High Angular Momentum States Research Articles

Analytical expression for continuum–continuum transition amplitude of hydrogen-like atoms with angular-momentum dependence

Abstract Attosecond chronoscopy typically utilises interfering two-photon transitions to access the phase information. Simulating these two-photon transitions is challenging due to the continuum–continuum transition term. The hydrogenic approximation within second-order perturbation theory has been widely used due to the existence of analytical expressions of the wave functions. So far, only (partially) asymptotic results have been derived, which fail to correctly describe the low-kinetic-energy behaviour, especially for high angular-momentum states. Here, we report an analytical expression that overcomes these limitations. It is based on the Appell’s F 1 function and uses the confluent hypergeometric function of the second kind as the intermediate state. We show that the derived formula quantitatively agrees with the numerical simulations using the time-dependent Schrödinger equation for various angular-momentum states, which improves the accuracy compared to the other analytical approaches that were previously reported. Furthermore, we give an angular-momentum-dependent asymptotic form of the outgoing wavefunction and the corresponding continuum–continuum dipole transition amplitudes.

Spin asymmetries for C -even quarkonium production as a probe of gluon distributions

Within the framework of transverse momentum dependent factorization in combination with nonrelativistic quantum chromodynamics (QCD), we study charmonium and bottomonium production in hadronic collisions. We focus on quarkonium states with even charge conjugation, for which the color-singlet production mechanism is expected to be also dominant in the small transverse momentum region, qT2≪4Mc,b2. It is shown that the distributions of linearly polarized gluons inside unpolarized, longitudinally, and transversely polarized protons contribute to the cross sections for scalar and pseudoscalar quarkonia in a very distinctive, parity-dependent way, whereas their effects on higher angular momentum states are strongly suppressed. We derive analytical expressions for single and double spin asymmetries, which would allow for the direct extraction of the gluon transverse momentum dependent distributions, mirroring the phenomenological studies of the Drell-Yan processes aimed at the extraction of their quark counterparts. By adopting Gaussian models for the gluon transverse momentum dependent distributions, which fulfill without saturating everywhere their positivity bounds, we provide numerical predictions for the transverse single-spin asymmetries. These observables could be measured at LHCSpin, the fixed target experiment planned at the LHC. Published by the American Physical Society 2024

Exploring the vibrational series of pure trilobite Rydberg molecules

In trilobite Rydberg molecules, an atom in the ground state is bound by electron-atom scattering to a Rydberg electron that is in a superposition of high angular momentum states. This results in a homonuclear molecule with a permanent electric dipole moment in the kilo-debye range. Trilobite molecules have previously been observed only with admixtures of low-l states. Here we report on the observation of two vibrational series of pure trilobite Rubidium-Rydberg molecules that are nearly equidistant. They are produced by three-photon photoassociation and lie energetically more than 15 GHz below the atomic 22F state of rubidium. We show that these states can be used to measure the electron-atom scattering length at low energies in order to benchmark current theoretical calculations. In addition to measuring their kilo-Debye dipole moments, we also show that the molecular lifetime is increased compared to the 22F state due to the high-l character. The observation of an equidistant series of vibrational states opens the way to observe coherent molecular wave packet dynamics.

Highly-twisted states of light from a high quality factor photonic crystal ring

Twisted light with orbital angular momentum (OAM) has been extensively studied for applications in quantum and classical communications, microscopy, and optical micromanipulation. Ejecting high angular momentum states of a whispering gallery mode (WGM) microresonator through a grating-assisted mechanism provides a scalable, chip-integrated solution for OAM generation. However, demonstrated OAM microresonators have exhibited a much lower quality factor (Q) than conventional WGM resonators (by >100×), and an understanding of the limits on Q has been lacking. This is crucial given the importance of Q in enhancing light-matter interactions. Moreover, though high-OAM states are often desirable, the limits on what is achievable in a microresonator are not well understood. Here, we provide insight on these two questions, through understanding OAM from the perspective of mode coupling in a photonic crystal ring and linking it to coherent backscattering between counter-propagating WGMs. In addition to demonstrating high-Q (105 to 106), a high estimated upper bound on OAM ejection efficiency (up to 90%), and high-OAM number (up to l = 60), our empirical model is supported by experiments and provides a quantitative explanation for the behavior of Q and the upper bound of OAM ejection efficiency with l. The state-of-the-art performance and understanding of microresonator OAM generation opens opportunities for OAM applications using chip-integrated technologies.

