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Journal of Physics B Atomic Molecular and Optical Physics

Control of atomic and molecular motion via the Stark effect in Rydberg states

A L Goodgame, T. P. Softley

Published Oct 7, 1999• 17 citations
Publisher

Abstract

A novel theoretical study of the control of translational motion of atomic and molecular Rydberg states in inhomogeneous static electric fields is presented. Simulations have been carried out demonstrating that, under realistic conditions, the deflection and focusing of Rydberg atoms and molecules should be achievable. Advantage is taken of the high susceptibility of the Rydberg states to external electric fields, allowing the use of much smaller fields than would be necessary for ground state neutrals. The simulations presented are for trajectories of Rydberg states with n = 18-20 in the fields of an electric dipole, quadrupole and hexapole. A deflection of 7 mm is predicted for n = 18 Rydberg states travelling parallel to the dipole after 100 µs time of flight. In the hexapole n = 20 Rydberg states are refocused to a spot size of the order of the laser beam waist (10 µm) after 20 µs. It is demonstrated that the hexapole can also act as a cylindrical lens if its axis is perpendicular to the Rydberg beam direction. Spontaneous emission and black-body decay rates are also calculated, and their variation with the applied field is investigated. The potential applications of this work might include the use of focusing and deflection for controlled low-energy collisions of Rydberg molecules with surfaces.

DOI
10.1088/0953-4075/32/20/303

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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.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 4, 2013•17 citations
A novel theoretical study of the control of translational motion of atomic and molecular Rydberg states in inhomogeneous static electric fields is presented. Simulations have been carried out demonstrating that, under realistic conditions, the deflection and focusing of Rydberg atoms and molecules should be achievable. Advantage is taken of the high susceptibility of the Rydberg states to external electric fields, allowing the use of much smaller fields than would be necessary for ground state neutrals. The simulations presented are for trajectories of Rydberg states with n = 18-20 in the fields of an electric dipole, quadrupole and hexapole. A deflection of 7 mm is predicted for n = 18 Rydberg states travelling parallel to the dipole after 100 µs time of flight. In the hexapole n = 20 Rydberg states are refocused to a spot size of the order of the laser beam waist (10 µm) after 20 µs. It is demonstrated that the hexapole can also act as a cylindrical lens if its axis is perpendicular to the Rydberg beam direction. Spontaneous emission and black-body decay rates are also calculated, and their variation with the applied field is investigated. The potential applications of this work might include the use of focusing and deflection for controlled low-energy collisions of Rydberg molecules with surfaces.
Hydrogen molecules are excited in a molecular beam to Rydberg states around n=17-18 and are exposed to the inhomogeneous electric field of an electric dipole. The large dipole moment produced in the selected Stark eigenstates leads to strong forces on the H2 molecules in the inhomogeneous electric field. The trajectories of the molecules are monitored using ion-imaging and time of flight measurements. With the dipole rods mounted parallel to the beam direction, the high-field-seeking and low-field-seeking Stark states are deflected towards and away from the dipole, respectively. The magnitude of the deflection is measured as a function of the parabolic quantum number k and of the duration of the applied field. It is also shown that a large deflection is observed when populating the (17d2)1 state at zero field and switching the dipole field on after a delay. With the dipole mounted perpendicular to the beam direction, the molecules are either accelerated or decelerated as they move towards the dipole. The Rydberg states are found to survive for over 100 micros after the dipole field is switched off before being ionized at the detector and the time of flight is measured. A greater percentage change in kinetic energy is achieved by initial seeding of the beam in helium or neon followed by inhomogeneous field deceleration/acceleration. Molecular dynamics trajectory simulations are presented highlighting the extent to which the trajectories can be predicted based on the known Stark map. The spectroscopy of the populated states is discussed in detail and it is established that the N+=2, J=1, MJ=0 states populated here have a special stability with respect to decay by predissociation.
The controlled deflection of Rydberg atoms in an inhomogeneous electric field is demonstrated and shown to be in agreement with predictions based on a well-defined Stark map. Krypton atoms in a supersonic beam are excited in a two-colour multiphoton process to selected Stark states with n = 16-19 and undergo deflections in the field of an electrostatic dipole. The spatial distribution of the deflected atoms is monitored by ion imaging. The atoms travelling ~10 cm in the beam direction after excitation are deflected from the beam axis by distances of up to 3 mm, the interaction with the field taking place over 40 µs. Simulations of the trajectories agree well with the experimental results, demonstrating that the detected Rydberg atoms are those which have not undergone decay processes in the 40 µs applied field.
Argon atoms in a pulsed supersonic expansion are prepared in selected Stark components of Rydberg states with effective principal quantum number in the range n * = 15–25. When traversing regions of inhomogeneous electric fields, these atoms get accelerated or decelerated depending on whether the Stark states are low- or high-field seeking states. Using a compact electrode design, which enables the application of highly inhomogeneous and time-dependent electric fields, the Rydberg atoms experience kinetic energy changes of up to 1.2 × 10 −21 J (i.e. 60 cm −1 in spectroscopic units) in a single acceleration/deceleration stage of 3 mm length. The resulting differences in the velocities of the low- and high-field seeking states are large enough that the corresponding distributions of times of flight to the Rydberg particle detector are fully separated. As a result, efficient spectral searches of the Rydberg states best suited for acceleration/deceleration experiments are possible. Numerical simulations of the particle trajectories are used to analyse the time-of-flight distributions and to optimize the time dependence of the inhomogeneous electric fields. The decay of the Rydberg states by fluorescence, collisions and transitions induced by black-body radiation takes place on a timescale long enough not to interfere significantly with the deceleration during the first ∼5 µs.
This thesis describes contributions to the development of a new method to control the translational motion of atoms and molecules in supersonic beams.This method, Rydberg-Stark deceleration, is in principle applicable to all atoms and molecules in the gas phase.It relies on the Stark effect exhibited by Rydberg states and enables the production of samples of translationally and internally cold atoms and molecules which have possible applications in high-resolution spectroscopic experiments, in the studies of collisions at low temperatures and in quantum information science.This method has been developed and tested in deceleration and trapping experiments on hydrogen and deuterium atoms, and hydrogen molecules initially moving in supersonic beams.Its power originates from the large dipole moments, easily exceeding 1000 Debye, induced in Rydberg states by electric fields.Large forces are exerted on Rydberg atoms and molecules
A surface-electrode decelerator and deflector for Rydberg atoms and molecules has been developed with the goal of performing collisional experiments. Translationally cold H2{\mathrm{H}}_{2}H2​ molecules in a supersonic beam were excited to Rydberg-Stark states of principal quantum number n=31n=31n=31, loaded into electric traps moving at a predetermined speed above the surface of a bent printed circuit board, decelerated, and deflected from the original direction of the supersonic beam by an angle of ${10}^{\ensuremath{\circ}}$. The phase-space characteristics of the deflected beam were characterized by measuring the time-of-flight distribution and images of the Rydberg molecules and comparing them to the results of numerical particle-trajectory simulations. More than 1000 H2{\mathrm{H}}_{2}H2​ molecules were deflected per experimental cycle at a repetition rate of 25 Hz. The phase-space characteristics of the deflector make it attractive to study ion-molecule reactions at low collision energies.
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.