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Journal of Physics Conference Series

Cooling effects in the Stark deceleration of Rydberg atoms/molecules with time-dependent electric fields

Yoshihiro Yamakita, R Takahashi, Koichi Ohno, Simon R. Procter, Glenn E. M. Maguire, T. P. Softley

Published Sep 1, 2007• 7 citations
Publisher

Abstract

This paper presents calculations for realizing the deceleration of H 2 Rydberg molecules with n = 16, where n is the principal quantum number. A double-dipole decelerator (Softley T P, Procter S R, Yamakita Y, Maguire G and Merkt F 2005 J. Elec. Spectrosc. Relat. Phenom. 144–147 113) operated with an optimum time-dependent electric field allows, in principle, complete deceleration of the Rydberg molecules to zero mean velocity. A bunch of molecules in a supersonic beam is decelerated from the initial velocity centered at ∼900 ms −1 and translational temperature 1 K to the final velocity 0 ms −1 and temperature 13 mK. The calculations are performed using the 4th-order symplectic integrator based on representations in phase space { q, p }, and show that an ensemble with narrow δ q 0 and broad δ p 0 distribution is converted to one at standstill with broad δ q and narrow δ p . Cooling effects are reinforced by field ionization in which the fast components that move to regions of high electric field are effectively filtered out.

DOI
10.1088/1742-6596/80/1/012045

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This paper presents calculations for realizing the deceleration of H 2 Rydberg molecules with n = 16, where n is the principal quantum number. A double-dipole decelerator (Softley T P, Procter S R, Yamakita Y, Maguire G and Merkt F 2005 J. Elec. Spectrosc. Relat. Phenom. 144–147 113) operated with an optimum time-dependent electric field allows, in principle, complete deceleration of the Rydberg molecules to zero mean velocity. A bunch of molecules in a supersonic beam is decelerated from the initial velocity centered at ∼900 ms −1 and translational temperature 1 K to the final velocity 0 ms −1 and temperature 13 mK. The calculations are performed using the 4th-order symplectic integrator based on representations in phase space { q, p }, and show that an ensemble with narrow δ q 0 and broad δ p 0 distribution is converted to one at standstill with broad δ q and narrow δ p . Cooling effects are reinforced by field ionization in which the fast components that move to regions of high electric field are effectively filtered out.
The interaction between inhomogeneous electric fields and the large electric dipole moments of atoms and molecules in Rydberg states of high principal quantum number can be used to efficiently accelerate and decelerate atoms and molecules in the gas phase. We describe here how hydrogen atoms and molecules initially moving with velocities of ∼600 m/s in supersonic beams can be decelerated to zero velocity and loaded into electric traps. The long observation times that are made possible by the electrostatic trapping enables one to study slow relaxation processes. Experiments are presented in which we have observed photoionization processes and transitions between Rydberg states induced by blackbody radiation at temperatures between 10 K and 300 K on a time scale of several milliseconds. Comparison of these processes in Rydberg states of H and H(2) suggests the importance, in H(2), of collisional processes and of the process of blackbody-radiation-induced predissociation.
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
The large electric dipole moments associated with highly excited Rydberg states of atoms and molecules make gas-phase samples in these states very well suited to deceleration and trapping using inhomogeneous electric fields. The methods of Rydberg-Stark deceleration with which this can be achieved are reviewed here. Using these techniques, the longitudinal motion of beams of atoms and molecules moving at speeds as high as 2500 m/s have been manipulated, with changes in kinetic energy of up to |Δ E kin|=1.3×10−20 J (|Δ E kin|/e=80 meV or |Δ E kin|/h c=650 cm −1) achieved, while decelerated and trapped samples with number densities of 106– 107 cm −3 and translational temperatures of ∼150 mK have been prepared. Applications of these samples in areas of research at the interface between physics and physical chemistry are discussed.
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.
In this paper, we investigate theoretically the Stark deceleration and cooling of subsonic NH3 molecular beams based on our second-generation electrostatic Stark decelerator with 180 stages. Firstly, we calculate the Stark shifts of NH3 molecules in the |J=1, K=1 ightangle states and show the stable area of longitudinal phase space for different synchronous phase angles. Secondly, we study the slowing performance of NH3 molecular beams in the traditional mode, and discuss the relationships between various parameters (such as the kinetic energy loss per stage, final velocity and the slowing efficiency) and the synchronous phase angle 0, as well as the dependence of final velocity on the applied voltages. It is found that a subsonic NH3 molecular beam can be decelerated from 280 to 6.7 m/s at 0=26.08 when the high voltages applied on the electrodes are 13 kV, corresponding to a removal of 99.9% kinetic energy. The translational temperature of the molecular packets in the moving frame is significantly reduced from 1.34 K to 80 mK. Finally, we study the slowing performance of NH3 molecules and the dependence of final velocity on the synchronous phase angle in an alternate operation mode. In this mode, a synchronous phase angle 0=0 is chosen to bunch the molecules by using the first 15 stages. The remaining 165 stages are then used to slow a subsonic molecular beam at a certain synchronous phase angle. Our result shows that a molecular beam with a mean velocity of 280 m/s can be decelerated to 20.7 m/s at 0=65.4 when the voltages applied are 6.5 kV, indicating a 99.4% kinetic energy removal, and the translational temperature of the molecular packets can be reduced from 1.34 K to 1.6 mK. By comparing the results obtained from the two operational modes, the temperature of the slowed molecular packet in the alternate mode is 50 times lower than that in the traditional mode. It is shown that our second-generation 180-stage Stark decelerator can effectively produce slow and cold molecules with relatively small electric dipole moment like NH3. These monochromatic NH3 molecular beams offer a promising starting point for high resolution spectroscopy, precision measurement, cold collisions and cold chemistry. This theoretical work provides a reliable basis in our further experimental research.
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.