Orbital Angular Momentum Quantum Number Research Articles

Structural properties of Li atom under quantum and classical plasmas: A composite variational framework

AbstractStructural properties of 1s2nl (2L) [n = 2–5, l = 0–4; where, n and l are the principal quantum number and orbital angular momentum quantum number, respectively] states of Li atom embedded in classical weakly coupled plasma (WCP) and dense quantum plasma (DQP) have been discussed. The Debye‐Hckel potential or the screened‐Coulomb potential (SCP) and exponential‐cosine‐screened Coulomb potential (ECSCP) have been used to mimic the WCP and DQP, respectively. Li atom has been treated as a composite system with a frozen core Li+ ion and a chemically active valence electron. The Rayleigh‐Ritz variational method with Hylleraas‐type basis set has been used to estimate the energy eigenvalue of 1s2 (1S) state of Li+ ion core and a pure exponential basis has been considered to compute the energy of nl (2L) states of the valence electron of Li atom. The influence of ECSCP and SCP on the radial probability distribution of the valence electron of the Li atom has also been studied.

Multi-trap optical tweezers based on composite vortex beams

As one of the indispensable instruments in many fields, optical tweezers are extensively utilized in micromanipulation. Vortex beams and diverse structured light fields make multi-trap optical tweezers possible. Here, the radiation forces of Laguerre-Gaussian (LG) composite vortex beams exerting on a Rayleigh dielectric particle are investigated. Our results show that the multi-trap optical tweezers can be produced by the Laguerre-Gaussian composite vortex beams, which can trap the particles with both high and low refractive indices in the focus plane at multiple positions. Moreover, by changing the orbital angular momentum (OAM) quantum numbers and energy ratios of the Laguerre-Gaussian modes participated in the superposition, the quantities of the optical traps and the distances between multiple traps can be conveniently adjusted. Our beams can be generated by several methods, which provides more convenience for the creation of multiple optical traps. The results presented in this work are potential in optical micromanipulation, as well as other applications in biology and chemistry.

Tunable magnetic properties and magnetocaloric effect of TmGa by Ho substitution

The influence of Ho substitution for Tm atoms on the magnetic properties and magnetocaloric effect (MCE) of TmGa compound was systematically investigated according to magnetic measurements and neutron powder diffraction (NPD) experiments. The magnetic transitions of ${\mathrm{Tm}}_{1\ensuremath{-}x}{\mathrm{Ho}}_{x}\mathrm{Ga}$ compounds show different types by Ho substitution due to the variation of spin and orbital angular momentum quantum number and the complete magnetic diagram of ${\mathrm{Tm}}_{1\ensuremath{-}x}{\mathrm{Ho}}_{x}\mathrm{Ga}$ compounds was obtained. The spin reorientation (SR) transition of ${\mathrm{Tm}}_{0.1}{\mathrm{Ho}}_{0.9}\mathrm{Ga}$ compound was directly confirmed by variable-temperature NPD experiments. Results show that the magnetic moment orders along the $c$ axis at the temperatures between ${T}_{\mathrm{SR}}$ and ${T}_{\mathrm{C}}$ and it cants away from the $c$ axis towards the $ab$ plane upon cooling below ${T}_{\mathrm{SR}}$. Furthermore, Ho substitution plays a dominant role in MCE of ${\mathrm{Tm}}_{1\ensuremath{-}x}{\mathrm{Ho}}_{x}\mathrm{Ga}$ compounds. When $x=0.15$, the peak value of magnetic entropy change reaches the maximum value of 18.0 J/kg K under field change of 0--2 T. The refrigerant temperature span ($\ensuremath{\delta}{T}_{\mathrm{FWHM}}$) and refrigeration capacity of ${\mathrm{Tm}}_{0.85}{\mathrm{Ho}}_{0.15}\mathrm{Ga}$ compound show enhancement of 23.0 and 21.6%, correspondingly, compared with TmGa compound. The giant MCE of ${\mathrm{Tm}}_{0.85}{\mathrm{Ho}}_{0.15}\mathrm{Ga}$ compound results from the optimization of spin and total angular momentum quantum number by Ho substitution.

