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 10 ms, 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.

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.

Precision Microwave Spectroscopy of the Positronium 2

We report the results of a new measurement of the positronium 2 ^{3}S_{1}→2 ^{3}P_{2} (ν_{2}) interval. Using a modified experimental arrangement we have significantly reduced the effects of microwave reflections, which in previous experiments resulted in shifts and asymmetric line shapes. With the improved apparatus we obtain an experimental value of ν_{2}=8627.94±0.95 MHz, which is within 1.3σ of the theoretical value 8626.71±0.08 MHz.

Quantum-state-dependent decay rates of electrostatically trapped Rydberg NO molecules.

Nitric oxide (NO) molecules travelling in pulsed supersonic beams have been prepared in long-lived Rydberg-Stark states by resonance-enhanced two-colour two-photon excitation from the X 2Π1/2 (v'' = 0, J'' = 3/2) ground state, through the A 2Σ+ (v' = 0, N' = 0, J' = 1/2) intermediate state. These excited molecules were decelerated from 795 ms-1 to rest in the laboratory-fixed frame of reference, in the travelling electric traps of a transmission-line Rydberg-Stark decelerator. The decelerator was operated at 30 K to minimise effects of blackbody radiation on the molecules during deceleration and trapping. The molecules were electrostatically trapped for times of up to 1 ms, and detected in situ by pulsed electric field ionisation. Measurements of the rate of decay from the trap were performed for states with principal quantum numbers between n = 32 and 50, in Rydberg series converging to the N+= 0, 1, and 2 rotational states of NO+. For the range of Rydberg states studied, the measured decay times of between 200 µs and 400 µs were generally observed to reduce as the value of n was increased. For some particular values of n deviations from this trend were seen. These observations are interpreted, with the aid of numerical calculations, to arise as a result of contributions to the decay rates, on the order of 1 kHz, from rotational and vibrational channel interactions. These results shed new light on the role of weak intramolecular interactions on the slow decay of long-lived Rydberg states in NO.

Precision Microwave Spectroscopy of the Positronium n=2 Fine Structure.

We report a new measurement of the positronium (Ps) 2^{3}S_{1}→2^{3}P_{0} interval. Slow Ps atoms, optically excited to the radiatively metastable 2^{3}S_{1} level, flew through a microwave radiation field tuned to drive the transition to the short-lived 2^{3}P_{0} level, which was detected via the time spectrum of subsequent ground state Ps annihilation radiation. After accounting for Zeeman shifts we obtain a transition frequency ν_{0}=18501.02±0.61 MHz, which is not in agreement with the theoretical value of ν_{0}=18498.25±0.08 MHz.

Slow Decay Processes of Electrostatically Trapped Rydberg NO Molecules.

Nitric oxide (NO) molecules initially traveling at 795 m/s in pulsed supersonic beams have been photoexcited to long-lived hydrogenic Rydberg-Stark states, decelerated and electrostatically trapped in a cryogenically cooled, chip-based transmission-line Rydberg-Stark decelerator. The decelerated and trapped molecules were detected in situ by pulsed electric field ionization. The operation of the decelerator was validated by comparison of the experimental data with the results of numerical calculations of particle trajectories. Studies of the decay of the trapped molecules on timescales up to 1 ms provide new insights into the lifetimes of, and effects of blackbody radiation on, Rydberg states of NO.

Coupling Rydberg Atoms to Microwave Fields in a Superconducting Coplanar Waveguide Resonator.

Rydberg helium atoms traveling in pulsed supersonic beams have been coupled to microwave fields in a superconducting coplanar waveguide (CPW) resonator. The atoms were initially prepared in the 1s55s ^{3}S_{1} Rydberg level by two-color two-photon laser excitation from the metastable 1s2s ^{3}S_{1} level. Two-photon microwave transitions between the 1s55s ^{3}S_{1} and 1s56s ^{3}S_{1} levels were then driven by the 19.556 GHz third-harmonic microwave field in a quarter-wave CPW resonator. This superconducting microwave resonator was fabricated from niobium nitride on a silicon substrate and operated at temperatures between 3.65 and 4.30 K. The populations of the Rydberg levels in the experiments were determined by state-selective pulsed electric field ionization. The coherence of the atom-resonator coupling was studied by time-domain measurements of Rabi oscillations.

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.

Rydberg-State-Resolved Resonant Energy Transfer in Cold Electric-Field-Controlled Intrabeam Collisions of NH3 with Rydberg He Atoms.

