Long-lived Rydberg States Research Articles

Parallel execution of quantum gates in a long linear ion chain via Rydberg mode shaping

We present a mechanism that permits the parallel execution of multiple quantum gate operations within a single long linear ion chain. Our approach is based on large coherent forces that occur when ions are electronically excited to long-lived Rydberg states. The presence of Rydberg ions drastically affects the vibrational mode structure of the ion crystal giving rise to modes that are spatially localized on isolated sub-crystals which can be individually and independently manipulated. We theoretically discuss this Rydberg mode shaping in an experimentally realistic setup and illustrate its power by analyzing the fidelity of two conditional phase flip gates executed in parallel. Our scheme highlights a possible route towards large-scale quantum computing via vibrational mode shaping which is controlled on the single ion level.

Experimental investigation of long-lived Rydberg states in ultracold argon

We report on our investigation of the formation and survival of long-lived Rydberg states in argon produced by pulsed laser excitation of ultracold metastable state argon atoms in a magneto-optical trap. The states studied have a ${}^{2}{P}_{1/2}$ core. Low angular momentum Rydberg states with this core normally autoionize rapidly. If, however, atoms are excited in the presence of electric fields, higher angular momentum states, traditionally termed ``ZEKE states'' (ZEKE is derived from ``zero kinetic energy'') can be formed. The lifetime of these states can be orders of magnitude greater than low angular momentum states. In this paper, we report on the time dependence of ZEKE Rydberg state population in an ultracold environment.

Mass-Analyzed Threshold Ionization (MATI) Spectroscopy of Atoms and Molecules Using VUV Synchrotron Radiation

Mass-analyzed threshold ionization (MATI) spectroscopy using synchrotron radiation (Advanced Light Source, Lawrence Berkeley National Laboratory) has been performed for Ar, N(2), O(2), N(2)O, H(2)O, C(2)H(2), and C(6)H(6). MATI allows for a better determination of ionization energies compared to those derived from photoionization efficiency curves traditionally used in synchrotron photoionization mass spectrometry. The separation of the long-lived Rydberg state from the directly formed prompt ion, essential for a meaningful MATI spectrum, has been accomplished by employing an arrangement of ion optics coupled to unique electric field pulsing schemes. For Ar, a number of resolved bands below the ionization energy are observed, and these are ascribed to high-n,l Rydberg states prepared in the MATI scheme. The first vibrational state resolved MATI spectra of N(2) and O(2) are reported, and spectral characteristics are discussed in comparison with previously reported threshold photoelectron spectroscopic studies. Although MATI performed with synchrotron radiation is intrinsically less sensitive compared to laser-based sources, this work demonstrates that MATI spectroscopy performed with widely tunable vacuum ultraviolet (VUV) radiation is a complementary technique for studying the ionization spectroscopy of polyatomic molecules.

Temperature dependence of binary and ternary recombination ofH3+ions with electrons

We study binary and the recently discovered process of ternary He-assisted recombination of H3+ ions with electrons in a low temperature afterglow plasma. The experiments are carried out over a broad range of pressures and temperatures of an afterglow plasma in a helium buffer gas. Binary and He-assisted ternary recombination are observed and the corresponding recombination rate coefficients are extracted for temperatures from 77 K to 330 K. We describe the observed ternary recombination as a two-step mechanism: First, a rotationally-excited long-lived neutral molecule H3* is formed in electron-H3+ collisions. Second, the H3* molecule collides with a helium atom that leads to the formation of a very long-lived Rydberg state with high orbital momentum. We present calculations of the lifetimes of H3* and of the ternary recombination rate coefficients for para and ortho-H3+. The calculations show a large difference between the ternary recombination rate coefficients of ortho- and para-H3+ at temperatures below 300 K. The measured binary and ternary rate coefficients are in reasonable agreement with the calculated values.