Investigation the three dimensional bound states in quantum dot nanowire systems

Electronic confined states of a cylindrical InP quantum dot embedded in infinite GaP nanowire is studied theoretically. To this end the Schrodinger equation is solved numerically in the effective mass approximation. The subband separation between the GaP nanowire and InP/GaP core–shell nanowire is utilized to predict the possible existence of the three dimensionally confined states of the system. Using this, the nanowire critical radius is calculated for each channel of angular momentum, the frontier of type I-Type II transition in the InP/GaP quantum dot nanowire system. It is shown that the lower limit of the continuum energy depends on the angular momentum and increases by it, causing discrete bound states of higher angular momentum to lie in the continuum of the lower ones. Surviving the energy states in the presence of external magnetic field reveals stronger confinement for electrons in states with negative angular momentum quantum numbers.

Multipolar Fermi-surface deformation in a Rydberg-dressed Fermi gas with long-range anisotropic interactions

We study theoretically the deformation of the Fermi surface (FS) of a three-dimensional gas of Rydberg-dressed $^6$Li atoms. The laser dressing to high-lying Rydberg $D$ states results in angle-dependent soft-core-shaped interactions whose anisotropy is described by multiple spherical harmonics. We show that this can drastically modify the shape of the FS and that its deformation depends on the interplay between the Fermi momentum $k_F$ and the reciprocal momentum $\bar{k}$ corresponding to the characteristic soft-core radius of the dressing-induced potential. When $k_F< \bar{k}$, the dressed interaction stretches a spherical FS into an ellipsoid. When $k_F\gtrsim \bar{k}$, complex deformations are encountered which exhibit multipolar characteristics. We analyze the formation of Cooper pairs around the deformed FS and show that they occupy large orbital angular momentum states ($p$, $f$, and $h$ wave) coherently. Our study demonstrates that Rydberg dressing to high angular momentum states may pave a route toward the investigation of unconventional Fermi gases and multiwave superconductivity.

Three dimensional confined states in core-shell diameter modulated nanowires

Three-dimensional confined states in a GaP nanowire which partially covered by a uniform InP shell have been investigated in this paper. To this end, based on the effective mass approximation and by using the finite element method electronic energy states of the system were calculated. To attain physical insight on the numerical results, we have utilized the concept of one dimensional angular momentum dependent effective potential. Our results indicate a peculiar effect of increasing the 3D confinement of electrons in the shell which partially covered the nanowire by increasing the angular momentum. Surviving the effective potential declares that this effect arises as a consequence of contact with the semi-infinite nanowire parts of the system and, as a result, leads the bound states of higher angular momentum to lie in the energy continuum of the lower ones. On the other hand, application of external magnetic field reduces the number of 3D confined states in the core–shell region. Analysis of the reverse structure, i.e. InP nanowire which partially covered with GaP, indicates a significant increase in electronic confinement in the core–shell section with respect to the InP/GaP counterpart as a result of lower electronic effective mass of InP regarding to GaP.

