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During the past years a rapidly growing interest in the field of cold molecules
has been observed.
The possibility to investigate molecular behavior at low temperatures motivates
physicists and chemists from diverse backgrounds to produce cold and
dense molecular samples [1].
Certainly, this development is inspired by the great success in the
closely related field of cold atoms which led to the demonstration of
Bose-Einstein
condensation (BEC) in ultracold atomic gases.
The extension of these investigations to molecules is desirable as due to
their complex internal strucure, molecules can have properties which are not
available with atoms, such as a permanent electric dipole moment.
In a dense and cold gas of polar molecules, the long-range and anisotropic
dipole-dipole interaction enables to tune the interparticle interaction by
applying external fields.
Cold molecules offer the possibility to enter a completely new regime in
chemistry, which is, for instance, relevant for chemical processes in the interstellar
medium, and they are interesting candidates for various high-precision
measurements.
[1] Special Issue on ultracold polar molecules, Eur. Phys. J. D 31, 149-445 (2004)
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| The velocities of a thermal gas in a reservoir at room temperature are distributed according to the Maxwell-Boltzmann distribution with a most probable velocity of a few 100 m/s. We consider molecules slow if they can be trapped with electric, magnetic or electromagnetic fields. A practical upper limit of neutral-particle trap depths is of the order of a kelvin which is easily achieved using electric fields. If this value is translated into a light polar molecule like ammonia (ND3), it corresponds to a maximum velocity of ~ 35 m/s. From the Maxwell-Boltzmann distribution it can be obtained that the fraction of particles below this maximum velocity amounts to 10-4. Although being a small fraction, for a gas at standard pressure and temperature this results in a density of 1015 cm-3. This small fraction but large number is the core motivation for the filtering technique. |
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| In this experiment we use a bent electrostatic quadrupole to filter slow polar molecules like ammonia (ND3) from an effusive beam. For the filtering process, the interaction of polar molecules with electric fields (Stark effect) is exploited and the molecules are injected at the electric-field minimum of the quadrupole. Molecules whose time-averaged dipole moments are oriented antiparallel (parallel) to the external electric field minimize their internal energy in weak (strong) field regions and they are called low-field seekers (high-field seekers). For the injected low-field-seeking molecules whose transverse kinetic energy is smaller than the Stark energy shift, transverse trapping results, while the rest escapes. Longitudinal velocity filtering in the bent section of the guide results from centripetal action keeping only the slowest molecules whereas longitudinally fast molecules escape. The guide filters the molecules according to their energy which allows an efficient transfer of the slow molecule fraction from the reservoir to a separate vacuum chamber. |
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| The figure shows a cut through the electric field of the quadrupole which is used in the experiment. The guide consists of four solid steel electrodes with a diameter of 2 mm separated by 1 mm. The total length of the quadrupole amounts to 50 cm whereas the radius of curvature of the bend is 1.25 cm. Neighboring electrodes carry voltages of opposite polarity. The electric field has a minimum in the center of the guide and it rises with the distance from the center. For electrode voltages of +/- 5 kV, a maximum electric field of up to 100 kV/cm can be achieved. The central region of the guide defines the trapping region for molecules in low-field-seeking states. |
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| The figure shows a time-of-flight measurement of the guided molecules recorded with a quadrupole mass spectrometer. For that purpose, the electric field on the electrodes is switched on and off and the signal dependence on the on-time is shown. The flux increases with the voltage as more and faster molecules can be guided. This explains the earlier rise in the signal for higher voltages. |
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| The velocity distribution of the guided molecules can be determined from the rising slope of the time-of-flight signal, where the velocity dependent detection efficiencies of the detector have to be taken into account. The distribution has a maximum at a velocity of 50 m/s which corresponds to a translational temperature of 4 K. |
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So far, electrostatic fields have been used to filter and guide molecules
in low-field-seeking states (LFS). Compared to LFS, the manipulation of
high-field-seekers (HFS) is much more difficult. This is due mainly to the
fact that electrostatic maxima are not allowed in free space, and hence HFS
are quickly lost on the electrodes. In future experiments with trapped samples
of cold molecules, collisions or the interaction with light fields are likely
to change HFS into LFS and vice versa. It is further interesting to note that
every molecule in the ground state is a HFS. Therefore, a method which is able
to manipulate both high- and low-field-seekers is vital. In our group, a method has been demonstrated which in principle allows two-dimensional trapping of HFS and LFS by applying time-varying electric fields to the present quadrupole guide setup. The image shows two dipolar field configurations which show a saddle-like potential. A time-varying electric field is generated by alternating between the two configurations with a repetition rate in the kHz range. Similar to the radio-frequency field of a Paul trap where ions can be trapped in a rotating saddle potential, time-varying electric fields can be used for confining neutral dipolar molecules. Independent whether the molecule is a HFS or a LFS, the saddle-like dipole potential confines the molecule in one direction and repels it in the perpendicular direction, depending on time. The time average of the force is small at every position. However, the molecule performs a micromotion which is locked to the external driving field so that the time-averaged force does not cancel, and the molecule experiences a net attractive force towards the center. For ammonia, a stability region in the frequency range between 5 and 12 kHz can be observed. In the experiment, it is expected that most of the detected molecules are LFS, as HFS are attraced by the quadrupole electric field when they leave the guide. An extension of this technique to three-dimensional trapping of atoms in their ground state is planned. However, the small trap depths due to small induced atomic dipole moments compared to molecules make precooling with a magneto-optical trap necessary for atomic samples. |
