Rydberg States Research Articles

Pulsed-ramped-field-ionisation zero-kinetic-energy photoelectron spectroscopy of the metastable rare-gas atoms Ar, Kr and Xe.

The photoionisation of the metastable rare-gas atoms Rg = Ar, Kr and Xe is investigated at the Rg+ […](ns)2(np)5 2P3/2 ← Rg[…](ns)2(np)5((n + 1)s) 13P2 photoionisation threshold (n = 3, 4 and 5 for Ar, Kr and Xe) using the technique of pulsed-ramped-field-ionisation zero-kinetic-energy (PRFI-ZEKE) photoelectron spectroscopy. This technique, which monitors the field ionisation of high Rydberg states induced by a slowly growing electric-field ramp after a prepulse of opposite polarity, was recently introduced to record photoelectron spectra with high resolution and high sensitivity [Harper, Chen, Boyé-Péronne and Gans, Phys. Chem. Chem. Phys., 2022, 117, 9353]. A tunable UV laser system with a bandwidth of 30 MHz is used here to establish the factors determining the resolution and overall accuracy of this new method. In particular, the effects of stray electric fields, and of the magnitude of the prepulse and the field ramp on PRFI-ZEKE photoelectron spectra are studied by combining experiments with numerical simulations of the field-ionisation of high Rydberg states and of the electron flight times from the ionisation spot to the detector. A spectral resolution of 0.05 cm-1 is demonstrated in the photoelectron spectrum of metastable Ar.

State-selective probing of CO2 autoionizing inner valence Rydberg states with attosecond extreme ultraviolet four-wave-mixing spectroscopy

Nonlinear spectroscopies can disentangle spectra that are congested due to inhomogeneous broadening. In conjunction with theoretical calculations, attosecond extreme ultraviolet (XUV) four-wave-mixing (FWM) spectroscopy is utilized here to probe the dynamics of autoionizing inner valence excited Rydberg states of the polyatomic molecule, ${\mathrm{CO}}_{2}$. This tabletop nonlinear technique employs a short attosecond XUV pulse train and two noncollinear, few-cycle near-infrared pulses to generate background-free XUV wave-mixing signals. FWM emission is observed from the $n=5--7$ states of the Henning sharp $nd{\ensuremath{\sigma}}_{g}$ Rydberg series that converges to the ionic $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}\phantom{\rule{4pt}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$ state. However, these transient emission signals decay with lifetimes of 33 $\ifmmode\pm\else\textpm\fi{}$ 6, 53 $\ifmmode\pm\else\textpm\fi{}$ 2, and 94 $\ifmmode\pm\else\textpm\fi{}$ 2 fs, respectively, which calculations show are consistent with the lifetimes of the short-lived $n=6--8$ members of the $ns{\ensuremath{\sigma}}_{g}$ character Henning diffuse Rydberg series. The oscillator strengths of transitions between states involved in all possible resonant FWM processes are calculated, verifying that the nonlinear spectra are dominated by pathways described by an initial excitation to the diffuse $ns{\ensuremath{\sigma}}_{g}$ Rydberg series and emission from the sharp $nd{\ensuremath{\sigma}}_{g}$ Rydberg series. The results substantiate not only that attosecond XUV FWM spectroscopy produces rigorous and meaningful measurements of ultrafast dynamics in polyatomic systems, but also that nonlinear spectroscopic techniques are versatile tools to selectively probe dynamics that are otherwise difficult to access.

Superradiance-induced multistability in one-dimensional driven Rydberg lattice gases

We study steady state phases of a one-dimensional array of Rydberg atoms coupled by a microwave (MW) field where the higher energy Rydberg state decays to the lower energy one via single-body and collective (superradiant) decay. Using mean-field approaches, we examine the interplay among the MW coupling, intra-state van der Waals (vdW) interaction, and single-body and collective dissipation between Rydberg states. A linear stability analysis reveals that a series of phases, including uniform, antiferromagnetic, oscillatory, and bistable and multistable phases can be obtained. Without the vdW interaction, only uniform phases are found. In the presence of the vdW interaction, multistable solutions are enhanced when increasing the strength of the superradiant decay rate. Our numerical simulations show that the bistable and multistable phases are stabilized by superradiance in a long chain. The critical point between the uniform and multistable phases and its scaling with the atom number is obtained. Through numerically solving the master equation of a finite chain, we show that the mean-field multistable phase could be characterized by expectation values of Rydberg populations and two-body correlations between Rydberg atoms in different sites.