Electron cyclotron motion excited surface plasmon and radiation with orbital angular momentum on a semiconductor thin film

In this work, surface plasmons (SPs) on a germanium (Ge) thin film in terahertz (THz) region that are excited by electron cyclotron motion (ECM) and the subsequent SP emission (SPE) by adding Ge gratings on the film are explored by finite-difference time-domain (FDTD) and particle-in-cell FDTD (PIC-FDTD) simulations. The optical properties of ECM-excited SPs are the same as those of SPs that are excited by electron straight motion (ESM). For operating at the flat band of SPs’ dispersion curve on the Ge film, changing the electron energy will only change the wavevector of SPs and hence the number of periods of SPs on the circular orbital. When the periodic gratings are deposited on the Ge film along the circular orbital of electrons, the emitted SPE contains the orbital angular momentum (OAM). The number of arms and chirality of the spiral patterns in phase map (i.e. the quantum number of OAM) of SPE are determined by the difference between the number of SPs’ periods and the number of gratings. Manipulations of the quantum number of OAM by changing the number of gratings for a fixed electron energy and by changing the electron energy for a fixed number of gratings are also demonstrated. This work provides an active OAM source and it is not required to launch circularly polarized beams or pumping beams into the structure.

Received Probability of Orbital-Angular-Momentum Modes Carried by Diffraction- and Attenuation- Resistant Beams in Weak Turbulent Oceans

High performance underwater wireless optical communication systems are the key to the construction of high quality underwater optical communication networks. However, seawater absorption and seawater turbulent diffraction should be the main factors limiting the performance of underwater optical communication systems. For this reason, we established the probability model of the orbital angular momentum (OAM) mode received by the communication system to study the influence of the absorbable turbulent seawater channel on the underwater optical communication system with an anti-diffraction and anti-attenuation random (DARR) beam as the signal carrier. In the study, the DARR beam with a large truncated Gaussian aperture was adopted as the signal carrier, seawater absorption was characterized by the complex refractive index of seawater, and seawater turbulence was described by the power spectrum of the refractive index of seawater. By analyzing the relationship between the received probability of the OAM mode of DARR beams and the dissipation rate of kinetic energy per unit of mass of fluid, the ratio of temperature and salinity, dissipation rate of the mean-squared temperature, and other parameters, we show that one can select longer wavelength, smaller OAM quantum number and smaller received diameter to increase the received probability of OAM signal modes. The disturbance of turbulent seawater to the OAM modes with different quantum numbers carried by the DARR beam is less than the corresponding OAM modes carried by the Laguerre–Gaussian beam. Our paper shows that the DARR beam can mitigate the absorption and disturbance of turbulent seawater.

Propagation of orbital angular momentum modes carried by hollow vortex Gaussian beams in anisotropic atmospheric turbulence.

We establish the propagation model of orbital angular momentum (OAM) modes carried by hollow vortex Gaussian (hvG) beams propagating in anisotropic atmospheric turbulence. Effects of light source parameters and atmospheric conditions on the OAM mode propagation performance are investigated in detail. The findings indicate the hvG beam with a smaller OAM quantum number, a larger beam order, or a longer source wavelength has more robust resistance to atmospheric turbulence interference. The waist width of the light source has different influences on the OAM mode propagation at different propagation distances. Atmospheric turbulences with larger values of anisotropy, inner-scale factor, non-Kolmogorov power spectrum index, and altitude are favorable for the OAM mode propagation. These research results are conducive to optimizing the design of light sources and space wireless communication systems with hvG beams.

