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

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

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

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

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.Comment: 6 pages, 5 figure