Stark Deceleration Research Articles

Deceleration of supersonic beams using inhomogeneous electric and magnetic fields

Methods for the production of cold atomic and molecular samples relying on the deceleration of pulsed supersonic beams are described and a review of the corresponding literature is presented. These methods include multistage Stark deceleration, multistage Zeeman deceleration, and Rydberg-Stark deceleration. Recent applications of the cold samples produced with these techniques are summarized.

Low-energy inelastic collisions of OH radicals with He atoms andD2molecules

We present an experimental study on the rotational inelastic scattering of OH ($X {}^{2}{\ensuremath{\Pi}}_{3/2},J=3/2,f$) radicals with He and ${\mathrm{D}}_{2}$ at collision energies between 100 and 500 cm${}^{\ensuremath{-}1}$ in a crossed beam experiment. The OH radicals are state selected and velocity tuned using a Stark decelerator. Relative parity-resolved state-to-state inelastic scattering cross sections are accurately determined. These experiments complement recent low-energy collision studies between trapped OH radicals and beams of He and ${\mathrm{D}}_{2}$ that are sensitive to the total (elastic and inelastic) cross sections [Sawyer et al., Phys. Rev. Lett. 101, 203203 (2008)], but for which the measured cross sections could not be reproduced by theoretical calculations [Pavlovic et al., J. Phys. Chem. A 113, 14670 (2009)]. For the OH-He system, our experiments validate the inelastic cross sections determined from rigorous quantum calculations.

Phase stability in a multistage Zeeman decelerator

The phase stability of a multistage Zeeman decelerator is analyzed by numerical particle-trajectory simulations and experimental measurements. A one-dimensional model of the phase stability in multistage Stark deceleration [Bethlem et al., Phys. Rev. Lett. 84, 5744 (2000)] has been adapted to multistage Zeeman deceleration and compared with one- and three-dimensional particle-trajectory simulations, including the analysis of the effect of finite switch-on and -off times of the deceleration pulses. The comparison reveals that transverse effects in the decelerator lead to a considerable reduction of the phase-space acceptance at low values of the phase angle and an enhancement at high values. The optimal combinations of phase angles and currents with which a preset amount of kinetic energy can be removed from atoms and molecules in a pulsed supersonic beam using a multistage decelerator are determined by simulation. Quantitative analysis of the phase-space acceptance within a given volume reveals that for our decelerator (8 $\mathrm{\ensuremath{\mu}}\mathrm{s}$ switch-off time) optimal conditions are achieved for values of the phase angle between ${45}^{\ifmmode^\circ\else\textdegree\fi{}}$ and ${55}^{\ifmmode^\circ\else\textdegree\fi{}}$. This conclusion is examined and confirmed by experimental measurements using deuterium atoms. Alternative approaches to generate optimal deceleration pulse sequences, such as the implementation of evolutionary algorithms or the use of higher-order modes of the decelerator, are discussed.

Creating cold stationary molecular gases by optical Stark deceleration

The deceleration of molecules from cold molecular beams using electric and magnetic fields has become an important means for producing stationary, cold dipolar or paramagnetic molecular gases that can be trapped and potentially cooled to ultra-cold temperatures in the μK range. We report on a general scheme for the creation of cold molecules of essentially any type by deceleration of a cold molecular beam using intense optical fields. Deceleration of benzene molecules to zero velocity is achieved by utilizing a single half oscillation of the center-of-mass motion of the molecules within a moving optical lattice. The lattice traveling at half the speed of the molecular beam is created by the interference of two near-counter-propagating fields at different frequencies. We show that by rapidly switching on the optical lattice for approximately the time required for a half oscillation, a bunch of approximately 105 benzene molecules can be rapidly decelerated and brought to rest in the laboratory frame.

Slowing polar molecules using a wire Stark decelerator

We have designed and implemented a new Stark decelerator based on wire electrodes, which is suitable for ultrahigh vacuum applications. The 100 deceleration stages are fashioned out of 0.6 mm diameter tantalum and the array's total length is 110 mm, approximately 10 times smaller than a conventional Stark decelerator with the same number of electrode pairs. Using the wire decelerator, we have removed more than 90% of the kinetic energy from metastable CO molecules in a beam.

