Long-lived Rydberg States Research Articles

High-Resolution Continuous-Wave Laser Spectroscopy of Long-Lived Rydberg States in NO.

High-resolution continuous-wave (cw) laser spectroscopy of nitric oxide (NO) molecules has been performed to study and characterize the energy-level structure of and effects of electric fields on the high Rydberg states. The experiments were carried out with molecules flowing through a room temperature gas cell. Rydberg-state photoexcitation was implemented using the resonance enhanced three-color three-photon excitation scheme. Excited molecules were detected by high-sensitivity optogalvanic methods. Detailed measurements were made of Rydberg states with principal quantum numbers n = 22 and 32 in the series converging to the lowest rotational and vibrational state of the NO+ cation. The experimental data were compared with the results of numerical calculations which provided insight into the orbital angular momentum character of the intermediate H 2Σ+ state, improved determinations of the nf and ng quantum defects, a bound on the magnitude of the nh quantum defect, and information on the decay rates of the nf and ng Rydberg states. These measurements represent a step-change in laser spectroscopic studies of high Rydberg states in small atmospheric molecules. They open opportunities for more detailed studies of slow decay processes of Rydberg NO molecules confined in electrostatic traps, the synthesis of ultralong range Rydberg bimolecules, and the development of optical methods for trace gas detection.

Electrostatic Trapping of N_{2} Molecules in High Rydberg States.

N_{2} molecules traveling in pulsed supersonic beams have been excited from their X ^{1}Σ_{g}^{+} ground electronic state to long-lived Rydberg states with principal quantum numbers between 39 and 48 using a resonance-enhanced two-color three-photon excitation scheme. The Rydberg states populated had static electric dipole moments exceeding 5000 D which allowed deceleration of the molecules to rest in the laboratory-fixed frame of reference and three-dimensional trapping using inhomogeneous electric fields. The trapped molecules were confined for up to 10ms, with effective trap decay time constants increasing with principal quantum number, and ranging from 450 to 700 μs. These observations, and comparison with the results of similar measurements with He atoms, indicate that the decay dynamics of the trapped Rydberg N_{2} molecules are dominated by spontaneous emission and do not exhibit significant contributions from effects of intramolecular interactions that lead to non-radiative decay.

Floquet-tailored Rydberg interactions

The Rydberg blockade is a key ingredient for entangling atoms in arrays. However, it requires atoms to be spaced well within the blockade radius, which limits the range of local quantum gates. Here we break this constraint using Floquet frequency modulation, with which we demonstrate Rydberg-blockade entanglement beyond the traditional blockade radius and show how the enlarged entanglement range improves qubit connectivity in a neutral atom array. Further, we find that the coherence of entangled states can be extended under Floquet frequency modulation. Finally, we realize Rydberg anti-blockade states for two sodium Rydberg atoms within the blockade radius. Such Rydberg anti-blockade states for atoms at close range enables the robust preparation of strongly-interacting, long-lived Rydberg states, yet their steady-state population cannot be achieved with only the conventional static drive. Our work transforms between the paradigmatic regimes of Rydberg blockade versus anti-blockade and paves the way for realizing more connected, coherent, and tunable neutral atom quantum processors with a single approach.

Effects of rotational excitation on decay rates of long-lived Rydberg states in NO.

Nitric oxide (NO) molecules in pulsed supersonic beams have been excited to long-lived Rydberg-Stark states in series converging to the lowest vibrational level in the ground electronic state of NO+ with rotational quantum numbers N+ = 2, 4, and 6. The molecules in these excited states were then guided, or decelerated and trapped in a chip-based Rydberg-Stark decelerator, and detected in situ by pulsed electric field ionization. Time constants, reflecting the decay of molecules in N+ = 2 Rydberg-Stark states, with principal quantum numbers n between 38 and 44, from the electrostatic traps were measured to be ∼300μs. Molecules in Rydberg-Stark states with N+ = 4 and 6, and the same range of values of n were too short-lived to be trapped, but their decay time constants could be determined from complementary sets of delayed pulsed electric field ionization measurements to be ∼100 and ∼25 μs, respectively.

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.

Role of Spin-Orbit Coupling in High-Order Harmonic Generation Revealed by Supercycle Rydberg Trajectories.

High-harmonic generation is typically thought of as a sub-laser-cycle process, with the electron's excursion in the continuum lasting a fraction of the optical cycle. However, it was recently suggested that long-lived Rydberg states can play a particularly important role in high harmonic generation by atoms driven by the combination of the counterrotating circularly polarized fundamental light field and its second harmonic. Here we report direct experimental evidence of very long and stable Rydberg trajectories contributing to high-harmonic generation in such fields. We track their dynamics inside the laser pulse using the spin-orbit evolution in the ionic core, utilizing the spin-orbit Larmor clock. We confirm their effect on harmonic emission both via microscopic simulations and by showing how this radiation can lead to a well-collimated macroscopic far-field signal. Our observations contrast sharply with the general view that long-lived Rydberg orbits should generate negligible contribution to the macroscopic far-field high harmonic response of the medium.