Pathways to excitation of atoms with bicircular laser pulses

We study the excitation of the hydrogen atom by bichromatic circularly polarized laser pulses using numerical solutions of the time-dependent Schr\"odinger equation. The results are in agreement with the selection rules for multiphoton processes in such fields, namely, excited states are populated in which orbital angular momentum and magnetic quantum numbers are either both odd or both even, independent of the relative helicity, peak intensity, and pulse duration of the pulses. For co-rotating pulses the results show that excitation predominantly proceeds to states with magnetic quantum number of the same helicity as the laser pulses. Besides pathways via direct photon absorption from the ground state our results indicate that a transfer of population among the Rydberg states occurs via $\mathrm{\ensuremath{\Lambda}}$-type transitions. In the case of counter-rotating pulses the largest excitation probability is found for Rydberg states that differ in magnetic quantum number by $\mathrm{\ensuremath{\Delta}}m=\ifmmode\pm\else\textpm\fi{}3$. This pattern allows us to estimate how many photons from each of the two bichromatic fields have been absorbed. Finally, we confirm that a population in Rydberg states beyond a maximum orbital angular quantum number is unlikely.

Laser spectroscopy of pionic helium atoms.

Charged pions1 are the lightest and longest-lived mesons. Mesonic atoms are formed when an orbital electron in an atom is replaced by a negatively charged meson. Laser spectroscopy of these atoms should permit the mass and other properties of the meson to be determined with high precision and could place upper limits on exotic forces involving mesons (as has been done in other experiments on antiprotons2-9). Determining the mass of the π- meson in particular could help to place direct experimental constraints on the mass of the muon antineutrino10-13. However, laser excitations of mesonic atoms have not been previously achieved because of the small number of atoms that can be synthesized and their typically short (less than one picosecond) lifetimes against absorption of the mesons into the nuclei1. Metastable pionic helium (π4He+) is a hypothetical14-16 three-body atom composed of a helium-4 nucleus, an electron and a π- occupying a Rydberg state of large principal (n≈16) and orbital angular momentum (l≈n-1) quantum numbers. The π4He+ atom is predicted to have an anomalously long nanosecond-scale lifetime, which could allow laser spectroscopy to be carried out17. Its atomic structure is unique owing to the absence of hyperfine interactions18,19 between the spin-0 π- and the 4He nucleus. Here we synthesize π4He+ in a superfluid-helium target and excite the transition (n,l)=(17,16)→(17,15) of the π--occupied π4He+ orbital at anear-infrared resonance frequency of 183,760 gigahertz. The laser initiates electromagnetic cascade processes that end with the nucleus absorbing the π- and undergoing fission20,21. The detection of emerging neutron, proton and deuteron fragments signals the laser-induced resonance in the atom, thereby confirming the presence of π4He+. This work enables the use of theexperimental techniques of quantum opticsto study ameson.

Lommel-Gaussian Pulsed Beams Carrying Orbital Angular Momentum Propagation in Asymmetric Oceanic Turbulence

By developing the complex phase perturbation for vortex pulsed beams in asymmetric oceanic turbulence and the spatiotemporal orthogonal basis for Lommel-Gaussian pulsed beam, we establish the received probability model of orbital angular momentum (OAM) modes for vortex pulsed beams propagating through asymmetric oceanic turbulence. Using this new model, we investigate the received probability and the pulse broadening of OAM modes of Lommel-Gaussian pulsed beam in asymmetric oceanic turbulence. Numerical simulation results show that Lommel-Gaussian pulsed beam causes a smaller pulse broadening when it propagates through oceanic turbulence with higher asymmetric factor, lower temperature structure constant, smaller inner scale and outer scale. In addition, Lommel-Gaussian pulsed beam with lower carrier frequency propagates through the oceanic turbulence with higher asymmetric factor, larger inner scale, smaller outer scale and smaller temperature structure constant, which obtains a higher received probability of signal OAM modes. For Lommel-Gaussian pulsed beams, the change of OAM quantum number has a week effect on the pulse broadening and the received probability.

Capacity of turbulent ocean links with carrier Bessel-Gaussian localized vortex waves.