Population transfer to high angular momentum states in infrared-assisted XUV photoionization of helium

An extreme-ultraviolet (XUV) laser pulse consisting of harmonics of a fundamental near-infrared (NIR) laser frequency is combined with the NIR pulse to systematically study two-color photoionization of helium atoms. A time-resolved photoelectron spectroscopy experiment is carried out where energy- and angle-resolved photoelectron distributions are obtained as a function of the NIR intensity and wavelength. Time-dependent Schrödinger equation calculations are performed for the conditions corresponding to the experiment and used to extract residual populations of Rydberg states resulting from excitation by the XUV + NIR pulse pair. The residual populations are studied as a function of the NIR intensity (3.5 × 1010 − 8 × 1012 W cm−2) and wavelength (760–820 nm). The evolution of the photoelectron distribution and the residual populations are interpreted using an effective restricted basis model, which includes the minimum set of states relevant to the features observed in the experiments. As a result, a comprehensive and intuitive picture of the laser-induced dynamics in helium atoms exposed to a two-color XUV–NIR light field is obtained.

Coulomb anti-blockade in a Rydberg gas

We perform a comprehensive investigation of the coupling between a Rydberg-dressed atomic gas and an ultra-cold plasma (UCP). Using simultaneous time-resolved measurements of both neutral atoms and ions, we show that plasma formation occurs via a Coulomb anti-blockade mechanism, in which background ions DC Stark shift nearby atoms into resonance at specific distances. The result is a highly correlated growth of the Rydberg population that shares some similarities with that previously observed for van der Waals interactions. We show that a rate equation model that couples the laser-driven Rydberg gas to the UCP via a Coulomb anti-blockade mechanism accurately reproduces both the plasma formation and its subsequent decay. Using long-lived high angular momentum states as a probe, we also find evidence of a crossover from Coulomb anti-blockade to Coulomb blockade at high density. As well as shedding light on loss mechanisms in Rydberg-dressed gases, our results open new ways to create low-entropy states in UCPs.

Building principle of triatomic trilobite Rydberg molecules

We investigate triatomic molecules that consist of two ground state atoms and a highly excited Rydberg atom, bound at large internuclear distances of thousands of \AA ngstroms. In the molecular state the Rydberg electron is in a superposition of high angular momentum states whose probability densities resemble the form of trilobite fossils. The associated potential energy landscape has an oscillatory shape and supports a rich variety of stable geometries with different bond angles and bond lengths. Based on an electronic structure investigation we analyze the molecular geometry systematically and develop a simple building principle that predicts the triatomic equilibrium configurations. %based on the properties of diatomic trilobite molecules. As a representative example we focus on $^{87}$Rb trimers correlated to the $n=30$ Rydberg state. Using an exact diagonalization scheme we determine and characterize localized vibrational states in these potential minima with energy spacings on the order of 100 MHz$\times h$.

Laser-stimulated deexcitation of Rydberg antihydrogen atoms

Antihydrogen atoms are routinely formed at CERN in a broad range of Rydberg states. Ground-state anti-atoms, those useful for precision measurements, are eventually produced through spontaneous decay. However given the long lifetime of Rydberg states the number of ground-state antihydrogen atoms usable is small, in particular for experiments relying on the production of a beam of antihydrogen atoms. Therefore, it is of high interest to efficiently stimulate the decay in order to retain a higher fraction of ground-state atoms for measurements. We propose a method that optimally mixes the high angular momentum states with low ones enabling to stimulate, using a broadband frequency laser, the deexcitation toward low-lying states, which then spontaneously decay to ground-state. We evaluated the method in realistic antihydrogen experimental conditions. For instance, starting with an initial distribution of atoms within the $n=20-30$ manifolds, as formed through charge exchange mechanism, we show that more than 80\% of antihydrogen atoms will be deexcited to the ground-state within 100 ns using a laser producing 2 J at 828 nm.