The resonant transfer of energy from the inversion sublevels in NH3 to He atoms in triplet Rydberg states with principal quantum number n = 38 has been controlled using electric fields below 15 V/cm in intrabeam collisions at translational temperatures of ∼1 K. The experiments were performed in pulsed supersonic beams of NH3 seeded in He at a ratio of 1:19. The He atoms were prepared in the metastable 1s2s 3S1 level in a pulsed electric discharge in the trailing part of the beams. The velocity slip between the heavy NH3 and the lighter metastable He was exploited to perform collision studies at center-of-mass collision speeds of ∼70 m/s. Resonant energy transfer in the atom-molecule collisions was identified by Rydberg-state-selective electric-field ionization. The experimental data have been compared to a theoretical model of the resonant dipole-dipole interactions between the collision partners based on the impact parameter method.

Electric Rydberg-Atom Interferometry.

An electric analogue of the longitudinal Stern-Gerlach matter-wave interferometer has been realized for atoms in Rydberg states with high principal quantum number n. The experiments were performed with He atoms prepared in coherent superpositions of the n=55 and n=56 circular Rydberg states in a zero electric field by a π/2 pulse of resonant microwave radiation. These atoms were subjected to a pulsed inhomogeneous electric field to generate a superposition of momentum states before a π pulse was applied to invert the internal states. The same pulsed inhomogeneous electric field was then reapplied for a second time to transform the motional states to have equal momenta before a further π/2 pulse was employed to interrogate the final Rydberg state populations. This Hahn-echo microwave pulse sequence, interspersed with a pair of equivalent inhomogeneous electric field pulses, yielded two spatially separated matter waves. Interferences between these matter waves were observed as oscillations in the final Rydberg state populations as the amplitude of the pulsed electric field gradients was adjusted.

Confinement of High- and Low-Field-Seeking Rydberg Atoms Using Time-Varying Inhomogeneous Electric Fields.

Helium atoms in high- and low-field-seeking Rydberg states with linear and quadratic Stark shifts have been confined in two dimensions and guided over a distance of 150 mm using time-varying inhomogeneous electric fields. This was achieved with an electrode structure composed of four parallel cylindrical rods to which voltages were applied to form oscillating and rotating saddle-point fields. These two modes of operation result in time-averaged pseudopotentials that confine samples in high- and low-field-seeking states about the axis of the device. The experimental data have been compared to the results of numerical particle trajectory calculations that include effects of blackbody radiation and electric field ionization. The results highlight important contributions from single-photon blackbody-induced transitions that cause large changes in the principal quantum number of the Rydberg atoms.

Probing resonant energy transfer in collisions of ammonia with Rydberg helium atoms by microwave spectroscopy.

We present the results of experiments demonstrating the spectroscopic detection of Förster resonance energy transfer from NH3 in the X1A1 ground electronic state to helium atoms in 1sns 3S1 Rydberg levels, where n = 37 and n = 40. For these values of n, the 1sns 3S1 → 1snp 3PJ transitions in helium lie close to resonance with the ground-state inversion transitions in NH3 and can be tuned through resonance using electric fields of less than 10 V/cm. In the experiments, energy transfer was detected by direct state-selective electric field ionization of the 3S1 and 3PJ Rydberg levels and by monitoring the population of the 3DJ levels following pulsed microwave transfer from the 3PJ levels. Detection by microwave spectroscopic methods represents a highly state selective, low-background approach to probing the collisional energy transfer process and the environment in which the atom-molecule interactions occur. The experimentally observed electric-field dependence of the resonant energy transfer process, probed both by direct electric field ionization and by microwave transfer, agrees well with the results of calculations performed using a simple theoretical model of the energy transfer process. For measurements performed in zero electric field with atoms prepared in the 1s40s 3S1 level, the transition from a regime in which a single energy transfer channel can be isolated for detection to one in which multiple collision channels begin to play a role has been identified as the NH3 density was increased.

Electrostatically Guided Rydberg Positronium.

We report experiments in which positronium (Ps) atoms were guided using inhomogeneous electric fields. Ps atoms in Rydberg-Stark states with principal quantum number n=10 and electric dipole moments up to 610 D were prepared via two-color two-photon optical excitation in the presence of a 670 V cm^{-1} electric field. The Ps atoms were created at the entrance of a 0.4 m long electrostatic quadrupole guide, and were detected at the end of the guide via annihilation gamma radiation. When the lasers were tuned to excite low-field-seeking Stark states, a fivefold increase in the number of atoms reaching the end of the guide was observed, whereas no signal was detected when high-field-seeking states were produced. The data are consistent with the calculated geometrical guide acceptance.

