States Of Principal Quantum Number Research Articles

New Method to Study Ion-Molecule Reactions at Low Temperatures and Application to the H2++H2→H3++H Reaction.

Studies of ion-molecule reactions at low temperatures are difficult because stray electric fields in the reaction volume affect the kinetic energy of charged reaction partners. We describe a new experimental approach to study ion-molecule reactions at low temperatures and present, as example, a measurement of the H2++H2→H3++H reaction with the H2+ ion prepared in a single rovibrational state at collision energies in the range Ecol /kB =5-60 K. To reach such low-collision energies, we use a merged-beam approach and observe the reaction within the orbit of a Rydberg electron, which shields the ions from stray fields. The first beam is a supersonic beam of pure ground-state H2 molecules and the second is a supersonic beam of H2 molecules excited to Rydberg-Stark states of principal quantum number n selected in the range 20-40. Initially, the two beams propagate along axes separated by an angle of 10°. To merge the two beams, the Rydberg molecules in the latter beam are deflected using a surface-electrode Rydberg-Stark deflector. The collision energies of the merged beams are determined by measuring the velocity distributions of the two beams and they are adjusted by changing the temperature of the pulsed valve used to generate the ground-state H2 beam and by adapting the electric-potential functions applied to the electrodes of the deflector. The collision energy is varied down to below Ecol /kB =10 K, that is, below Ecol ≈1 meV, with an energy resolution of 100 μeV. We demonstrate that the Rydberg electron acts as a spectator and does not affect the cross sections, which are found to closely follow a classical Langevin-capture model in the collision energy range investigated. Because all neutral atoms and molecules can be excited to Rydberg states, this method of studying ion-molecule reactions is applicable to other reactions involving singly charged cations.

Radiative and collisional processes in translationally cold samples of hydrogen Rydberg atoms studied in an electrostatic trap

Supersonic beams of hydrogen atoms, prepared selectively in Rydberg–Stark states of principal quantum number n in the range between 25 and 35, have been deflected by , decelerated and loaded into off-axis electric traps at initial densities of atoms cm−3 and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially prepared states, the initial Rydberg-atom density in the trap, and the temperature of the environment of the trap, which could be varied between 7.5 and 300 K using a cryorefrigerator. At room temperature, the population of trapped Rydberg atoms was found to decay faster than expected on the basis of their natural lifetimes, primarily because of absorption and emission stimulated by the thermal radiation field. At the lowest temperatures investigated experimentally, the decay was found to be multiexponential, with an initial rate scaling as and corresponding closely to the natural lifetimes of the initially prepared Rydberg–Stark states. The decay rate was found to continually decrease over time and to reach an almost n-independent rate of more than (1 ms)−1 after 3 ms. To analyze the experimentally observed decay of the populations of trapped atoms, numerical simulations were performed which included all radiative processes, i.e., spontaneous emission as well as absorption and emission stimulated by the thermal radiation. These simulations, however, systematically underestimated the population of trapped atoms observed after several milliseconds by almost two orders of magnitude, although they reliably predicted the decay rates of the remaining atoms in the trap. The calculations revealed that the atoms that remain in the trap for the longest times have larger absolute values of the magnetic quantum number m than the optically prepared Rydberg–Stark states, and this observation led to the conclusion that a much more efficient mechanism than a purely radiative one must exist to induce transitions to Rydberg–Stark states of higher values. While searching for such a mechanism, we discovered that resonant dipole–dipole collisions between Rydberg atoms in the trap represent an extremely efficient way of inducing transitions to states of higher values. The efficiency of the mechanism is a consequence of the almost perfectly linear nature of the Stark effect at the moderate field strengths used to trap the atoms, which permits cascades of transitions between entire networks of near-degenerate Rydberg-atom-pair states. To include such cascades of resonant dipole–dipole transitions in the numerical simulations, we have generalized the two-state Förster-type collision model used to describe resonant collisions in ultracold Rydberg gases to a multi-state situation. It is only when considering the combined effects of collisional and radiative processes that the observed decay of the population of Rydberg atoms in the trap could be satisfactorily reproduced for all n values studied experimentally.