High-pressure vibrational properties of dense rubidium

At ambient conditions, alkali metals adopt the body centered cubic structure, while if compressed up to tens of GPa and above, they exhibit complex low-symmetry modifications, due to the density-driven transition of the valence electrons from the $s$ state to states of higher angular momentum. These high-pressure, low-symmetry phases, whose unit cells may include up to tens of atoms, allow rich Raman activity, which was previously observed only in lighter alkalis Na and Li. Here we report an extensive study of the optical phonons of highly dense Rb up to 100 GPa in diamond anvil cells, conducted by challenging experimental Raman spectroscopy measurements and ab initio computer simulations. The relative (relative to the normal condition value) density behavior of Raman frequencies of Rb is compared to that of Na and Li, once the frequencies of the two light alkali elements have been rescaled by $\sqrt{{M}_{\mathrm{Na}}/{M}_{\mathrm{Rb}}}$ and $\sqrt{{M}_{\mathrm{Li}}/{M}_{\mathrm{Rb}}}$, respectively, where ${M}_{\mathrm{Na}}$, ${M}_{\mathrm{Li}}$, and ${M}_{\mathrm{Rb}}$ are the atomic masses of the here considered alkali elements. Importantly, while the rescaled density behaviors of Na and Li agree with each other, Rb significantly differs, which highlights the different nature of the valence electron transition being of the $s\text{\ensuremath{-}}d$ and of the $s\text{\ensuremath{-}}p$ type in heavy and light alkali metals, respectively, a result that calls for further similar investigations of K and Cs.

Microwave-optical two-photon excitation of Rydberg states

We report efficient microwave-optical two photon excitation of Rb Rydberg atoms in a magneto optical trap. This approach allows the excitation of normally inaccessible states and provides a path toward excitation of high angular momentum states. The efficiency stems from the elimination of the Doppler width, the use of a narrow band pulsed laser, and the enormous electric dipole matrix element connecting the intermediate and final states of the transition. The excitation is efficient in spite of the low optical and microwave powers, of order 1 kW and 1 mW, respectively. This is an application of the large dipole coupling strengths between Rydberg states to achieve two photon excitation of Rydberg atoms.

Investigation of electronic bound states of a radially modulated nanowire: Level anti-crossing and bound states in continuum

In this paper the electronic confinement energy states of a radially modulated cylindrical nanowire are numerically calculated, assuming that the modulated section has finite length and its radius is greater than the remaining section of the nanowire. The Schrodinger equation is solved within the effective mass approximation using the finite element method to specify the necessary conditions for emersion of 3-dimensionally confined states and to investigate size and magnetic field dependence of the confinement energies. Our results show that for any local increment of nanowire radius, there is at least one bound state for each channel of angular momentum. The energies of bound states of higher angular momentum are shown to lie in the energy continuum of lower angular momentums. In addition, there is some level crossing and anti-crossing in the size dependence of confinement energies which can be explained on the basis of symmetry. It is observed that in the vicinity of the level anti-crossing, the oscillator strengths associated to intersubband transitions from ground state change dramatically and vanish for some specific width of modulation.

Quantum Key Distribution with High Order Fibonacci-like Orbital Angular Momentum States

The coding space in quantum communication could be expanded to high-dimensional space by using orbital angular momentum (OAM) states of photons, as both the capacity of the channel and security are enhanced. Here we present a novel approach to realize high-capacity quantum key distribution (QKD) by exploiting OAM states. The innovation of the proposed approach relies on a unique type of entangledphoton source which produces entangled photons with OAM randomly distributed among high order Fiboncci-like numbers and a new physical mechanism for efficiently sharing keys. This combination of entanglement with mathematical properties of high order Fibonacci sequences provides the QKD protocol which is immune to photon-number-splitting attacks and allows secure generation of long keys from few photons. Unlike other protocols, reference frame alignment and active modulation of production and detection bases are unnecessary.

Direct Atomic-Orbital-Based Relativistic Two-Component Linear Response Method for Calculating Excited-State Fine Structures.

In this work, we present a linear-response formalism of the complex two-component Hartree-Fock Hamiltonian that includes relativistic effects within the Douglas-Kroll-Hess and the Exact-Two-Component frameworks. The method includes both scalar and spin relativistic effects in the variational description of electronic ground and excited states, although it neglects the picture-change and explicit spin-orbit contributions arising from the two-electron interaction. An efficient direct formalism of solving the complex two-component response function is also presented in this work. The presence of spin-orbit couplings in the Hamiltonian and the two-component nature of the wave function and Fock operator allows the computation of excited-state zero-field splittings of systems for which relativistic effects are dominated by the one-electron term. Calculated results are compared to experimental reference values to assess the quality of the underlying approximations. The results show that the relativistic two-component linear response methods are able to capture the excited-state zero-field splittings with good agreement with experiments for the systems considered here, with all approximations exhibiting a similar performance. However, the error increases for heavy elements and for states of high orbital angular momentum, suggesting the importance of the two-electron relativistic effect in such situations.