Quantum Computing with Circular Rydberg Atoms

Rydberg atom arrays are a leading platform for quantum computing and simulation, combining strong interactions with highly coherent operations and flexible geometries. However, the achievable fidelities are limited by the finite lifetime of the Rydberg states, as well as technical imperfections such as atomic motion. In this work, we propose a novel approach to Rydberg atom arrays using long-lived circular Rydberg states in optical traps. Based on the extremely long lifetime of these states, exceeding seconds in cryogenic microwave cavities that suppress radiative transitions, and gate protocols that are robust to finite atomic temperature, we project that arrays of hundreds of circular Rydberg atoms with two-qubit gate errors around $10^{-5}$ can be realized using current technology. This approach combines several key elements, including a quantum nondemolition detection technique for circular Rydberg states, local manipulation using the ponderomotive potential of focused optical beams, a gate protocol using multiple circular levels to encode qubits, and robust dynamical decoupling sequences to suppress unwanted interactions and errors from atomic motion. This represents a significant improvement on the current state-of-the-art in quantum computing and simulation with neutral atoms.

Controlled multi-photon subtraction with cascaded Rydberg superatoms as single-photon absorbers

The preparation of light pulses with well-defined quantum properties requires precise control at the individual photon level. Here, we demonstrate exact and controlled multi-photon subtraction from incoming light pulses. We employ a cascaded system of tightly confined cold atom ensembles with strong, collectively enhanced coupling of photons to Rydberg states. The excitation blockade resulting from interactions between Rydberg atoms limits photon absorption to one per ensemble and rapid dephasing of the collective excitation suppresses stimulated re-emission of the photon. We experimentally demonstrate subtraction with up to three absorbers. Furthermore, we present a thorough theoretical analysis of our scheme where we identify weak Raman decay of the long-lived Rydberg state as the main source of infidelity in the subtracted photon number and investigate the performance of the multi-photon subtractor for increasing absorber numbers in the presence of Raman decay.

Accurate determination of ionization energy of 1, 3-diethoxybenzene via photoionization efficiency spectrum in electrostatic field

Ionization energy (IE) is an important characteristic parameter of atoms or molecules. It plays an important role in the process of photophysics and photochemistry. The precise ionization energy is very important for relevant research. Especially, it is very useful for adjusting the signal of the zero-kinetic energy (ZEKE) spectrum, and it also plays a key role in judging the number of rotamers and molecular configuration. In linear time-of-flight mass spectrometers, pulsed electric fields are usually used to drive photo-ionized ions to the detector to produce the photoionization efficiency (PIE) spectrum. The ionization energy is directly obtained from the PIE curve. The uncertainty of the measured IE is usually greater than or equal to ± 10 cm<sup>–1</sup>. The ZEKE spectroscopy is based on the long-lived Rydberg state field ionization technology. In the ZEKE experiments, the laser excites molecules to the Rydberg state and then a pulsed field ionization (PFI) is used for measurement. A peak with high signal-to-noise ratio and narrow linewidth signal appears near the ionization threshold. Therefore, the more accurate ionization energy can be obtained, and the uncertainty of the measured value is about ± 5 cm<sup>–1</sup>. The 1,3-diethoxybenzene is an important benzene derivative, and experiments have confirmed that there are two rotamers, i.e. I (down-up) and III (down-down) in the supersonic molecular beam. In this paper, a linear time-of-flight mass spectrometer is used to measure the photoionization efficiency curves of 1,3-diethoxybenzene in electrostatic fields. From the linear fitting of the ionization energy values measured under different electric fields (Stark effect) to the square root of the field strengths, the precise ionization energy values of rotamer I and rotamer III are determined to be (62419 ± 2) cm<sup>–1</sup> and (63378 ± 2) cm<sup>–1</sup>, respectively. Compared with the accuracies of the values measured by the usual pulsed electric field acceleration mechanism and the ZEKE spectroscopy, the accuracy is improved from about ± 10 and ± 5 to ± 2 cm<sup>–1</sup>, respectively. The physical mechanism, advantages and disadvantages of different methods are analyzed and discussed. The present research results show that the ionization energy measured in the electrostatic field is more accurate, the physical meaning of the measurement process is clear, and the threshold data are easy to collect. This is the first report on the precise ionization energy of 1,3-diethoxybenzene rotamers.