Pulsed excitation of Rydberg-atom-pair states in an ultracold Cs gas

Pulsed laser excitation of a dense ultracold Cs vapor has been used to study the pairwise interactions between Cs atoms excited to $n{p}_{3/2}$ Rydberg states of principal quantum numbers in the range $n=22--36$. Molecular resonances were observed that correspond to excitation of Rydberg-atom-pair states correlated not only to the $n{p}_{3/2}+n{p}_{3/2}$ dissociation asymptotes, but also to $n{s}_{1/2}+(n+1){s}_{1/2}, n{s}_{1/2}+{n}^{\ensuremath{'}}{f}_{j}$, and $(n\ensuremath{-}4){f}_{j}+(n\ensuremath{-}3){f}_{j}\phantom{\rule{4pt}{0ex}}(j=5/2,7/2)$ dissociation asymptotes. These pair resonances are interpreted as arising from dipole-dipole and higher-order long-range-interaction terms between the Rydberg atoms on the basis of (i) their spectral positions, (ii) their response to static and pulsed electric fields, and (iii) millimeter-wave spectra between pair states correlated to different pair-dissociation asymptotes. The Rydberg-atom-pair states were found to spontaneously decay by Penning ionization and the dynamics of the ionization process were investigated during the first 15 $\ensuremath{\mu}\mathrm{s}$ following initial photoexcitation. To interpret the experimental observations, a potential model was derived that is based on the numerical determination of the eigenvalues and eigenfunctions of the long-range interaction Hamiltonian. With this potential model, which does not include adjustable parameters, all experimental observations could be accounted for, and the results demonstrate that long-range-interaction models provide a global and accurate description of interactions in ultracold Rydberg gases and that they correctly account for, and enable the analysis of, phenomena as diverse as the formation of Rydberg macrodimers, Penning ionization in dense Rydberg gases, and Rydberg-excitation-blockade effects.

Pulsed excitation of Rydberg-atom-pair states in an ultracold Cs gas

Pulsed laser excitation of a dense ultracold Cs vapor has been used to study the pairwise interactions between Cs atoms excited to $n$p$_{3/2}$ Rydberg states of principal quantum numbers in the range $n=22-36$. Molecular resonances were observed that correspond to excitation of Rydberg-atom-pair states correlated not only to the $n$p$_{3/2}+n$p$_{3/2}$ dissociation asymptotes, but also to $n$s$_{1/2}+(n+1)$s$_{1/2}$, $n$s$_{1/2}+n'$f$_{j}$, and $(n-4)$f$_{j}+(n-3)$f$_{j}$ $(j=5/2,7/2)$ dissociation asymptotes. These pair resonances are interpreted as arising from dipole-dipole, and higher-order long-range-interaction terms between the Rydberg atoms on the basis of i) their spectral positions, ii) their response to static and pulsed electric fields, and iii) millimeter-wave spectra between pair states correlated to different pair-dissociation asymptotes. The Rydberg-atom--pair states were found to spontaneously decay by Penning ionization and the dynamics of the ionization process were investigated during the first 10 $\mu$s following initial photoexcitation. To interpret the experimental observations, a potential model was derived that is based on the numerical determination of the eigenvalues and eigenfunctions of the long-range interaction Hamiltonian. With this potential model, which does not include adjustable parameters, all experimental observations could be accounted for, and the results demonstrate that long-range-interaction models provide a global and accurate description of interactions in ultracold Rydberg gases and that they correctly account for, and enable the analysis of, phenomena as diverse as the formation of Rydberg macrodimers, Penning ionization in dense Rydberg gases, and Rydberg-excitation blockade effects.

Surface-electrode decelerator and deflector for Rydberg atoms and molecules

A surface-electrode decelerator and deflector for Rydberg atoms and molecules has been developed with the goal of performing collisional experiments. Translationally cold ${\mathrm{H}}_{2}$ molecules in a supersonic beam were excited to Rydberg-Stark states of principal quantum number $n=31$, loaded into electric traps moving at a predetermined speed above the surface of a bent printed circuit board, decelerated, and deflected from the original direction of the supersonic beam by an angle of ${10}^{\ensuremath{\circ}}$. The phase-space characteristics of the deflected beam were characterized by measuring the time-of-flight distribution and images of the Rydberg molecules and comparing them to the results of numerical particle-trajectory simulations. More than 1000 ${\mathrm{H}}_{2}$ molecules were deflected per experimental cycle at a repetition rate of 25 Hz. The phase-space characteristics of the deflector make it attractive to study ion-molecule reactions at low collision energies.

