The three investigated He-sdOs have a relatively high hydrogen mass fraction (10%) that is unexplained by both single (He core flash) and binary evolution (He-WD merger) scenarios. The O(He) star JL 9 is probably a binary helium-WD merger, but its hydrogen content (6%) is also at odds with merger models. We found that RL 104 is the ‘coolest’ (Teff= 80 000 K) member of the PG1159 class in a pre-WD stage. Its optical spectrum is remarkable because it exhibits C IVlines involving Rydberg states with principal quantum numbers up ton= 22. Its rather low mass (0.48−0.02+0.03 M⊙) is difficult to reconcile with the common evolutionary scenario for PG1159 stars due to it being the outcome of a (very) late He-shell flash. The same mass-problem faces a merger model of a close He-sdO plus CO WD binary that predicts PG1159-like abundances. Perhaps RL 104 originates from a very late He-shell flash in a CO/He WD formed by a merger of two low-mass He-WDs.

Gauge effects in bound-bound Rydberg transition matrix elements

Accurate data on electric-dipole transition matrix elements (EDTMs) for bound-bound Rydberg-atom transitions have become increasingly important in science and technology. Here we compute radial EDTMs of rubidium in length, velocity, and acceleration forms for electric-dipole-allowed transitions between states with principal and angular-momentum quantum numbers $n$ and $\ensuremath{\ell}$ ranging from 15 to 100. Wave functions are computed based upon model potentials from [Phys. Rev. A 49, 982 (1994)]. Length-gauge EDTMs of strong low-$\ensuremath{\ell}$ Rydberg transitions, often employed in research and technology, are found to deviate from the fundamentally more accurate velocity-gauge form by approximately-$n$-independent and series-dependent shifts. The shift amount peaks at about $0.34\phantom{\rule{4pt}{0ex}}e{a}_{0}$ for the Rb $nD\ensuremath{\leftrightarrow}\phantom{\rule{4pt}{0ex}}(n+1)P$ series, a particularly strong Rydberg-transition series in Rb. The shift corresponds to relative EDTM corrections of up to $\ensuremath{\approx}{10}^{\ensuremath{-}3}$, which can be of concern in high-precision applications. We discuss the physical reasons for the observed gauge differences, explain the conditions for applicability of the velocity- and length-gauge forms for different transition series, and present a decision tree of how to choose EDTMs.