Internal state populations and velocity distributions of monatomic species ejected after the 1064 nm laser irradiation of barium

The plumes accompanying 1064 nm nanosecond pulsed laser ablation of barium in vacuum at three moderate incident laser fluences in the range of 5.3–10.8 J/cm2 have been studied using both wavelength and time resolved optical emission spectroscopy and time-of-flight laser-induced fluorescence. Neutral atoms and both singly and doubly charged monatomic cations in excited states up to near the corresponding ionization limits are identified in the optical emission spectra. The population distributions of low-lying (≤1.41 eV) “dark” states of Ba atoms measured by laser-induced fluorescence revel that the metastable D3J and D12 abundances in the plume are higher than predictions based on assuming a Boltzmann distribution. The D3J and D12 populations are seen, respectively, to decrease slightly and nearly no vary with raising fluence, which contrasts with the increasing trend that is observed in the ground-state Ba(S10) population. At all fluences, the time-of-flight distributions of the whole dark states and of various of the emitting levels are bimodal and well described by Maxwell–Boltzmann and shifted Maxwell–Boltzmann velocity functions, respectively, with different average translational temperatures ⟨T⟩ for each state. The ⟨T⟩ values for the dark states are insensitive to the fluence, while for all emitting species marked variations of ⟨T⟩ with fluence are found. These observations have been rationalized in terms of material ejection from the target being dominated by a phase explosion mechanism, which is the main contributor to the Ba(S10) population. Thermionic emission from the target surface can also release initial densities of free electrons and cations which, at the prevailing irradiances, will arguably interact with the incident laser radiation by inverse bremsstrahlung, leading to further excitation and ionization of the various plume species. Such a heating mechanism ensures that the energy injected to the plume will alter the propagation velocities of the primary inverse bremsstrahlung absorbers, i.e., cations, to a major extent than those of neutral atoms with increasing fluence. Electron-ion recombination occurring early in the plume expansion can lead to the generation of both neutral and ionic species in a manifold of long-lived Rydberg states, from which a radiative cascade will likely ensue. The distinct fluence dependences of the Ba(D3J) and Ba(D12) populations and velocity distributions show up the major complexity that distinguishes their populating mechanisms with respect to the remaining species.

Silicon as a model ion trap: Time domain measurements of donor Rydberg states

One of the great successes of quantum physics is the description of the long-lived Rydberg states of atoms and ions. The Bohr model is equally applicable to donor impurity atoms in semiconductor physics, where the conduction band corresponds to the vacuum, and the loosely bound electron orbiting a singly charged core has a hydrogen-like spectrum according to the usual Bohr–Sommerfeld formula, shifted to the far-infrared because of the small effective mass and high dielectric constant. Manipulation of Rydberg states in free atoms and ions by single and multiphoton processes has been tremendously productive since the development of pulsed visible laser spectroscopy. The analogous manipulations have not been conducted for donor impurities in silicon. Here, we use the FELIX pulsed free electron laser to perform time-domain measurements of the Rydberg state dynamics in phosphorus- and arsenic-doped silicon and we have obtained lifetimes consistent with frequency domain linewidths for isotopically purified silicon. This implies that the dominant decoherence mechanism for excited Rydberg states is lifetime broadening, just as for atoms in ion traps. The experiments are important because they represent a step toward coherent control and manipulation of atomic-like quantum levels in the most common semiconductor and complement magnetic resonance experiments in the literature, which show extraordinarily long spin lattice relaxation times—key to many well known schemes for quantum computing qubits—for the same impurities. Our results, taken together with the magnetic resonance data and progress in precise placement of single impurities, suggest that doped silicon, the basis for modern microelectronics, is also a model ion trap.

Nonergodic and conformational control of the electron capture dissociation of protein cations.

Electron capture dissociation (ECD) MS is proving to be unusually valuable for "top down" protein sequencing and identification/localization of posttranslational modifications, because the ECD product ions can represent cleavages between most of a protein's amino acids. As proposed, this unusual reactivity results from immediate local utilization, before randomization, of much of the relatively large ( approximately 6 eV) energy from the electron reaction with the multiply charged protein ion, minimizing the effect of differences in the backbone bond dissociation energies. However, others conclude that e(-) capture produces a labile free radical species for which backbone cleavage is the lowest energy reaction. Supporting the nonergodic mechanism, ECD of ubiquitin (M + 12H)(12+) ions also yields thermalized radical (M + 12H)(11+.) ions that instead lose H. when activated. Also, the ECD spectrum of ubiquitin (M + 13H)(13+) ions is nearly unchanged by heating from 25 degrees C to 125 degrees C, demonstrating that this increase in thermal energy is small compared to the energy driving the reaction. These results support initial capture of the electron in a long-lived high-n Rydberg state, followed by internal conversion to the product valence state at an energy well above the dissociation barriers. The instantaneous conformation of the valence state is critical, with the observed products supporting an alpha-helical structure in which the protonated side chain of each basic residue is intercalated to hydrogen-bond to as many as three amide carbonyls. Activation (e.g., heat, collisions, lowered charge) can disrupt this conformation to allow additional H(+)-side-chain interactions and provide more complete sequence coverage.