Based on the power spectrum of the index fluctuation with the outer scale of seawater turbulence, we develop the channel capacity of oceanic turbulence links with carrier Bessel-Gaussian vortex localized waves. By this capacity model, we investigate the influences of seawater turbulence and carrier parameters on the channel capacity. The results show that a higher rate of dissipation of kinetic energy per unit mass of fluid, larger inner scale, or lower dissipation rate of the mean-squared temperature causes the higher channel capacity; the Bessel-Gaussian localized vortex wave with a larger source transverse size, smaller Bessel cone angle, lower orbital angular momentum quantum number, or broader initial half-pulse width has stronger resistance to oceanic turbulent perturbation. This work provides a theoretical basis for realizing high-capacity oceanic optical communication with carrier Bessel-Gaussian vortex localized waves.

Transmittance of finite-energy frozen beams in oceanic turbulence

Frozen waves have the good characteristic for resisting the diffraction and absorption in absorbing medium, which can solve the low transmittance of light waves in seawater. By the turbulence spectrum of seawater and the theory of frozen waves, we develop a frozen wave theory for random field and establish a transmittance model for finite energy frozen beams and analyze the diffracting- and absorption-resistance of finite energy frozen waves from the beam transmission wavelength, beam waist, beam orbital angular momentum quantum number, inner scale of turbulence, outer scale of turbulence, the “temperature structure” constant and the ratio of temperature and salinity. The transmittance of for finite energy frozen waves decreases as the propagation distance increases, and by designing longitudinal profile we can compensate the attenuation loss of the transmittance. We derive that the frozen wave has an optimal wavelength window in “seawater transmission window”. Our results theoretically provide a feasible basis for the establishment of underwater multipoint base station optical communication network.

Autoionization rates of core-excited magnesium Rydberg atoms in electric fields using the core fluorescence as a reference

$[{\mathrm{M}}^{+*}]nl$ core-excited Rydberg states of the alkaline-earth-metal atoms can decay by electronic autoionization ($[{\mathrm{M}}^{+*}]nl\ensuremath{\rightarrow}{\mathrm{M}}^{+}+\ensuremath{\varepsilon}{l}^{\ensuremath{'}}$) or by fluorescence of the core ($[{\mathrm{M}}^{+*}]nl\ensuremath{\rightarrow}[{\mathrm{M}}^{+}]nl+h\ensuremath{\nu}$). The two processes can be detected separately by monitoring the prompt ${\mathrm{M}}^{+}$ autoionization yield and the delayed pulsed-field-ionization yield of the $[{\mathrm{M}}^{+}]nl$ Rydberg states. Whereas the former process strongly depends on the principal ($n$) and orbital angular-momentum ($l$) quantum numbers, the latter is independent of $n$ and $l$ because it is essentially a property of the ion core. We present an experimental study of the competition between autoionization and core fluorescence in $[\mathrm{Ne}]3{p}_{3/2}nl$ core-excited Rydberg states of Mg atoms and of its dependence on $n$ and weak electric fields. We analyze the experimental results using a kinetic model, from which we extract the electronic-autoionization rates by using the ${\mathrm{Mg}}^{+}\phantom{\rule{4pt}{0ex}}3{p}_{3/2}--3{s}_{1/2}$ core fluorescence (${\ensuremath{\tau}}_{\mathrm{fl}}=3.8$ ns) as an internal clock. The autoionization rate of the $3{p}_{3/2}n{d}_{3/2}$ ($J=3$) and of the fully Stark-mixed $3{p}_{3/2}nk\phantom{\rule{4pt}{0ex}}(m=0,\ifmmode\pm\else\textpm\fi{}2)$ series are $[1.9\ifmmode\times\else\texttimes\fi{}{10}^{16}/{{n}^{*}}^{3}]\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ and $[8(3)\ifmmode\times\else\texttimes\fi{}{10}^{15}/{n}^{4}]\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, which would translate for the lowest Rydberg states ($3d$ with ${n}^{*}=2.62$) to autoionization rates of $\ensuremath{\sim}{10}^{15}$ and $\ensuremath{\sim}{10}^{14}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, respectively, as fast as Auger decay processes.

