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Molecular Physics

Motional dynamics of Rydberg NO molecules in a transmission-line Rydberg-Stark decelerator

Adam Deller, M. H. Rayment, S. D. Hogan

Published Jul 17, 2026• 0 citations
Publisher

Abstract

The dynamics of nitric oxide (NO) molecules in a cryogenically cooled, transmission-line Rydberg-Stark decelerator have been studied experimentally and through numerical particle trajectory calculations. The molecules, initially travelling in pulsed supersonic beams, were prepared in states with principal quantum number n = 43, in the Rydberg series converging to the N+=2 rotational state of NO+ using the nℓ X+ 1Σ+←A 2Σ+←X 2Π1/2 resonance-enhanced two-colour two-photon excitation scheme. Deceleration from 795 m/s to rest in the laboratory-fixed frame of reference was achieved in a time of ∼250 μs. The observed motional dynamics of the decelerated and trapped Rydberg molecules is in good quantitative agreement with the results of the calculations. The translational temperature of the trapped molecules was determined to be ∼8 K from their rate of expansion after the trap was switched off. These results are of importance in the interpretation of measurements of lifetimes and decay processes of cold electrostatically trapped Rydberg molecules, and in the optimisation of the operation of this type of decelerator for heavier species.

DOI
10.1080/00268976.2026.2701441

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•Mar 28, 2016•0 citations
The dynamics of nitric oxide (NO) molecules in a cryogenically cooled, transmission-line Rydberg-Stark decelerator have been studied experimentally and through numerical particle trajectory calculations. The molecules, initially travelling in pulsed supersonic beams, were prepared in states with principal quantum number n = 43, in the Rydberg series converging to the N+=2 rotational state of NO+ using the nℓ X+ 1Σ+←A 2Σ+←X 2Π1/2 resonance-enhanced two-colour two-photon excitation scheme. Deceleration from 795 m/s to rest in the laboratory-fixed frame of reference was achieved in a time of ∼250 μs. The observed motional dynamics of the decelerated and trapped Rydberg molecules is in good quantitative agreement with the results of the calculations. The translational temperature of the trapped molecules was determined to be ∼8 K from their rate of expansion after the trap was switched off. These results are of importance in the interpretation of measurements of lifetimes and decay processes of cold electrostatically trapped Rydberg molecules, and in the optimisation of the operation of this type of decelerator for heavier species.
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.
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.
Hydrogen and deuterium Rydberg atoms, initially moving at velocities of 600 and 560 m s −1 , respectively, in pulsed supersonic beams, have been decelerated and electrostatically trapped following adiabatic 90° deflection from their initial axis of propagation to minimize collisions with the trailing edge of the gas pulses. The time evolution of the potential energy surfaces, over which the atoms undergoing deceleration travel during the trap-loading process, is analogous to that of a moving electrodynamic trap. It has been studied in the laboratory-fixed frame of reference and in the continuously moving frame of reference defined by the instantaneous position of the electric-field minimum around which the atoms are located. The importance of the quadratic Stark effect in the deceleration of samples in Rydberg states with principal quantum numbers above 35 has also been investigated by comparison of experimental results with predictions resulting from the numerical calculation of particle trajectories. The data presented for deuterium atoms represent the first application of Rydberg–Stark deceleration and trapping for this atom. Comparison of the rate of loss of n = 30 H and D atoms from the trap enables one to conclude that it is not affected by the particle dynamics during deceleration and trap loading.
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.
Hydrogen atoms in supersonic expansions with velocities in the range from 700to800m∕s700\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}800\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}700to800m∕s have been excited to Rydberg-Stark states with principal quantum number nnn between 20 and 40, decelerated to zero velocity in the lab frame using time-dependent inhomogeneous electric fields, and trapped in a two-dimensional electrostatic trap with an initial density of $\ensuremath{\approx}5\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The motion of the atomic cloud in the trap was observed by measuring the times of flight and images of the H+{\mathrm{H}}^{+}H+ ions produced by pulsed field ionization. The velocity distribution of the trapped atoms can be described by an effective temperature of 350mK350\phantom{\rule{0.3em}{0ex}}\mathrm{mK}350mK. The decay of the population of trapped atoms does not follow a single-exponential behavior and has contributions from radiative and collisional processes.
The experimental realisation of a set of surface-based devices for controlling the positions and velocities of Rydberg atoms initially travelling in pulsed supersonic beams is described. The unique aspect of these devices is that they are based on the geometry of two-dimensional electrical transmission-lines and are therefore suited to integration with chip-based microwave circuits to realise a complete Rydberg laboratory on a chip. Such a chip-based laboratory could be exploited in hybrid approaches to quantum information processing, and for studies of collisions and decay processes of highly excited atoms and molecules. The devices operate through the generation of inhomogeneous electric fields and take advantage of the large electric dipole moments associated with high Rydberg states to exert forces on the atoms. In the experiments, helium atoms in Rydberg-Stark states with principal quantum numbers ranging from 48 to 52 and electric dipole moments of 10000 D are employed. The devices developed include electrostatic guides which permitted control over the transverse motion of beams of atoms. These were used to transport samples, initially travelling at 1950 m/s and deflect them away from their initial axis of propagation. The guided atoms were detected by pulsed electric field ionisation. To control the longitudinal motion of the samples, the transmission-lines were modified to permit the generation of sets of continuously moving electric traps. The resulting transmission-line decelerators were then employed to guide, accelerate and decelerate atoms trapped in three-dimensions. Accelerations up to 2.3 x 10^{7} m/s^{2} were applied to decelerate samples from 2000 m/s to zero-velocity in the laboratory-fixed frame of reference, leading to the removal of 80 meV of kinetic energy, the largest achieved in any Stark decelerator to date. The decelerated atoms were trapped in stationary electric traps and detected in situ. The phase-space acceptances of the decelerators were calculated to characterise the effects of acceleration and deceleration on the trapped atoms. The results of the calculations were employed in the interpretation of the experimental data, and to identify effects of collisions and blackbody transitions.