Threshold photoionization in time-of-flight mass spectrometry.

Multi-photon excitation in a time-of-flight mass spectrometer (TOF-MS) is shown to lead to threshold ions with defined internal energy. A powerful technique for the production of threshold ions is based on the excitation of high long-lived Rydberg states embedded in the ionization continuum. The Rydberg molecules are separated with suitable separation techniques from ions produced by a direct multi-photon ionization process. Finally, the ionization of the Rydberg molecules in a delayed pulsed electric field leads to threshold ions. This work reviews several separation techniques, and reports on applications of threshold ionization for investigation of the structure, energetics, and dynamics of neutral molecules, molecular cations, and cluster cations.

Formation of long-lived Rydberg states of H 2 at K impregnated surfaces

The formation of Rydberg states of hydrogen molecules H 2 * at potassium promoted iron oxide surfaces at 900–1000 K is studied using pulsed laser fragmentation neutral time-of-flight measurements. Both neutral Rydberg states H 2 * and ions H 2 + are observed to reach the detector, as well as electronically excited clusters of hydrogen of the Rydberg matter type. The Rydberg states H 2 * and ions H 2 + are not formed by the laser since the fluence is too low, and such particles are not observed from hydrogen molecules in the gas phase. They also carry an excess kinetic energy of <1 eV due to laser fragmentation. This kinetic energy corresponds probably to Coulomb repulsion in the excited clusters with interionic distances of a few nanometers. The size of the signal of H 2 * varies strongly with the laser fluence at high fluences. The molecular Rydberg states are believed to be formed by transfer of electronic excitation energy from the Rydberg states of the alkali atoms K *, which are formed at the sample surface.

Coherent stabilization of zero-electron-kinetic-energy states

The accuracy of zero-electron-kinetic-energy (ZEKE) photoelectron spectroscopy rests on the ultralong lifetimes of the high-n, high-l Rydberg states that are responsible for the ZEKE signal. However, a few-photon process cannot excite electrons directly from the low-l ground state to the high-l ZEKE manifold. In this paper we show that using the dynamics of Rydberg Stark states in slowly time dependent external fields it is possible to control coherently the angular momentum of Rydberg electrons, and therefore also their lifetime. We derive explicitly two different schemes based on simple, short electric dc pulses, which populate precisely those high-l, long-lived Rydberg states that are necessary for accurate ZEKE experiments. The high-l states that we construct are also Stark eigenstates, therefore a moderate dc external field can eventually enforce cylindrical symmetry and lock the ZEKE electrons in the stable, long-lived high-l manifold.

Vibrational spectroscopy of molecular and van der Waals complex cations by mass analyzed pulsed field threshold ionization spectroscopy

Mass analyzed threshold ionization spectroscopy is a versatile technique to measure vibrational spectra of the electronic ground state of polyatomic molecular ions and their complexes with noble gas atoms. The method is based on the separation of promptly produced ions from molecules in high long-lived Rydberg states converging to a selected ionization threshold. After field ionization of the Rydberg states molecular ions in defined vibrational states are produced. We demonstrate for the first time that the so produced threshold ions can be trapped and stored in an electrodynamical ion trap without any background from non-energy-selected prompt ions. As a new result the van der Waals vibrations of the fluorobenzene-Ar complex cation are presented and compared with the respective vibrations in the neutral complex. While the frequency of the stretching mode increases after ionization of the complex, the long axis in-plane bending mode is strongly reduced in frequency. Excitation to vibrational states with more than 543 cm −1 leads to a dissociation of the complex cations and to the appearance of daughter (fluorobenzene) threshold ions. The dissociation energy of the ionic complex E 0 ≈ 543 cm −1 and the respective value of the neutral complex is d 0 ≈ 321 cm −1.