Excitation of Rydberg wave packets with chirped laser pulses

We study Rydberg wave packets produced by pairs of time separated femtosecond laser pulses. The time separation ranges from femtosecond to picosecond time scales. The wave packets consist predominantly of $f$ states of principal quantum numbers $n=22$--32 in Li. With a direct analysis of the field ionization spectra the $n$-level-resolved classical orbit times are displayed. By chirping the second excitation pulse we demonstrate controlled amplitude oscillations of $n$-level amplitudes on femtosecond time scales.

Trapping cold molecular hydrogen

Translationally cold H(2) molecules excited to non-penetrating |M(J)| = 3 Rydberg states of principal quantum number in the range 21-37 have been decelerated and trapped using time-dependent inhomogeneous electric fields. The |M(J)| = 3 Rydberg states were prepared from the X (1)Σ(+)(u)(v = 0, J = 0) ground state using a resonant three-photon excitation sequence via the B (1)Σ(+)(u)(v = 3, J = 1) and I (1)Π(g) (v = 0, J = 2) intermediate states and circularly polarized laser radiation. The circular polarization of the vacuum ultraviolet radiation used for the B ← X transition was generated by resonance-enhanced four-wave mixing in xenon and the degree of circular polarization was determined to be 96%. To analyse the deceleration and trapping experiments, the Stark effect in Rydberg states of molecular hydrogen was calculated using a matrix diagonalization procedure similar to that presented by Yamakita et al., J. Chem. Phys., 2004, 121, 1419. Particular attention was given to the prediction of zero-field positions of low-l states and of avoided crossings between Rydberg-Stark states with different values of |M(J)|. The calculated Stark maps and probabilities for diabatic traversal of the avoided crossings were used as input to Monte-Carlo particle-trajectory simulations. These simulations provide a quantitatively satisfactory description of the experimental data and demonstrate that particle loss caused by adiabatic traversals of avoided crossings between adjacent |M(J)| = 3 Stark states of H(2) is small at principal quantum numbers beyond n = 25. The main source of trap losses was found to be from collisional processes. Predissociation following the absorption of blackbody radiation is estimated to be the second most important trap-loss mechanism at room temperature, and trap loss by spontaneous emission is negligible under our experimental conditions.

Measurement of Rydberg-state lifetimes using cold trapped atoms

In this paper, we demonstrate the use of a cold trapped sample of neutral atoms to perform high-precision measurement of the lifetime for a sequence of Rydberg states of 8 5 Rb. States of principal quantum number lying between n = 31 and n = 45 are produced and their lifetimes measured using field ionization. Experimental results are compared with existing theories. This is an important demonstration concerning the possibilities of high-precision spectroscopy in the time domain using cold atomic samples.

Electron capture from coherent elliptic Rydberg states

Experimental relative cross sections for electron capture by singly charged ions (Na{sup +}) from coherent elliptic states of principal quantum number n=25 are presented. An interval of reduced impact velocities from about 1{endash}2 is covered. Absolute reaction cross sections could not be determined precisely, but the eccentricity of the coherent elliptic states and their orientation relative to the ion-impact velocity were varied to expose the dependence of the electron-capture process on the initial motion of the electron. The dependencies on eccentricity and orientation are generally strong and they vary sharply with impact velocity. Qualitatively, the observations agree fairly well with classical trajectory Monte Carlo (CTMC) calculations, as expected for the large quantum numbers involved, but significant deviations of a systematic nature do remain, showing that some aspects of the capture reactions studied are described poorly by classical physics as represented by the CTMC model. {copyright} {ital 1997} {ital The American Physical Society}

Microwave forced autoionization of Na2 Rydberg states.

We have examined the ionization of ${\mathrm{Na}}_{2}$ Rydberg states of principal quantum number n=11--16 converging to rotational-vibrational, v=3--6 and R10, states of ${\mathrm{Na}}_{2}^{+}$ by 8-GHz microwave fields. Rydberg states lying below the lowest, v=0, R=0 (v and R are the vibrational and rotational quantum numbers of the molecular ion), ion limit of ${\mathrm{Na}}_{2}^{+}$ are observed to ionize at approximately E=1/3${\mathit{n}}_{0}^{5}$, where ${\mathit{n}}_{0}$ is the effective quantum number relative to the v=R=0 limit. The agreement with this dependence is not nearly as good as in an atom, and the possible reasons for the deviations are discussed.