Electrostatic trapping vibrationally excited Rydberg NO molecules

Nitric oxide (NO) molecules travelling in pulsed supersonic beams have been laser photoexcited to long-lived Rydberg states in series converging to the lowest lying, , and first excited, , vibrational states in the ground electronic state of NO. After excitation, the molecules were decelerated in the travelling electric traps of a chip-based Rydberg–Stark decelerator. Deceleration to rest in the laboratory-fixed frame of reference allowed subsequent electrostatic trapping before in situ detection by pulsed electric field ionisation. The decay rates of the molecules from the traps were measured for states with principal quantum numbers between 32 and 48. Comparison of the corresponding trap decay time constants, ranging from 245 to s for states with , with those recorded for molecules in states with , allowed bounds to be placed on the vibrational autoionisation rates of the ℓ-mixed Stark states prepared in the experiments of Hz.

Ion-Pair Formation in n-Butyl Bromide through 5p Ryberg State Predissociation.

The ultrafast photodynamics of n-butyl bromide are explored with femtosecond time-resolved mass spectrometry. Absorption of two UV (400 nm) pump photons induces the direct dissociation of the C-Br bond from the A state within 160 fs. Absorption of three UV pump photons excites the molecule into the 5p Rydberg state which undergoes several relaxation pathways including to the ion-pair state. Relaxation to the ion-pair state is tracked through the transient of the C4H9+ fragment and suggests an E state lifetime of 10.8 ± 0.5 ps, in close agreement with the tunneling time of smaller molecules. Predissociation from the 5p Rydberg states leads to the β-elimination of H-Br and formation of C4H8+ within 3.0 ± 0.25 ps. A portion of the excited parent molecule avoids the ion-pair formation and instead relaxes through the Rydberg excited state manifold into the D state within 30.2 ± 0.21 ps.

High-resolution photoelectron spectroscopy of the ground and first excited electronic states of MgKr+

We report on the characterisation of the lowest three electronic states of MgKr, the X ground state associated with the Mg(3s) + Kr(4p) dissociation limit and the A and B excited states associated with the Mg(3p) + Kr(4p) dissociation limits. The vibrational structure of the X ground state was measured by pulsed-field-ionisation zero-kinetic-energy photoelectron spectroscopy starting from the a metastable state of MgKr generated by laser ablation of a Mg rod in a Kr supersonic beam. The vibrational assignment was derived from the isotopic structure of the spectra and the adiabatic ionisation energy of the ionising transition was determined to be 38182.4(2.0) cm. Partially rotationally resolved spectra of the A X and B X transitions were recorded by monitoring the yield of Mg ions produced by dissociation of MgKr using the technique of isolated-core Rydberg-dissociation spectroscopy. Analytical potential-energy functions of the X, A, and B states were derived using a global model of these states that includes the spin-orbit interaction. The observation of the highest vibrational levels of the B state and the onset of the Kr + Mg(3p) dissociation continuum enabled the precise determination of the dissociation energies of the X, A and B states of MgKr and of the a state of MgKr. The X, A and B states of MgKr are important stepping stones to access the Rydberg states of MgKr and the ground state of MgKr by resonant multiphoton excitation.

Dynamic interference in strong-field multiphoton excitation and ionization

By numerically solving the time-dependent Schr\"odinger equation, we theoretically investigated the dynamic interference in multiphoton excitation and ionization of hydrogen irradiated by 400-nm linearly polarized laser pulses. Interference of the multiphoton excitation paths at the rising and falling edges of the laser pulses gives rise to the fast oscillations of the intensity-dependent yield of the excited states. Our results show that the period of the oscillation increases abruptly when the laser intensity increases above the eight-photon ionization threshold. By tracing the population evolution of the ground state, we find that the depletion of the ground state on the rising edge of the laser pulse closes the multiphoton excitation path at the falling edge of the pulse. The slower oscillation comes from the interference of the excitation paths at different instants during the rising edge of the laser pulses. The change in the interference paths in the high-laser-intensity region also occurs in multiphoton ionization. The photoelectrons released at different instants of the rising edge of the laser pulses possess different parities. This difference is imprinted in the up-down asymmetry along the laser polarization direction in the photoelectron momentum distribution. The dynamic interference of the Rydberg states provides rich information about the dynamics in strong-field ionization.