Preparation and characterization of long-lived molecular Rydberg states: Application to HD

The decay dynamics by predissociation and rotational autoionization of high Rydberg states of HD close to the first few rotational levels of the ground vibronic state of the HD+ cation have been studied by delayed pulsed field ionization following resonant (1+1′) two-photon absorption via the B state. Although predissociation and autoionization both contribute to the rapid decay of Rydberg states with principal quantum number n≪100, the highest Rydberg states (n≳100) are stable for more than 20 μs. In contrast to H2, channels associated with an HD+ (v+=0, N+=even) ion core are coupled to channels associated with an HD+ (v+=0, N+=odd) ion core. We demonstrate that complex resonances that arise from rotational channel interactions between low (n∼25) Rydberg states characterized by a core with rotational angular momentum quantum number N++2 and the pseudocontinuum of very high Rydberg states characterized by an N+ core can be used with high efficiency to produce long-lived high Rydberg states. An investigation of the pulsed field ionization characteristics of these complex resonances enables us to measure the branching between diabatic and adiabatic field ionization and to determine the optimal conditions required to extend the method of H-photofragment Rydberg translational spectroscopy pioneered by Schnieder et al. [J. Chem. Phys. 92, 7027 (1990)] to molecular species.

Pulsed field threshold ionization of van der Waals complexes. The dissociation energy of ionic and neutral dibenzo- p-dioxin·Ar and · 84Kr

The technique of mass selective pulsed field threshold ionization of high long-lived Rydberg states has been applied to dibenzo- p-dioxin (DD), DD·Ar, and DD· 84Kr yielding adiabatic ionization energies of 61283, 61071, and 61005 cm −1, respectively. A sharp energetic threshold for the disappearance of the parent threshold ion signal of (DD·Ar) + and the appearance of the daughter threshold ion signal is observed. This leads to accurate values of the dissociation energy E 0 = 717 cm −1 in (DD·Ar) +, E 0 = 918 cm −1 in (DD· 84Kr) + and to D 0 = 505 cm −1 in DD·Ar, D 0 = 640 cm −1 in DD· 84Kr.

Photodissociation of state-selected cluster ions studied by mass-selective, pulsed-field threshold ionization spectroscopy

Abstract Delayed pulsed-field ionization of long-lived high Rydberg states yields vibrationally and partly rotationally resolved spectra of polyatomic molecular ions and of cluster ions when the resulting threshold ions are measured as a function of the excitation energy. The field ionized threshold ions are monitored and separated from the non-energy-selected ions in a reflecting field mass spectrometer with high mass resolution. The decay of the molecular or cluster ion core is monitored by the appearance of threshold ions at the daughter ion mass as a function of the selectively excited vibrational state. In this way, upper limits for dissociation thresholds of neutral and ionized dimers are obtained which are smaller than recent theoretical values from the literature. The appearance of daughter fragment ions after delayed pulsed-field ionization indicates that high Rydberg orbits are not destroyed by the dissociation of the core. Possible applications of our technique for the production of state-selected ions are discussed.

Electron Impact Excitation of Delayed Ionization of C60-Evidence for Rydberg States

A supersonic molecular beam apparatus with a quadrupole mass spectrometer has been used to study the delayed ionization of C[sub 60] by electron impact. Time-of-flight (TOF) analysis through the quadrupole is used to separate the direct ionization of C[sub 60] from delayed ionization. The excitation function for this delayed ionization has been measured as a function of electron energy. The threshold for the excitation function is 32 eV, with a peak at 46 eV and a full width at half-maximum of only 15 eV. It is suggested that the excitation function is closely related to the cross section and that the shape of this function indicates a forbidden transition may be excited. The relative magnitudes of the delayed ionization signals are almost independent of the mass setting of the quadrupole which has been used to suggest that most of the delayed ionization signal results from field ionization of a long-lived Rydberg state from C[sub 60]. 25 refs., 5 figs.