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| The bent electrostatic quadrupole guide constitutes a source of translationally cold polar molecules. This source is used to demonstrate a novel electrostatic trap for polar molecules which can be continuously loaded. The ability to trap cold polar molecules at a sufficiently high density opens the perspective to observe cold collisions and, furthermore, a completely new regime of chemical reactions can be entered. The image shows the prototype of a large-volume (0.6 cm3) electrostatic trap. With such a trap, we have demonstrated storage times of ~130 ms for ND3 molecules with a density of ~108 cm-3 at a temperature of 300 mK. The trap consists of five ring-shaped electrodes and two spherical electrodes at both ends. Neighboring electrodes carry voltages of opposite polarity giving rise to an inhomogeneous electric field which is large near the electrodes and small in the center. The electrodes carry voltages of up to +/-5 kV which gives rise to a maximum trapping field strength of 40 kV/cm. For ammonia molecules, the trap depth amounts to ~800 mK and similar values can be determined for formaldehyde (CH2O) and methylchloride (CH3Cl). The central ring electrode is intersected two times and it is possible to adapt two quadrupole segments, one for filling and one for extraction of the trapped gas. Slow molecules from the quadrupole guide (input) enter the trap volume through one opening and they are kept within the trap if their kinetic energy is lower than the trap depth. Once inside the trap, the molecules oscillate in the trap potential and the trapping results from the fact that it takes some time until the molecules find one of the exits. When the trap is continuously loaded, a steady state is reached with an equal number of molecules entering and leaving the trap per time interval. |
| The figure shows the detector signal at the output quadrupole as a function of time while the voltage at the input quadrupole is switched. The electrodes carry voltages of +/-4.5 kV. When the input quadrupole is switched on at t=0, slow molecules are guided and the trap is filled resulting in an increasing signal at the output quadrupole guide. The flux from the trap is determined to ~3x108 s-1. After the input quadrupole is switched off at t=1s, a signal decay is observed which allows to estimate the lifetime of the molecules in the trap. As the lifetime of the molecules in the trap depends on how fast they find an exit, the lifetime is velocity dependent. Therefore, the decay cannot be described by an exponential function and, hence, not by a (1/e)-lifetime. The figure shows the background corrected decay trace of the molecules from the trap. An alternative measure for the trap lifetime is the time after which half the molecules have left the trap. From the data for +/-4.5 kV a lifetime of ~130 ms can be derived. Our simulations show that the lifetime is mainly limited by the exit channels whereas collisions with the background gas do not contribute significantly. |
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| The temperature of the trapped ND3 sample is determined by a measurement of the molecules' velocity distribution. The distribution can be obtained by a time-of-flight measurement where the output quadrupole is switched and the arrival time is recorded. All electrodes were set to voltages of +/-4.5 kV. The figures shows the measured data (squares) which is in good agreement with the simulation results (triangles). The temperature of the molecules was determined to be 300 mK. |
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The filtering techniques developed so far constitute powerful tools for the
manipulation of cold polar molecules in HFS or LFS states. The results show
that it is possible to efficiently filter
translationally cold molecules at comparatively high densities from a thermal
reservoir and to trap them in an inhomogeneous electric field for about 130 ms.
For the future, it would be interesting to investigate to which extent the trap lifetime can be elongated by the use of a trap with a larger volume. An important goal behind the extension of the trap lifetime is to see indications of cold collisions in the trap. The investigation of cold collisions between polar molecules is very important as they provide valuable information for future evaporative cooling experiments. A remarkable step forward to a cold and dense sample of molecules would be a combination of the guiding and trapping technique with buffer-gas cooling in a cryogenic environment. In this way, cold molecules can be produced by thermalization with cold helium vapor. It should be possible to guide the cold molecules out of the cryogenic cell and to trap them at room temperature. In this way we hope to combine the best of two worlds which allows us to investigate internally and externally cold molecules using our trapping methods at room temperature with the advantage of a better optical access. Go to Top of Page |
| We acknowledge financial support by the DFG under SPP 1116. |
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At present, an experimental setup for three-dimensional electric trapping of neutral atoms
is under construction. The trap setup designed in our group is shown in the left figure and
the trap center is marked by a red point. In such an AC-trap, the simultaneous trapping of
laser-cooled atoms and cold molecules should be possible. If the trapping attempts are
successful, the AC-trapping technique will provide a powerful tool for the observation of
atom-molecule collisions. Furthermore, the setup allows to investigate the collision properties
under the influence of strong external electric fields. As ultracold atoms can be easily provided by a magneto-optical trap (MOT), the electric trap is first tested with cold Rubidium atoms. The pre-cooling of the atoms is necessary as the trap potential experienced by the atoms is small due to their small induced dipole moments. Atoms in the ground state are high-field seekers (HFS) and for electric trapping, an effective potential minimum similar to the situation in an rf ion trap is required. Note, however, that the interaction energy of a neutral particle is given by the Stark energy and not by the Coulomb energy as it is the case for charged particles. A confining potential for atoms (and molecules) can be achieved by applying the switching sequence shown in the right side of the figure to the electrodes. In one switching cycle, high voltages of opposite polarity are subsequently applied to opposite electrode pairs whereas the remaining electrodes are grounded. Stable trapping conditions for atoms can be achieved by chosing switching frequencies of the order of 1 kHz for voltages of +/-5 kV. |
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The small dimensions of the AC-trap forbid an operation of the MOT in the center of this trap so that the
MOT is operated outside at a distance of XX cm (left figure). After a cold atomic cloud is generated, the
cold atoms are loaded into a magnetic trapping field which is generated by the MOT coils. These coils are
mounted on a translation stage so that the atoms can be transfered in the center of the AC-trap
(right figure).
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For more detailed information, please read our publications (see below) or contact us. |
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Michael Motsch, Martin Zeppenfeld, Christian Sommer, Markus Schenk, Laurens van Buuren, Pepijn Pinkse, and Gerhard Rempe. Former members:
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last modified:
24-Mar-2006