Nonadiabatic transitions in a Stark decelerator

In a Stark decelerator, polar molecules are slowed down and focussed by an inhomogeneous electric field which switches between two configurations. For the decelerator to work, it is essential that the molecules follow the changing electric field adiabatically. When the decelerator switches from one configuration to the other, the electric field changes in magnitude and direction, and this can cause molecules to change state. In places where the field is weak, the rotation of the electric field vector during the switch may be too rapid for the molecules to maintain their orientation relative to the field. Molecules that are at these places when the field switches may be lost from the decelerator as they are transferred into states that are not focussed. We calculate the probability of nonadiabatic transitions as a function of position in the periodic decelerator structure and find that for the decelerated group of molecules the loss is typically small, while for the un-decelerated group of molecules the loss can be very high. This loss can be eliminated using a bias field to ensure that the electric field magnitude is always large enough. We demonstrate our findings by comparing the results of experiments and simulations for the Stark deceleration of LiH and CaF molecules. We present a simple method for calculating the transition probabilities which can easily be applied to other molecules of interest.

Deceleration of molecules in a supersonic beam by the optical field in a low-finesse cavity

We study the dynamics of a supersonic molecular beam in a low-finesse optical cavity and demonstrate that most molecules in the beam can be decelerated to zero central velocity by the intracavity optical field in a process analogous to electrostatic Stark deceleration. We show that the rapid switching of the optical field for slowing the molecules is automatically generated by the cavity-induced dynamics. We further show that $\sim1\%$ of the molecules can be optically trapped at a few millikelvin in the same cavity.

Loading Stark-decelerated molecules into electrostatic quadrupole traps

Beams of neutral polar molecules in a low-field seeking quantum state can be slowed down using a Stark decelerator, and can subsequently be loaded and confined in electrostatic quadrupole traps. The efficiency of the trap loading process is determined by the ability to couple the decelerated packet of molecules into the trap without loss of molecules and without heating. We discuss the inherent difficulties to obtain ideal trap loading, and describe and compare different trap loading strategies. A new “split-endcap” quadrupole trap design is presented that enables improved trap loading efficiencies. This is experimentally verified by comparing the trapping of OH radicals using the conventional and the new quadrupole trap designs.

State-to-state inelastic scattering of Stark-decelerated OH radicals with Ar atoms

The Stark deceleration method exploits the concepts of charged particle accelerator physics to produce molecular beams with a tunable velocity. These tamed molecular beams offer interesting perspectives for precise crossed beam scattering studies as a function of the collision energy. The method has advanced sufficiently to compete with state-of-the-art beam methods that are used for scattering studies throughout. This is demonstrated here for the scattering of OH radicals (X(2)Pi(3/2), J = 3/2, f) with Ar atoms, a benchmark system for the scattering of open-shell molecules with atoms. Parity-resolved integral state-to-state inelastic scattering cross sections are measured at collision energies between 80 and 800 cm(-1). The threshold behavior and collision energy dependence of 13 inelastic scattering channels is accurately determined. Excellent agreement is obtained with the cross sections predicted by close-coupling scattering calculations based on the most accurate ab initio OH + Ar potential energy surfaces to date.

Cold Molecules: Preparation, Applications, and Challenges

Research with cold molecules has developed rapidly in recent years. There is now a variety of established methods for cooling molecules into the millikelvin range. Nevertheless, a focal point of current research is directed toward finding new ways to bring the temperature of molecules even closer to absolute zero. Samples of cold molecules offer not only important applications for high-resolution spectroscopy, which benefit from the increased interaction time of slow molecules with electromagnetic radiation; they also promise access to an exotic regime of chemical reactivity, in which phenomena such as quantum tunneling and quantum resonances predominate. This review begins with an introduction to the methods by which cold molecules can be prepared, with special emphasis on Stark deceleration and traps. In addition to applications of cold molecules that have already been partially achieved, an important focus of the review concentrates on possible future applications, and both aspects are illustrated with selected examples.

Low-energy collisions ofNH3andND3with ultracold Rb atoms

We carry out quantum inelastic scattering calculations of collisions of Rb atoms with inverting ${\text{NH}}_{3}$ and ${\text{ND}}_{3}$ molecules in the energy range between 0 and $100\text{ }{\text{cm}}^{\ensuremath{-}1}$, which are important for experiments using velocity-controlled molecular beams to probe scattering resonances. We focus on molecules initially in the upper level of the ammonia inversion doublet for $j=1$, $k=1$, which is low-field seeking and can be controlled in a Stark decelerator. We calculate the integral elastic and state-to-state inelastic cross sections in the coupled-states approximation. We demonstrate the presence of both shape and Feshbach resonances in the elastic and inelastic cross sections at low collision energies and discuss their origin in terms of the bound states of the Rb-${\text{ND}}_{3}$ complex. We also consider elastic and inelastic cross sections in the ultracold regime, using close-coupling calculations, in order to assess the viability of sympathetic cooling of ${\text{ND}}_{3}$ by Rb. The inelastic cross section for relaxation to the lower level of the inversion doublet is smaller than expected for such a strongly coupled system but is still likely to be too large to allow sympathetic cooling for ${\text{ND}}_{3}$ in low-field-seeking states. However, there is a good prospect that sympathetic cooling will be possible for molecules in high-field-seeking states even when the collision partner is a magnetically trapped atom in a low-field-seeking state.

Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice

We propose a new scheme to realize a multistage optical Stark deceleration for a supersonic molecular beam using a time-varying red-detuned quasi-cw optical lattice with a length of up to 10 mm. We analyze the motion of the slowed molecules inside the optical decelerator, and study the dependences of the velocity of the slowed molecular packet on the synchronous phase angle and the number of the deceleration stages (i.e., the number of the optical-lattice cells) by using Monte-Carlo method. Our study shows that the proposed optical Stark decelerator cannot only efficiently slow a pulsed supersonic beam from 230 m/s to zero (standstill), but also obtain an ultracold molecular packet with a temperature of sub-mK due to bunching effect in the multistage optical Stark decelerator, which can be trapped in the optical lattice by rapidly turning off the modulation signal of the lattice. Also, we compare the decelerated results of our multistage optical Stark decelerator with a single-stage optical one, and find that our scheme cannot only obtain a colder molecular packet under the same molecular-beam parameters and deceleration conditions, but also be directly used to trap the slowed cold molecules after the deceleration, while don't need to use another molecular trap.

High-energy-resolution molecular beams for cold collision studies

Stark deceleration allows for precise control over the velocity of a pulsed molecular beam and, by the nature of its limited phase-space acceptance, reduces the energy width of the decelerated packet. We describe an alternate method of operating a Stark decelerator that further reduces the energy spread over the standard method of operation. In this alternate mode of operation, we aggressively decelerate the molecular packet using a high phase angle. This technique brings the molecular packet to the desired velocity before it reaches the end of the decelerator; the remaining stages are then used to longitudinally and transversely guide the packet to the detection/interaction region. The result of the initial aggressive slowing is a reduction in the phase-space acceptance of the decelerator and thus a narrowing of the velocity spread of the molecular packet. In addition to the narrower energy spread, this method also results in a velocity spread that is nearly independent of the final velocity. Using the alternate deceleration technique, the energy resolution of molecular collision measurements can be improved considerably.

Stark deceleration of lithium hydride molecules

We describe the production of cold, slow-moving LiH molecules. The molecules are produced in the ground state using laser ablation and supersonic expansion, and 68% of the population is transferred to the rotationally excited state using narrowband radiation at the rotational frequency of 444 GHz. The molecules are then decelerated from 420 to 53 m s−1 using a 100 stage Stark decelerator. We demonstrate and compare two different deceleration modes, one where every stage is used for deceleration, and another where every third stage decelerates and the intervening stages are used to focus the molecules more effectively. We compare our experimental data to the results of simulations and find good agreement. These simulations include the velocity dependence of the detection efficiency and the probability of transitions between the weak-field seeking and strong-field seeking quantum states. Together, the experimental and simulated data provide information about the spatial extent of the source of molecules. We consider the prospects for future trapping and sympathetic cooling experiments.

Operation of a Stark decelerator with optimum acceptance

With a Stark decelerator, beams of neutral polar molecules can be accelerated, guided at a constant velocity, or decelerated. The effectiveness of this process is determined by the six-dimensional (6D) volume in phase space from which molecules are accepted by the Stark decelerator. Couplings between the longitudinal and transverse motion of the molecules in the decelerator can reduce this acceptance. These couplings are nearly absent when the decelerator operates such that only every third electric-field stage is used for deceleration, while extra transverse focusing is provided by the intermediate stages. For many applications, the acceptance of a Stark decelerator in this so-called $s=3$ mode significantly exceeds that of a decelerator in the conventionally used $(s=1)$ mode. This has been experimentally verified by passing a beam of OH radicals through a $2.6\text{\ensuremath{-}}\mathrm{m}$-long Stark decelerator. The experiments are in quantitative agreement with the results of trajectory calculations, and can qualitatively be explained with a simple model for the 6D acceptance. These results imply that the 6D acceptance of a Stark decelerator in the $s=3$ mode of operation approaches the optimum value, i.e., the value that is obtained when any couplings are neglected.