Long-lived circular Rydberg states of laser-cooled rubidium atoms in a cryostat

The exquisite properties of Rydberg levels make them particularly appealing for emerging quantum technologies. The lifetime of low-angular-momentum laser-accessible levels is however limited to a few $100\,\mu\mathrm{s}$ by optical transitions and microwave blackbody radiation (BBR) induced transfers at room temperature. A considerable improvement would be obtained with the few $10\,\mathrm{ms}$ lifetime of circular Rydberg levels in a cryogenic environment reducing the BBR temperature. We demonstrate the preparation of long-lived circular Rydberg levels of laser-cooled Rubidium atoms in a cryostat. We observe a $3.7\,\mathrm{ms}$ lifetime for the circular level of principal quantum number $n=52$. By monitoring the transfers between adjacent circular levels, we estimate in situ the microwave BBR temperature to be $(11\pm 2)\,\mathrm{K}$. The measured atomic coherence time ($270\,\mu\mathrm{s}$) is limited here only by technical magnetic field fluctuations. This work opens interesting perspectives for quantum simulation and sensing with cold circular Rydberg atoms.

Excitation and characterization of long-lived hydrogenic Rydberg states of nitric oxide.

High Rydberg states of nitric oxide (NO) with principal quantum numbers between 40 and 100 and lifetimes in excess of 10 µs have been prepared by resonance enhanced two-color two-photon laser excitation from the X 2Π1/2 ground state through the A 2Σ+ intermediate state. Molecules in these long-lived Rydberg states were detected and characterized 126 µs after laser photoexcitation by state-selective pulsed electric field ionization. The laser excitation and electric field ionization data were combined to construct two-dimensional spectral maps. These maps were used to identify the rotational states of the NO+ ion core to which the observed series of long-lived hydrogenic Rydberg states converge. The results presented pave the way for Rydberg-Stark deceleration and electrostatic trapping experiments with NO, which are expected to shed further light on the decay dynamics of these long-lived excited states, and are of interest for studies of ion-molecule reactions at low temperatures.

Laser Trapping of Circular Rydberg Atoms.

Rydberg atoms are remarkable tools for quantum simulation and computation. They are the focus of an intense experimental activity, mainly based on low-angular-momentum Rydberg states. Unfortunately, atomic motion and levels lifetime limit the experimental timescale to about 100 μs. Here, we demonstrate two-dimensional laser trapping of long-lived circular Rydberg states for up to 10ms. Our method is very general and opens many opportunities for quantum technologies with Rydberg atoms. The 10ms trapping time corresponds to thousands of interaction cycles in a circular-state-based quantum simulator. It is also promising for quantum metrology and quantum information with Rydberg atoms, by bringing atom-field interaction times into unprecedented regimes.

Sub-Doppler Spectroscopy of Excited Atoms in a Multilayer Gas Cell

The potential for spectroscopy in a multilayer cell with rarefied gas medium is theoretically investigated where said cell can be used as a compact analog of a large number of plane-parallel beams of atoms (or molecules) in an optically excited quantum level. In particular, this situation occurs for metastable and highly excited long-lived Rydberg states of atoms and molecules. Velocity selection of atoms (molecules) excited to said quantum level by broadband optical pumping was found to be efficient because of their characteristic transit and collisional relaxation in said cell. Sub-Doppler resonances at the optical transition frequencies from a given level were narrow as a result of the selection when the monochromatic probe light beam was absorbed.

Experimental progress in positronium laser physics

The field of experimental positronium physics has advanced significantly in the last few decades, with new areas of research driven by the development of techniques for trapping and manipulating positrons using Surko-type buffer gas traps. Large numbers of positrons (typically ≥106) accumulated in such a device may be ejected all at once, so as to generate an intense pulse. Standard bunching techniques can produce pulses with ns (mm) temporal (spatial) beam profiles. These pulses can be converted into a dilute Ps gas in vacuum with densities on the order of 107 cm−3 which can be probed by standard ns pulsed laser systems. This allows for the efficient production of excited Ps states, including long-lived Rydberg states, which in turn facilitates numerous experimental programs, such as precision optical and microwave spectroscopy of Ps, the application of Stark deceleration methods to guide, decelerate and focus Rydberg Ps beams, and studies of the interactions of such beams with other atomic and molecular species. These methods are also applicable to antihydrogen production and spectroscopic studies of energy levels and resonances in positronium ions and molecules. A summary of recent progress in this area will be given, with the objective of providing an overview of the field as it currently exists, and a brief discussion of some future directions.Graphical abstract

Nonadiabatic effects on the positions and lifetimes of the low-lying rovibrational levels of the GK 1Σ and H 1Σ states of H2.