Many-Body Radiative Decay in Strongly Interacting Rydberg Ensembles.

When atoms are excited to high-lying Rydberg states they interact strongly with dipolar forces. The resulting state-dependent level shifts allow us to study many-body systems displaying intriguing nonequilibrium phenomena, such as constrained spin systems, and are at the heart of numerous technological applications, e.g., in quantum simulation and computation platforms. Here, we show that these interactions also have a significant impact on dissipative effects caused by the inevitable coupling of Rydberg atoms to the surrounding electromagnetic field. We demonstrate that their presence modifies the frequency of the photons emitted from the Rydberg atoms, making it dependent on the local neighborhood of the emitting atom. Interactions among Rydberg atoms thus turn spontaneous emission into a many-body process which manifests, in a thermodynamically consistent Markovian setting, in the emergence of collective jump operators in the quantum master equation governing the dynamics. We discuss how this collective dissipation-stemming from a mechanism different from the much studied superradiance and subradiance-accelerates decoherence and affects dissipative phase transitions in Rydberg ensembles.

The fine and hyperfine structures of the low-n 3Π u Rydberg states of H2 revisited

The experimental fine and hyperfine structures of low Rydberg states with 2–4 measured in the 1970's for various vibration-rotation levels by Lichten and collaborators, and by Miller and Freund, are reanalysed in the framework of molecular frame-transformation multichannel quantum defect theory MQDT. Instead of the level by level treatment in terms of an effective Hamiltonian as was carried out at the time, a global theory is applied to all levels at once. It is found that the essence of the observed level patterns is well represented by MQDT in terms of a substantially reduced number of dynamical parameters – quantum defects – although the experimental accuracy of the experiments is not yet quite reached. Possible reasons for the remaining discrepancies are given. Since quantum defect theory MQDT, a formalism derived from scattering theory, is still rather little used in the domain of modern ultra-high precision spectroscopy, the occasion is taken here to review some of its key elements.

Laser photo-ionization study of nat Ag using opto-galvanic signal at SPES offline laser lab

Resonant Ionization Laser Ion Source (RILIS) is one of the most advancing techniques for the production of radioactive ion beams (RIBs) in ISOL facilities. SPES project at INFN-LNL is a second generation ISOL facility which aims to produce several isotopes in a couple of years. Within the framework of this project, resonant photo-ionization schemes of several elements are studied in the offline laser lab, to be later implemented in the SPES Laser Ion Source. Silver is one of the elements being studied for the stated purpose. In this article, we report a resonant photo-ionization scheme of silver tested with a hollow cathode lamp (HCL). Evidence of high lying Rydberg states around 60945.32 cm−1 has also been observed by studying the fast opto-galvanic signal detected.

Dynamics of frustrated tunneling ionization driven by inhomogeneous laser fields

We theoretically investigated frustrated tunneling ionization (FTI) driven by spatially inhomogeneous strong laser fields induced by surface plasmon resonance within a bow-tie metal nanostructure. The results show that the FTI probability and the principal quantum number distribution exhibit similar oscillatory behavior as a function of the pulse duration. Our analysis reveals that the periodic defocusing and refocusing of the electron spatial distribution due to the inhomogeneous laser field is responsible for the oscillatory structures. In addition, the initial tunneling coordinates and the angular momentum distributions of the FTI events and theirs pulse duration dependence are also explored. Moreover, our results show that the frequency of the oscillatory structures depends sensitively on the electron quiver amplitude and the inhomogeneity strength. Thus, the electron quiver amplitude and the size of the gap between bow-tie nanostructure are useful and efficient knobs for controlling the yield and properties of exited Rydberg states.