The propagation parameters of a Lommel–Gaussian beam in atmospheric turbulence

Analytical formulas of the propagation parameters (including the angular width and propagation factor) of the Lommel–Gaussian beams in atmospheric turbulence are derived on the basis of extended Huygens–Fresnel integral and second-order moments of Wigner distribution function. Evolution properties of the propagation parameters of Lommel–Gaussian beams propagating in atmospheric turbulence are investigated numerically. The results show that the Lommel–Gaussian beams are less affected with smaller structure constant, as well as bigger orbital angular momentum quantum number, wavelength, and inner scale. Furthermore, the beam propagation is independent of the modulus of the asymmetry parameter. The results may be useful for the practical application of the Lommel–Gaussian beam in free space optical communications.

Interpretation of the narrow J/ψ p peaks in Λb → J/ψ p K− decay in the compact diquark model

Recently, the LHCb Collaboration have updated their analysis of the resonant J/ψp mass spectrum in the decay Λb0→J/ψpK−. In the combined Run 1 and Run 2 LHCb data, three peaks are observed, with the former Pc(4450)+ state split into two narrow states, Pc(4440)+ and Pc(4457)+, having the masses M=(4440.3±1.3−4.7+4.1) MeV and M=(4457.3±0.6−1.7+4.1) MeV, and decay widths Γ=(20.6±4.9−10.1+8.7) MeV and Γ=(6.4±2.0−1.9+5.7) MeV, respectively. In addition, a third narrow peak, Pc(4312)+, having the mass M=(4311.9±0.7−0.6+6.8) MeV and decay width Γ=(9.8±2.7−4.5+3.7) MeV is also observed. The LHCb analysis is not sensitive to broad J/ψp contributions like the former Pc(4380)+, implying that there could be more states present in the data. Also the spin-parity, JP, assignments of the states are not yet determined. We interpret these resonances in the compact diquark model as hidden-charm diquark-diquark-antiquark baryons, having the following spin and angular momentum quantum numbers: Pc(4312)+={c¯[cu]s=1[ud]s=0;LP=0,JP=3/2−}, the S-wave state, and the other two as P-wave states, with Pc(4440)+={c¯[cu]s=1[ud]s=0;LP=1,JP=3/2+} and Pc(4457)+={c¯[cu]s=1[ud]s=0;LP=1,JP=5/2+}. The subscripts denote the spins of the diquarks and LP=0,1 is the orbital angular momentum quantum number of the pentaquark. These assignments are in accord with the heavy-quark-symmetry selection rules for Λb-baryon decays, in which the spin S=0 of the light diquark [ud]s=0 is conserved. The masses of observed states can be accommodated in this framework and the two heaviest states have the positive parities as opposed to the molecular-like interpretations. In addition, we predict several more states in the J/ψp mass spectrum, and urge the LHCb Collaboration to search for them in their data.

Bandwidth-limited orbital angular momentum mode of Bessel Gaussian beams in the moderate to strong non-Kolmogorov turbulence

We investigate the effects of the moderate to strong fluctuation on the propagation of orbital angular momentum (OAM) modes carried by Bessel Gaussian beams in turbulent atmosphere. The analytic expression of the received probability of the signal and crosstalk OAM mode is derived based on the theories of extended Rytov and non-Kolmogorov turbulence. Our results show that turbulence with smaller non-Kolmogorov index, smaller inner-scale factor is more easily to induce OAM crosstalk between modes. With the increase of turbulence strength, the OAM spreads from adjacent modes to peripheral modes. Our results also indicate that the received signal intensity can be improved by use of Bessel Gaussian beams with small initial radii of beam, low OAM quantum number and long wavelength.

Effects of anisotropic oceanic turbulence on the power of the bandwidth-limited OAM mode of partially coherent modified Bessel correlated vortex beams.

