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Physical Review Letters

Longitudinal Focusing and Cooling of a Molecular Beam

Floris M. H. Crompvoets, Rienk T. Jongma, Hendrick L. Bethlem, André J. A. van Roij, Gerard Meijer

Published Aug 13, 2002• 75 citations
Publisher

Abstract

A neutral polar molecule experiences a force in an inhomogeneous electric field. This electric field can be designed such that a beam of polar molecules is exposed to a harmonic potential in the forward direction. In this potential the longitudinal phase-space distribution of the ensemble of molecules is rotated uniformly. This property is used to longitudinally focus a pulsed beam of ammonia molecules and to produce a beam with a longitudinal velocity spread of 0.76 m/s, corresponding to a temperature of 250 mu K.

DOI
10.1103/physrevlett.89.093004

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Journal of Physics B Atomic Molecular and Optical Physics•Oct 28, 1992•18 citations
A neutral polar molecule experiences a force in an inhomogeneous electric field. This electric field can be designed such that a beam of polar molecules is exposed to a harmonic potential in the forward direction. In this potential the longitudinal phase-space distribution of the ensemble of molecules is rotated uniformly. This property is used to longitudinally focus a pulsed beam of ammonia molecules and to produce a beam with a longitudinal velocity spread of 0.76 m/s, corresponding to a temperature of 250 mu K.
A polar molecule experiences a force in an inhomogeneous electric field. Using this force, neutral molecules can be decelerated and trapped. It is shown here that this can in principle be done without loss in phase-space density. Using a series of 64 pulsed inhomogeneous electric fields a supersonic beam of ammonia molecules (14NH3,{(}^{14}{\mathrm{NH}}_{3},(14NH3​, 14ND3,{}^{14}{\mathrm{ND}}_{3},14ND3​, 15ND3){}^{15}{\mathrm{ND}}_{3})15ND3​) is decelerated. Subsequently, the decelerated molecules are loaded into an electrostatic quadrupole trap. Densities on the order of 107molecules/cm3{10}^{7} {\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}/\mathrm{c}\mathrm{m}}^{3}107molecules/cm3 at a temperature of 25 mK are obtained for 14ND3{}^{14}{\mathrm{ND}}_{3}14ND3​ and 15ND3{}^{15}{\mathrm{ND}}_{3}15ND3​ separately and simultaneously. This corresponds to a phase-space density in the trap of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13},$ 50 times less than the initial phase-space density in the beam.
The interaction of polar molecules with an inhomogeneous, electrostatic field to filter molecules from an effusive room-temperature source is exploited to create a slow molecule beam. Whether a dipolar molecule is trapped in or expelled from the electric field minimum depends on the orientation of the molecular dipole with respect to the electric field. These molecules are called low and high-field seekers, respectively. Thus, an electric field configuration with a field minimum on axis acts as a 2-dimensional trap for low-field seeking molecules with small transverse velocity components. A linear quadrupolar is opted, which is one of the simplest suitable geometries. The longitudinal velocity is limited by a bent section, where the centripetal force due to the radius of curvature and electric field gradient guide only the slowest molecules around the bend.
A series of pulsed electric fields can be arranged such that it creates a traveling potential well in which neutral dipolar molecules can be confined. This provides a method to transport, to decelerate, and to cool a sample of neutral molecules while maintaining the initial phase-space density. This method is described using the concept of phase stability. The oscillating motion of molecules in the traveling potential well, reaching a minimum velocity spread corresponding to a translational temperature of 4 mK, is experimentally observed.
We have focused and decelerated benzonitrile (C7H5N)({\mathrm{C}}_{7}{\mathrm{H}}_{5}\mathrm{N})(C7​H5​N) molecules from a molecular beam, using an array of time-varying inhomogeneous electric fields in alternating-gradient configuration. Benzonitrile is prototypical for large asymmetric top molecules that exhibit rich rotational structure and a high density of states. At the rotational temperature of 3.5K3.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}3.5K in the pulsed molecular beam, many rotational states are populated. Benzonitrile molecules in their absolute ground state are decelerated from 320to289m∕s320\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}289\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}320to289m∕s, and similar changes in velocity are obtained for excited rotational states. All measurements agree well with the outcome of trajectory calculations. These experiments demonstrate that such large polyatomic molecules are amenable to the powerful method of Stark deceleration.
Polar molecules in high-field seeking states cannot be trapped in static traps as Maxwell's equations do not allow a maximum of the electric field in free space. It is possible to generate an electric field that has a saddle point by superposing an inhomogeneous electric field to an homogeneous electric field. In such a field, molecules are focused along one direction, while being defocused along the other. By reversing the direction of the inhomogeneous electric field the focusing and defocusing directions are reversed. When the fields are being switched back and forth at the appropriate rate, this leads to a net focusing force in all directions. We describe possible electrode geometries for creating the desired fields and discuss their merits. Trapping of 15ND3^{15}\mathrm{ND}_{3}15ND3​ ammonia molecules in a cylindrically symmetric ac trap is demonstrated. We present measurements of the spatial distribution of the trapped cloud as a function of the settings of the trap and compare these to both a simple model assuming a linear force and to full three-dimensional simulations of the experiment. With the optimal settings, molecules within a phase-space volume of 270mm3(m∕s)3270\phantom{\rule{0.3em}{0ex}}{\mathrm{mm}}^{3}\phantom{\rule{0.2em}{0ex}}(\mathrm{m}∕\mathrm{s}{)}^{3}270mm3(m∕s)3 remain trapped. This corresponds to a trap depth of about 5mK5\phantom{\rule{0.3em}{0ex}}\mathrm{mK}5mK and a trap volume of about 20mm320\phantom{\rule{0.3em}{0ex}}{\mathrm{mm}}^{3}20mm3.
An electrostatic mirror for neutral polar molecules has been constructed using an array of electrodes of alternating polarity between which a high potential was applied. This configuration produces an exponentially evanescing electric field that interacts with polar molecules by the Stark effect. The spatial gradients of the Stark energies produce forces which were used to reflect a pulsed beam of chloromethane (CH 3 Cl) molecules with a reflectivity of 25% at grazing angles of incidence of around 5 mrad. Reflections have also been produced with applied voltages as low as 100 V or with grazing angles greater than 20 mrad. This type of device could be useful for the manipulation of slow molecular beams and would permit the construction of optical elements for the de Broglie waves of molecules.