Collision experiments with Stark-decelerated beams

The crossed molecular beam technique has been established as a mature and important experimental method for detailed studies of molecular interactions, and has contributed enormously to our present understanding of molecular reaction dynamics. The Stark deceleration technique yields unprecedented control over both the internal and external degrees of freedom of polar molecules in a molecular beam, offering new possibilities in scattering experiments. In particular, Stark-decelerated molecular beams allow detailed molecular scattering studies as a function of the collision energy, from low to high collision energies, and with a very high energy resolution. We discuss a variety of experimental geometries that exploit this new molecular beam technology for scattering experiments, ranging from crossed beam arrangements and molecular synchrotrons to surface scattering set-ups.

Sympathetic cooling by collisions with ultracold rare gas atoms, and recent progress in optical Stark deceleration

We propose a general scheme for sympathetic cooling of molecules to microK temperatures on a timescale of seconds. Experimental parameters have been estimated from theory, which indicate the viability of the scheme. This method, which is particularly suited to optical Stark deceleration, utilises ultracold, laser cooled metastable rare gas atoms quenched to their ground state as collision partners to co-trapped molecular species within a deep optical trap (150 mK). We also describe the measurement of the role of laser-induced molecular alignment on the dipole force in optical Stark deceleration and outline progress towards the realisation of chirped optical Stark deceleration for producing slow molecular beams with mK energy spreads.

Theoretical study of slowing supersonic CH3F molecular beams using electrostatic Stark decelerator

We have calculated the Stark effect of CH3F molecules in external electrical fields, the rotational population of supersonic CH3F molecules in different quantum states, and analyse the motion of weak-field-seeking CH3F molecules in a state | J = 1, KM = −1〉 inside the electrical field of a Stark decelerator by using a simple analytical model. Three-dimensional Monte Carlo simulation is performed to simulate the dynamical slowing process of molecules through the decelerator, and the results are compared with those obtained from the analytical model, including the phase stability, slowing efficiency as well as the translational temperature of the slowed molecular packet. Our study shows that with a modest dipole moment (∼1.85 Debye) and a relatively slight molecular weight (∼34.03), CH3F molecules in a state |J = 1, KM = −1〉 are a good candidate for slowing with electrostatic field. With high voltages of ±10 kV applied on the decelerator, molecules of 370 m/s can be brought to a standstill within 200 slowing stages.

Prospects for measuring the electric dipole moment of the electron using electrically trapped polar molecules

Heavy polar molecules can be used to measure the electric dipole moment of the electron, which is a sensitive probe of physics beyond the Standard Model. The value is determined by measuring the precession of the molecule's spin in a plane perpendicular to an applied electric field. The longer this precession evolves coherently, the higher the precision of the measurement. For molecules in a trap, this coherence time could be very long indeed. We evaluate the sensitivity of an experiment where neutral molecules are trapped electrically, and compare this to an equivalent measurement in a molecular beam. We consider the use of a Stark decelerator to load the trap from a supersonic source, and calculate the deceleration efficiency for YbF molecules in both strong-field seeking and weak-field seeking states. With a 1 s holding time in the trap, the statistical sensitivity could be ten times higher than it is in the beam experiment, and this could improve by a further factor of five if the trap can be loaded from a source of larger emittance. We study some effects due to field inhomogeneity in the trap and find that rotation of the electric field direction, leading to an inhomogeneous geometric phase shift, is the primary obstacle to a sensitive trap-based measurement.

Stark deceleration of OH radicals in low-field-seeking and high-field-seeking quantum states

The Stark deceleration of OH radicals in both low-field-seeking and high-field-seeking levels of the rovibronic $^{2}\ensuremath{\Pi}_{3∕2}$, $v=0$, $J=3∕2$ ground state is demonstrated using a single experimental setup. Applying alternating-gradient focusing, OH radicals in their low-field-seeking $^{2}\ensuremath{\Pi}_{3∕2}$, $v=0$, $J=3∕2$, $f$ state have been decelerated from $345\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}239\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}$, removing 50% of the kinetic energy using only 27 deceleration stages. The alternating-gradient decelerator allows one to independently control longitudinal and transverse manipulation of the molecules. Optimized high-voltage switching sequences for the alternating-gradient deceleration are applied, in order to adjust the dynamic focusing strength in every deceleration stage to the changing velocity over the deceleration process. In addition we have also decelerated OH radicals in their high-field-seeking $^{2}\ensuremath{\Pi}_{3∕2}$, $v=0$, $J=3∕2$, $e$ state from $355\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}316\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}$. For the states involved, a real crossing of hyperfine levels occurs at $640\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}$, which is examined by varying a bias voltage applied to the electrodes.