Atom-based power-frequency electric field measurement using the radio-frequency-modulated Rydberg spectroscopy

The radio-frequency modulated electromagnetically induced transparency (EIT) in a ladder three-level system with Rydberg state is studied. Under the influence of a fast radio-frequency field, the EIT peak splits into a series of sidebands. When attaching a power-frequency electric field directly to the fast radio-frequency field, the odd-order sidebands of the Rydberg-EIT oscillate sensitively with the power-frequency field. The oscillation frequency is equal to twice the power frequency; the oscillation amplitude is monotonically increasing with the amplitude of the power-frequency field when the change of Stark-shift is smaller than the radio frequency. Our work paves the way for measurement of power-frequency electric field based on Rydberg atoms.

Hyperfine structure of nP1/2 Rydberg states in Rb85

We measure the hyperfine structure of $n{P}_{1/2}$ Rydberg states for $n=$ 42, 43, 44, and 46 using mm-wave spectroscopy on an ensemble of laser-cooled $^{85}\mathrm{Rb}$ atoms. Systematic uncertainties in our measurement from the Zeeman splittings induced by stray magnetic fields and dipole-dipole interactions between two Rydberg atoms are factored in with the obtained statistical uncertainty. Our final measurement of the $n{P}_{1/2}$ hyperfine coupling constant is ${A}_{\text{HFS}}=1.443(31)$ GHz. This measurement is useful for studies of long-range Rydberg molecules, Rydberg electrometry, and quantum simulation with dipole-dipole interactions involving $n{P}_{1/2}$ atoms.

Wavepacket dynamics of the excited (S1) state of 2,5-difluoroaniline by accidental resonance with the Rydberg states.

Coherent nuclear wavepacket behavior obtained by time-resolved spectroscopy is a good choice to capture the real-time evolution of molecular configuration. Using femtosecond time-resolved photoelectron imaging, we investigate the real-time evolution of the vibrational wavepacket of 2,5-difluoroaniline following the coherent excitation of an out-of-plane vibrational mode in the S1 state at 289.8nm. Probed by an accidental resonance with the Rydberg states, the periodic oscillations with the frequency of 99cm-1 are observed from the photoelectron kinetic energy (PKE) distributions, corresponding to the energy difference between the out-of-plane mode X1 0 of C-F bond and the band origin. Moreover, phase reversal of π rad between 0.66-0.75 and 1.00-1.08eV is also observed in the PKE region. Combined with the scan of the potential energy surface in the ground cationic D0 state, the observed two ionization channels corresponding to different phases are attributed to the periodic geometry changes between the planar and the non-planar structures when the coherent wavepacket evolves from the initial vertical Franck-Condon region toward the global minimum of the S1 potential energy surface.

Demonstration of a Quantum Gate Using Electromagnetically Induced Transparency.

We demonstrate a native CNOT gate between two individually addressed neutral atoms based on electromagnetically induced transparency. This protocol utilizes the strong long-range interactions of Rydberg states to enable conditional state transfer on the target qubit when operated in the blockade regime. An advantage of this scheme is it enables implementation of multiqubit CNOT^{k} gates using a pulse sequence independent of qubit number, providing a simple gate for efficient implementation of digital quantum algorithms and stabilizer measurements for quantum error correction. We achieve a loss corrected gate fidelity of F_{CNOT}^{cor}=0.82(6), and prepare an entangled Bell state with F_{Bell}^{cor}=0.66(5), limited at present by laser power. We present a number of technical improvements to advance this to a level required for fault-tolerant scaling.

Photoionization and Photofragmentation Dynamics of I2 in Intense Laser Fields: A Velocity-Map Imaging Study.

The photoionization and photofragmentation dynamics of I2 in intense femtosecond near-infrared laser fields were studied using velocity-map imaging of cations, electrons, and anions. A series of photofragmentation pathways originating from different cationic electronic states were observed following single ionization, leading to I+ fragments with distinct kinetic energies, which could not be resolved in previous studies. Photoelectron spectra indicate that these high-lying dissociative states are primarily produced through nonresonant ionization from several molecular orbitals (MO) of the neutral. The photoelectron spectra also show clear signatures of resonant ionization pathways (Freeman resonances) to low-lying bound ionic states via Rydberg states of the neutral moiety. To investigate the role of these Rydberg states further, we imaged anionic products (I-) formed through ion-pair dissociations of neutral molecules excited to these Rydberg states by the intense femtosecond laser pulse. Collectively, these results shed significant new light on the complex dynamics of I2 molecules in intense laser fields and on the important role of neutral Rydberg states in a full description of strong-field phenomena in molecules.