An ab initio study of SbH2 and BiH2: The Renner effect, spin–orbit coupling, local mode vibrations and rovibronic energy level clustering in SbH2

We present the results of ab initio calculations for the lower electronic states of the Group 15 (pnictogen) dihydrides, SbH2 and BiH2. For each of these molecules the two lowest electronic states become degenerate at linearity and are therefore subject to the Renner effect. Spin–orbit coupling is also strong in these two heavy-element containing molecules. For the lowest two electronic states of SbH2, we construct the three dimensional potential energy surfaces and corresponding dipole moment and transition moment surfaces by multi-reference configuration interaction techniques. Including both the Renner effect and spin–orbit coupling, we calculate term values and simulate the rovibrational and rovibronic spectra of SbH2. Excellent agreement is obtained with the results of matrix isolation infrared spectroscopic studies and with gas phase electronic spectroscopic studies in absorption. For the heavier dihydride BiH2 we calculate bending potential curves and the spin–orbit coupling constant for comparison. For SbH2 we further study the local mode vibrational behavior and the formation of rovibronic energy level clusters in high angular momentum states.

Towards Superheavies: Spectroscopy of 94 &lt; Z &lt; 98, 150 &lt; N &lt; 154 Nuclei

The heaviest nuclei where excitations above the ground state can be studied lie near Z ~ 100. These nuclear structure studies are important testing grounds for theoretical models that aim to describe superheavy nuclei. To study the highest neutron orbitals (150 ≤ N ≤ 154), we have populated high angular momentum states in a series of Pu (Z = 94), Cm (Z = 96) and Cf (Z = 98) nuclei, via inelastic and transfer reactions, with heavy beams on long-lived radioactive actinide targets. Multiple collective excitation modes and structures were identified, and their configurations deduced. Quasiparticle alignments are mapped, with odd-A band structures helping identify specific orbital contributions via blocking arguments. Higher-order multipole shapes are observed to play a significant role in disentangling competing neutron and proton alignments. The N > 152 data provide new perspectives on physics beyond the N = 152 sub-shell gap.

Ultracold Long-Range Rydberg Molecules with Complex Multichannel Spectra

A generalized class of ultralong-range Rydberg molecules is predicted which consist of a multichannel Rydberg atom whose outermost electron creates a chemical bond with a distant ground state atom. Such multichannel Rydberg molecules exhibit favorable properties for laser excitation, because states exist where the quantum defect varies strongly with the principal quantum number. The resulting occurrence of near degeneracies with states of high orbital angular momentum promotes the admixture of low l into the high l deeply bound "trilobite" molecule states, thereby circumventing the usual difficulty posed by electric dipole selection rules. Such states also can exhibit multiscale binding possibilities that could present novel options for quantum manipulation.

Strong-field excitation of helium: bound state distribution and spin effects.

Using field ionization combined with the direct detection of excited neutral atoms we measured the distribution of principal quantum number n of excited He Rydberg states after strong-field excitation at laser intensities well in the tunneling regime. Our results confirm theoretical predictions from semiclassical and quantum mechanical calculations and simultaneously underpin the validity of the semiclassical frustrated tunneling ionization model. Moreover, since our experimental detection scheme is spin sensitive in the case of He atoms, we show that strong-field excitation leads to strong population of triplet states. The origin of it lies in the fact that high angular momentum states are accessible in strong-field excitation. Thus, singlet-triplet transitions become possible due to the increased importance of spin-orbit interaction rather than due to direct laser induced spin-flip processes.