Cavity-induced level shifts of rubidium Ryberg states

Rubidium atoms, prepared in Ryberg states of principal quantum numbers n in the range 20 to 35 and then sent between two perfectly reflecting parallel mirrors, suffer energy level shifts that may be measurable now. The results of a calculation of these shifts is presented here, based upon the theory advanced recently by Barton. For the level 30 S, for example, we report an energy shift of Δ=61 Hz.

Measuring the van der Waals forces between a Rydberg atom and a metallic surface.

We have observed the deflection of Rydberg atoms towards a metallic surface by the van der Waals force. Cs and Na atoms in states of principal quantum number n were sent between two parallel gold-coated mirrors, spaced by a gap w (2.1 \ensuremath{\mu}m\ensuremath{\le}w\ensuremath{\le}8.5 \ensuremath{\mu}m). We measured the value ${n}_{m}$ at which the transmission cuts off and from the variation of ${n}_{m}$ versus w, we obtained a measure of the atom-surface interaction. For $12<n<30$ this interaction is 3--4 orders of magnitude larger than for ground-state atoms, and it obeys the scaling laws of the Lennard-Jones model.

Field ionization and forced autoionization of Li2.

Bound ${\mathrm{Li}}_{2}$ states of principal quantum number n=12--14 converging to v=2 and 3 levels of the ground state of ${\mathrm{Li}}_{2}$${\mathrm{}}^{+}$ can be ionized by fields of \ensuremath{\sim}200 V/cm, 2 orders of magnitude less than expected for direct field ionization of these levels. The result is shown to be due to forced autoionization. The field depresses the ionization limit of the series converging to the lowest rotational-vibrational ${\mathrm{Li}}_{2}$${\mathrm{}}^{+}$ levels, and the n=12--14 levels in question autoionize to the Stark-induced continuum.

Improved excitation rate coefficients for the N = 2 and N = 3 levels of CA XIX and Fe XXV including fine structure

Reently calculated collision strengths, including relativistic and resonance effects, are employed to compute Maxwellian averaged collision strengths for 78 transitions involving states of principal quantum numbers 2-1 and 3-1 in Ca XIX and Fe XXV. These rate parameters are tabulated at temperatures of interest in astrophysical and labortory plasmas with radiation in the hard X-ray wavelength range. For some transitions, significant differences are found with the earlier calculations of Pradhan, Norcross, and Hummer (1981).

Acceptor excited states in indium phosphide

Selective donon-acceptor pair luminescence and luminescence excitation spectra reveal acceptor excitations to all excited states of principal quantum number 2, odd as well as even parity. These transition energies are independent of the D-A pair separation R for sufficiently large R and are then identical to those on isolated acceptors. However, they decrease significantly at small R and some splittings are revealed in our measurements on a bulk grown crystal in which the most common contaminant acceptor Zn is dominant. The p state transition energies are used together with the known ionization energy of the Zn acceptor to derive valence band parameters for InP according to the theory of Baldereschi and Lipari. We find γ 1 = 5.6 ± 0.7, γ 2 = 2.0 ± 0.3, γ 3 = 2.4 ± 0.3, where γ 1 is adjusted to fit the cyclotron resonance data of Leotin et al. Some reservations concerning the completeness of this theory are acknowledge. Information on the s acceptor excited state is consistent with that obtained from acceptor bound exciton “two-hole” satellites for this remarkable quality bulk crystal.

Electron-detachment cross sections to low-lying excited states of hydrogen in collisions of negative hydrogen ions with helium and argon

The intensities of the four lowest Lyman lines (Ly- alpha , Ly- beta , Ly- gamma and Ly- delta ) of atomic hydrogen produced in electron-detachment collisions of 1-6 keV negative hydrogen ions on helium and argon were measured. By applying an electric field in the direction of the ion beam, excited states of hydrogen were Stark-mixed and the effects on the emission intensities were studied. Electron-detachment cross sections were evaluated from the intensity measurements for states of principal quantum numbers 2 to 5. For both gases, electron detachment to the 2p1/2,3/2 state is much larger than detachment to the 2s1/2 state. The preference for 2p1/2,3/2 excitation also occurs with respect to detachment to the higher np1/2, 3/2 (n=3-5) states of the hydrogen atom.