Controlling Positronium Annihilation with Electric Fields.

We show that the annihilation dynamics of excited positronium (Ps) atoms can be controlled using parallel electric and magnetic fields. To achieve this, Ps atoms were optically excited to n=2 sublevels in fields that were adjusted to control the amount of short-lived and long-lived character of the resulting mixed states. Inclusion of the former offers a practical approach to detection via annihilation radiation, whereas the increased lifetimes due to the latter can be exploited to optimize resonance-enhanced two-photon excitation processes (e.g., 1^{3}S→2^{3}P→nS/nD), either by minimizing losses through intermediate state decay, or by making it possible to separate the excitation laser pulses in time. In addition, photoexcitation of mixed states with a 2^{3}S_{1} component represents an efficient route to producing long-lived pure 2^{3}S_{1} atoms via single-photon excitation.

Selective production of Rydberg-stark states of positronium.

Rydberg positronium (Ps) atoms have been prepared in selected Stark states via two-step (1s→2p→nd/ns) optical excitation. Two methods have been used to achieve Stark-state selection: a field ionization filter that transmits the outermost states with positive Stark shifts, and state-selected photoexcitation in a strong electric field. The former is demonstrated for n=17 and 18 while the latter is performed for n=11 in a homogeneous electric field of 1.9 kV/cm. The observed spectral intensities and their dependence on the polarization of the laser radiation are in agreement with calculations that include the perturbations of the intermediate n=2 manifold. Our results pave the way for the generation of Rydberg Ps atoms with large electric dipole moments that are required for the realization of schemes to control their motion using inhomogeneous electric fields, an essential feature of some proposed Ps free-fall measurements requiring focused beams of long-lived atoms.

Driving Rydberg-Rydberg transitions from a coplanar microwave waveguide.

The coherent interaction between ensembles of helium Rydberg atoms and microwave fields in the vicinity of a solid-state coplanar waveguide is reported. Rydberg-Rydberg transitions, at frequencies between 25 and 38 GHz, have been studied for states with principal quantum numbers in the range 30-35 by selective electric-field ionization. An experimental apparatus cooled to 100 K was used to reduce effects of blackbody radiation. Inhomogeneous, stray electric fields emanating from the surface of the waveguide have been characterized in frequency- and time-resolved measurements and coherence times of the Rydberg atoms on the order of 250 ns have been determined. These results represent a key element in the development of an experimental architecture to interface Rydberg atoms with solid-state devices.

Surface-electrode Rydberg-Stark decelerator.

Hydrogen atoms in Rydberg states with principal quantum numbers between 23 and 70 have been accelerated, decelerated, and electrostatically trapped using a surface-electrode Rydberg-Stark decelerator. By applying a set of oscillating electrical potentials to a two-dimensional array of electrodes on a printed circuit board (PCB), a continuously moving, three-dimensional electric trap with a predefined velocity and acceleration is generated. From an initial longitudinal velocity of 760 m/s, final velocities of the Rydberg atoms ranging from 1200 m/s to zero velocity in the laboratory-fixed frame of reference were achieved. Accelerated or decelerated atoms were detected directly by pulsed electric-field ionization. Atoms trapped at zero mean velocity above the PCB were reaccelerated off the PCB before field ionization.

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.

Collisional and radiative processes in adiabatic deceleration, deflection, and off-axis trapping of a Rydberg atom beam.

A supersonic beam of Rydberg hydrogen atoms has been adiabatically deflected by 90°, decelerated to zero velocity in less than 25 µs, and loaded into an electric trap. The deflection has allowed the suppression of collisions with atoms in the trailing part of the gas pulse. The processes leading to trap losses, i.e., fluorescence to the ground state, and transitions and ionization induced by blackbody radiation have been monitored over several milliseconds and quantitatively analyzed.

Rydberg-state-enabled deceleration and trapping of cold molecules.

Hydrogen molecules in selected core-nonpenetrating Rydberg-Stark states have been decelerated from a mean initial velocity of 500 m/s to zero velocity in the laboratory frame and loaded into a three-dimensional electrostatic trap. Trapping times, measured by pulsed electric field ionization of the trapped molecules, are found to be limited by collisional processes. As Rydberg states can be deexcited to the absolute ground state, the method can be applied to generate cold samples of a wide range of species.