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 $\mu$s have been prepared by resonance enhanced two-color two-photon laser excitation from the X $^2\Pi_{1/2}$ ground state through the A $^2\Sigma^+$ intermediate state. Molecules in these long-lived Rydberg states were detected and characterized 126 $\mu$s 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.Comment: 12 pages, 10 figure

Experimental demonstration of a Rydberg-atom beam splitter

Inhomogeneous electric fields generated above two-dimensional electrode structures have been used to transversely split beams of helium Rydberg atoms into pairs of spatially separated components. The atomic beams had initial longitudinal speeds of between 1700 and 2000 m/s and were prepared in Rydberg states with principle quantum number $n=52$ and electric dipole moments of up to 8700 D by resonance-enhanced two-color two-photon laser excitation from the metastable 1s2s $^3$S$_1$ level. Upon exiting the beam splitter the ensembles of Rydberg atoms were separated by up to 15.6 mm and were detected by pulsed electric field ionization. Effects of amplitude modulation of the electric fields of the beam splitter were shown to cause particle losses through transitions into unconfined Rydberg-Stark states.Comment: 6 pages, 5 figure

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 F\"{o}rster resonance energy transfer from NH$_3$ in the X\,^1A_1 ground electronic state to helium atoms in 1s$n$s\,$^3$S$_1$ Rydberg levels, where $n=37$ and $n=40$. For these values of $n$ the 1s$n$s\,$^3$S$_1\rightarrow$1s$n$p\,$^3$P$_J$ transitions in helium lie close to resonance with the ground-state inversion transitions in NH$_3$, 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 $^3$S$_1$ and $^3$P$_J$ Rydberg levels, and by monitoring the population of the $^3$D$_J$ levels following pulsed microwave transfer from the $^3$P$_J$ 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 preformed using a simple theoretical model of the energy transfer process. For measurements performed in zero electric field with atoms prepared in the 1s40s\,$^3$S$_1$ 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 NH$_3$ density was increased.Comment: 10 pages, 8 figure

Electrostatic trapping and in situ detection of Rydberg atoms above chip-based transmission lines

Beams of helium atoms in Rydberg-Stark states with principal quantum number $n=48$ and electric dipole moments of 4600~D have been decelerated from a mean initial longitudinal speed of 2000~m/s to zero velocity in the laboratory-fixed frame-of-reference in the continuously moving electric traps of a transmission-line decelerator. In this process accelerations up to $-1.3\times10^{7}$~m/s$^2$ were applied, and changes in kinetic energy of $\Delta E_{\mathrm{kin}}=1.3\times10^{-20}$~J ($\Delta E_{\mathrm{kin}}/e = 83$~meV) per atom were achieved. Guided and decelerated atoms, and those confined in stationary electrostatic traps, were detected in situ by pulsed electric field ionisation. The results of numerical calculations of particle trajectories within the decelerator have been used to characterise the observed deceleration efficiencies, and aid in the interpretation of the experimental data.Comment: 13 pages, 5 figure

Rydberg-Stark states in oscillating electric fields

Experimental and theoretical studies of the effects of weak radio-frequency electric fields on Rydberg-Stark states with electric dipole moments as large as 10000 D are reported. High-resolution laser spectroscopic studies of Rydberg states with principal quantum number $n=52$ and $53$ were performed in pulsed supersonic beams of metastable helium with the excited atoms detected by pulsed electric field ionisation. Experiments were carried out in the presence of sinusoidally oscillating electric fields with frequencies of 20~MHz, amplitudes of up to 120~mV/cm, and dc offsets of up to 4.4~V/cm. In weak fields the experimentally recorded spectra are in excellent agreement with the results of calculations carried out using Floquet methods to account for electric dipole couplings in the oscillating fields. This highlights the validity of these techniques for the accurate calculation of the Stark energy level structure in such fields, and the limitations of the calculations in stronger fields where $n-$mixing and higher-order contributions become important.Comment: 19 pages, 11 figures in Molecular Physics, (2015

Preparation of circular Rydberg states in helium using the crossed fields method

Helium atoms have been prepared in the circular $|n=55,\ell=54,m_{\ell}=+54\rangle$ Rydberg state using the crossed electric and magnetic fields method. The atoms, initially travelling in pulsed supersonic beams, were photoexcited from the metastable 1s2s\,^3S_1 level to the outermost, $m_{\ell}=0$ Rydberg-Stark state with $n=55$ in the presence of a strong electric field and weak perpendicular magnetic field. Following excitation, the electric field was adiabatically switched off causing the atoms to evolve into the circular state with $m_{\ell}=+54$ defined with respect to the magnetic field quantization axis. The circular states were detected by ramped electric field ionization along the magnetic field axis. The dependence of the circular state production efficiency on the strength of the excitation electric field, and the electric-field switch-off time was studied, and microwave spectroscopy of the circular-to-circular $|55,54,+54\rangle\rightarrow|56,55,+55\rangle$ transition at $\sim38.5$~GHz was performed.Comment: 10 pages, 8 figure

A dynamical systems model of unorganised segregation

We consider Schelling's bounded neighbourhood model (BNM) of unorganised segregation of two populations from the perspective of modern dynamical systems theory. We derive a Schelling dynamical system and carry out a complete quantitative analysis of the system for the case of a linear tolerance schedule in both populations. In doing so, we recover and generalise Schelling's qualitative results. For the case of unlimited population movement, we derive exact formulae for regions in parameter space where stable integrated population mixes can occur. We show how neighbourhood tipping can be adequately explained in terms of basins of attraction. For the case of limiting population movement, we derive exact criteria for the occurrence of new population mixes and identify the stable cases. We show how to apply our methodology to nonlinear tolerance schedules, illustrating our approach with numerical simulations. We associate each term in our Schelling dynamical system with a social meaning. In particular we show that the dynamics of one population in the presence of another can be summarised as follows {rate of population change} = {intrinsic popularity of neighbourhood} - {finite size of neighbourhood} - {presence of other population} By approaching the dynamics from this perspective, we have a complementary approach to that of the tolerance schedule.Comment: 17 pages (inc references), 9 figure