Rényi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States.

The various facets of the internal disorder of quantum systems can be described by means of the Rényi entropies of their single-particle probability density according to modern density functional theory and quantum information techniques. In this work, we first show the lower and upper bounds for the Rényi entropies of general and central-potential quantum systems, as well as the associated entropic uncertainty relations. Then, the Rényi entropies of multidimensional oscillator and hydrogenic-like systems are reviewed and explicitly determined for all bound stationary position and momentum states from first principles (i.e., in terms of the potential strength, the space dimensionality and the states's hyperquantum numbers). This is possible because the associated wavefunctions can be expressed by means of hypergeometric orthogonal polynomials. Emphasis is placed on the most extreme, non-trivial cases corresponding to the highly excited Rydberg states, where the Rényi entropies can be amazingly obtained in a simple, compact, and transparent form. Powerful asymptotic approaches of approximation theory have been used when the polynomial's degree or the weight-function parameter(s) of the Hermite, Laguerre, and Gegenbauer polynomials have large values. At present, these special states are being shown of increasing potential interest in quantum information and the associated quantum technologies, such as e.g., quantum key distribution, quantum computation, and quantum metrology.

Effect of Nonequilibrium Electron-Energy Distributions on Efficiency of Rydberg State Population via Resonant Recombination

Effect of Nonequilibrium Electron-Energy Distributions on Efficiency of Rydberg State Population via Resonant Recombination

Electron temperature relaxation in the clusterized ultracold plasmas

Ultracold plasmas are a promising candidate for the creation of strongly coupled Coulomb systems. Unfortunately, the values of the coupling parameter Γe actually achieved after photoionization of the neutral atoms remain relatively small because of the considerable intrinsic heating of the electrons. A conceivable way to get around this obstacle might be to utilize a spontaneous ionization of the ultracold Rydberg gas, where the initial kinetic energies could be much less. However, the spontaneous avalanche ionization will result in a very inhomogeneous distribution (clusterization) of the ions, which can change the efficiency of the electron relaxation in the vicinity of such clusters substantially. In the present work, this hypothesis is tested by an extensive set of numerical simulations. As a result, it is found that despite a less initial kinetic energy, the subsequent relaxation of the electron velocities in the clusterized plasmas proceeds much more violently than in the case of the statistically uniform ionic distribution. The electron temperature, first, experiences a sharp initial jump (presumably, caused by the “virialization” of energies of the charged particles) and, second, exhibits a gradual subsequent increase (presumably, associated with a multi-particle recombination of the electrons at the ionic clusters). As a possible tool to reduce the anomalous temperature increase, we also considered a two-step plasma formation, involving the blockaded Rydberg states. This leads to a suppression of the clusterization due to a quasi-regular distribution of ions. In such a case, according to the numerical simulations, the subsequent evolution of the electron temperature proceeds more gently, approximately with the same rate as in the statistically uniform ionic distribution.

Control of coherent extreme-ultraviolet emission around atomic potential through laser chirp

Substantial neutral atoms can tunnel to excited states in an intense laser field and subsequently generate coherent emission through free induction decay. We experimentally observe an enhanced coherent emission in the harmonic slightly below the threshold, which is consistent with the free induction decay of Rydberg states produced by the frustrated tunnelling ionization (FTI) process. We further find that the intensity of the coherent emission significantly depends on the chirp of laser pulses. The simulations based on the strong field approximation model show that laser chirp affects the probability that the returned electrons recombine to the Rydberg states. Our result shows that coherent emission can be controlled by laser chirp, which facilitates understanding the dynamics of the Rydberg atom and coupling mechanism between the below-threshold harmonics and atomic energy level. In addition, the coherent below-threshold FTI emission we observed has small divergence which is good for EUV light source applications.