We study the impacts of anisotropic turbulence on the bandwidth-limited orbital angular momentum (OAM) mode of partially coherent modified Bessel correlated beam propagation in oceanic turbulence. In a paraxial link, a power model of the bandwidth-limited OAM mode is established. We find that small-scale eddies of turbulence are an important factor that affects the power of the bandwidth-limited OAM mode transfer in a region of strong salinity fluctuation. By choosing the mode carrying lower OAM quantum number, we can transfer OAM information more efficiently, and by utilizing OAM modes with large energy level difference between modes, one can achieve multichannel communication.

Probability distribution of the orbital angular momentum mode of the ultrashort Laguerre-Gaussian pulsed beam propagation in oceanic turbulence

Abstract By introducing the orbital angular momentum (OAM) eigenfunctions of the pulsed beam and two-frequency mutual coherence function in oceanic turbulence, we establish the received probability distribution of OAM modes of the ultrashort Laguerre-Gaussian pulsed beam propagating through oceanic turbulence. Our results show that the higher rate of dissipation of kinetic energy per unit mass of fluid, larger inner scale, smaller ratio of temperature and salinity contributions to the refractive index spectrum, or lower dissipation rate of the mean-squared temperature will cause the smaller pulse duration by its full-width half-maximum. The pulse duration has a weak dependence on the OAM quantum number. In addition, the smaller OAM quantum number and the larger transmission distance cause the smaller pulse delay. Our results will be useful for vortex pulsed beam in the optical ocean communication and remote sensing.

Effects of anisotropic oceanic turbulence on the propagation of the OAM mode of a partially coherent modified Bessel correlated vortex beam

ABSTRACTWe have studied the impacts of anisotropic turbulence on the orbital angular momentum (OAM) mode of a partially coherent modified Bessel correlated vortex beam propagation in an oceanic channel. In the weak turbulence paraxial channel, a new model of the probability density of OAM modes has been established. Effects of specific parameters of the oceanic turbulence on it have been studied, it is shown that there is an optimizing receiving aperture diameter in the specific interval of the ratio of temperature and salinity , which can reduce the effect of on the normalized energy weight of OAM modes and the reception of fluctuation signal. The effect of oceanic turbulence with higher anisotropy on the OAM signal is weaker than the turbulence possessing lower anisotropy. We can choose the mode carrying lower OAM quantum number to transfer information more efficiently, and we can utilize the OAM mode with large energy level difference between modes and so on to reduce mode interference and enhance the information capacity of optical communication links.

Influence of oceanic turbulence on propagation of the Gaussian pulsed X wave carrying orbital angular momentum

Abstract By developing the two-frequency mutual coherence function of the vortex wave, we derive the analytical expression of the coherence function of the Gaussian pulsed X wave carrying orbital angular momentum propagating in the anisotropic turbulence of ocean. Employing this coherence function, we establish the received probability density of orbital angular momentum modes including the time factor. Applying this probability density, we investigate the influences of turbulence and beam parameters on the received signal probability. Our results show that the anisotropic oceanic turbulence with a smaller ratio of temperature and salinity contributions to the refractive index spectrum, higher rate of dissipation of kinetic energy per unit mass of fluid, larger inner scale, or lower dissipation rate of the mean-squared temperature causes the larger signal probability density; the Gaussian pulsed X wave with large sources transverse size, small Bessel cone angle, low orbital angular momentum quantum number or broad initial half-pulse width has stronger resistance to oceanic turbulent interference. This work provides theoretical preparation for the implementation of the spatiotemporal communication with ultrafast vortex pulse.

Orbital-angular-momentum-enhanced estimation of sub-Heisenberg-limited angular displacement with two-mode squeezed vacuum and parity detection.

We report on an orbital-angular-momentum-enhanced scheme for angular displacement estimation based on two-mode squeezed vacuum and parity detection. The sub-Heisenberg-limited sensitivity for angular displacement estimation is obtained in an ideal situation. Several realistic factors are also considered, including photon loss, dark counts, response-time delay, and thermal photon noise. Our results indicate that the effects of realistic factors on the sensitivity can be offset by raising orbital angular momentum quantum number ℓ. This implies that the robustness and the practicability of the system can be improved via raising ℓ without changing mean photon number N.