Mass analyzed threshold ionization: structural information for a mass spectrum and mass information for ionic spectroscopy

Mass analyzed threshold ionization spectroscopy is a technique for simultaneously recording a mass spectrum and an optical spectrum for each parent ion present. In this method a laser is tuned through the ionization continuum of the sample, while the instrument is set up to record a given mass only when the light is tuned to an ionization threshold. The presence of an ionization threshold is signaled by the presence of long-lived high Rydberg states which are field ionized after they are separated from directly produced ions. A reflectron mass spectrometer then provides mass information to go with the optical spectrum of the ions provided by scanning the laser. Vibrational structure of the ionic ground state is easiest to obtain, but future development may enable rotational information to be gained as well. The technique should find use in resolving isomeric ambiguity in mass spectra, in determining the structure of species present in mixtures, and for examining the photophysics of both the neutral and ionic states of the molecule of interest.

Decay energetics of molecular clusters studied by multiphoton mass spectrometry and pulsed field threshold ionization

New developments in time-of-flight mass spectrometry combined with multi-photon ionization provide hitherto unachievable information on the decay of weakly bound cluster ions. Dissociation thresholds of cluster ions are important for the understanding of their binding and structure. We present two experimental methods that allow the determination of dissociation energies of weakly bound ionic and neutral clusters. Besides the breakdown technique observing the metastable ion efficiency curves, a novel method is presented and described which is based on delayed pulsed field ionization of long-lived Rydberg states close to the ionization energy. In this way state-selected benzene—noble gas ions are produced and their decay is observed in a reflectron mass spectrometer. Results for dissociation thresholds of various molecular dimers and larger complexes of aromatic molecules are presented. The pronounced differences in dissociation energy between the neutrals and the ions are interpreted in terms of charge-transfer resonance interaction in the ionic complex leading to structural changes after the ionization process.

Dissociation energy of neutral and ionic benzene-noble gas dimers by pulsed field threshold ionization spectroscopy

Delayed pulsed field threshold ionization of clusters excited to high long-lived Rydberg states is used to study their dissociation behavior. Benzene–Ar and benzene–Kr dimers are excited by resonance enhanced two-photon ionization to Rydberg levels close to various ionization thresholds. The field ionized threshold ions are monitored and separated from the non-energy-selected ions in a reflecting field mass spectrometer with high mass resolution. The appearance of threshold ions at the daughter ion mass indicates the onset of a dissociation process. Daughter ions are first observed for the 16161(3/2) level of the two investigated dimers. This leads to an upper limit of the dissociation energy of benzene–Ar of 340 cm−1 which is probably higher than the true dissociation energy. For the first time threshold ions are observed for large internal energies of some 5 eV in the core indicating that high Rydberg states maintain their long lifetime even if the core is electronically or vibrationally excited by several eV.

Preparation of ions in selected rotational states by delayed pulsed field ionization

A novel method of preparing ions in selected rovibronic states is presented. It is based on pulsed field ionization of long-lived high-n Rydberg states lying just below the different rovibronic energy levels of the ion. The potential of the method is illustrated with the example of hydrogen: A clean population of H2+ ions is prepared in the X 2∑g+ (v+=2, N+=0, 1, 2, 3) states. The method ought to be applicable to the preparation of a wide range of small molecular ions in selected rotational states and opens new possibilities in the study of state-to-state ion–molecule reactions.

Zero kinetic energy (ZEKE) photoelectron spectroscopy of ammonia by nonresonant two-photon ionization from the neutral ground state

Rotationally resolved zero kinetic energy-pulsed field ionization (ZEKE-PFI) photoelectron spectra of NH3 were obtained by nonresonant two-photon ionization from the X̃(1A1′) electronic ground state. The ZEKE spectra were recorded up to an internal ion energy of 9500 cm−1 by pulsed field ionization of long-lived Rydberg states of very high principal quantum numbers. Rovibronic bands of the NH3+ cation with v2+=1–9 (umbrella mode), v4+=1, and for the first time the mode ν1 in the combination band v+=1121 of the X̃+(2A2″) electronic ground state are observed in the ZEKE spectra. Rotational constants and band origins are determined in the analysis. The adiabatic ionization energy obtained by a recent ZEKE measurement is confirmed at 82 159±1 cm−1.