The term values of rovibrational levels of the GK 1Σ+g and H 1Σ+g states of H2 have been measured with absolute and relative accuracies down to 10-4 cm-1 (≈3 MHz) and 10-6 cm-1 (≈30 kHz), respectively, by measuring transitions to long-lived high-n Rydberg states using single-mode cw laser radiation and a collimated supersonic beam of cold H2 molecules. The term values are compared with those determined in earlier experimental and theoretical investigations and the comparison points at discrepancies and a need for improved theoretical treatments of nonadiabatic, relativistic and radiative corrections for these states. The lifetimes of several low-lying rovibrational levels of the GK, H and I+ 1Πg states have been determined in pump-probe experiments. These lifetimes reveal a significant dependence on the electronic, vibrational and rotational excitation and also deviate from results obtained in earlier experimental and theoretical investigations.

Angle-Resolved Spectroscopy of Positronium Emission from a Cu(110) Surface.

The affinity A_{Ps} of positronium (Ps) atoms for a metal is the negative of the maximum kinetic energy with which Ps is emitted into vacuum when thermalized positrons in a metal encounter the surface. When this quantity is measured by ground state Ps time of flight (TOF), the precision is severely limited by the short triplet state lifetime of 142ns. By quickly converting the emitted Ps atoms into long-lived Rydberg states, we are able to dramatically increase the TOF to allow precision measurements of A_{Ps}. From our measurements made on a Cu(110) sample at T=128 K, we find A_{Ps}(128 K)=(-2.476±0.010_{stat}±0.013_{syst}) eV, compared with the result A_{Ps}(128 K)=(-2.545±0.010_{num}±0.010_{syst}) eV found using highly accurate generalized gradient approximations for both electrons and positrons within density functional theory. Such precision opens up opportunities in the quest for an improved density functional.

Influence of magnetic field on laser-produced barium plasmas: Spectral and dynamic behaviour of neutral and ionic species

The expansion dynamics and spectral behaviour of plasma produced by a Nd:YAG laser (λ = 1.064 μm, pulse width: 8 ns) from barium target and expanding in 0.45 T transverse magnetic field in vacuum (10−5 Torr pressure) are investigated using time-of-flight optical emission spectroscopy. The experiments are carried out at various laser fluences from 12 to 31 J/cm2. The temporal profiles of neutral (Ba I 553.5 and 577.7 nm) lines are temporally broadened, while that of ionic (Ba II 413.0 and 455.4 nm) lines show strong confinement in the presence of a magnetic field. In the absence of magnetic field, the temporal profile of Ba I 553.5 nm is exactly reproduced by fitting with two Shifted Maxwell Boltzmann (SMB) Distribution components, while in the presence of a magnetic field the profile could only be fitted with three components. The field enhanced and field induced SMB components of neutral profile are correlated with populations of ground state, metastable states, and long-lived Rydberg states present in the barium plasma, while SMB components of ionic lines are explained on the basis of the presence of super-elastic collisions among the excited species in the plasma. The spatial variation of electron temperature and temporal variation of electron density are deduced and correlated to the different collisional processes in the barium plasma. The ionic profiles show efficient confinement in the presence of a magnetic field at higher fluences.

Laser Multiphoton Ionization of Tetrakis(dimethylamino)ethylene

The tetrakis(dimethylamino)ethylene (TDAE) molecule possesses the lowest known molecular ionization potential (<5.4 eV) and exhibits an intense Rydberg series between the first and second ionization limit (∼14 eV). The ionization of TDAE using multiphoton ionization photoelectron spectroscopy was carried out using laser light at a variety of wavelengths with a hemispherical energy analyzer. Interestingly, photoelectron signal due to direct two-photon ionization was not seen, rather ionization from a fluorescent charge-transfer state located ∼2.5 eV below the ionization limit was evident and in general agreement with a previous study. In addition, a second intense peak exists corresponding to thermal energy electrons. Measurements of the angular distribution for the electrons due to photoionization from the intermediate state are peaked along the electric field vector of the laser and the thermal electrons direction is independent of this angle. From this, we propose that the thermal peak is most likely due to thermionic emission initiated through excitation of a known long-lived Rydberg state at ∼6.5 eV. Alternately, we speculate that excitation leading to thermionic emission could result from a "collective" excitation mechanism.

Atom control and gravity measurements using Rydberg positronium

We consider some of the obstacles that will have to be overcome in order to perform a direct measurement of the gravitational free-fall of positronium atoms. Foremost among these are the production of positronium atoms in a cryogenic environment, efficient excitation of these atoms to suitably long-lived Rydberg states, and their subsequent control via the interaction of their large electric dipole moments with inhomogeneous electric fields. Recent developments in all of these areas can be directly applied to a positronium free-fall gravity measurement, making such an endeavour both timely and feasible.

Dark Entangled Steady States of Interacting Rydberg Atoms

We propose a scheme for rapid generation of high fidelity steady-state entanglement between a pair of atoms. A two-photon excitation process toward long-lived Rydberg states with finite pairwise interaction, a dark-state interference effect in the individual atoms, and spontaneous emission from their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly dependent on the Rydberg interaction strength.