Optimizing the density of Stark decelerated radicals at low final velocities: a tutorial review
© Haas et al.; licensee Springer. 2017
Received: 7 July 2017
Accepted: 13 September 2017
Published: 25 September 2017
The Stark deceleration technique can produce molecular beams with very low velocities. In order to maximize the density of decelerated molecules, experimental parameters such as the velocity, the velocity spread and the spatial spread of the initial molecular beam as well as the operation characteristics of the decelerator have to be chosen appropriately. In this tutorial review, we describe procedures for the optimization of the density of Stark decelerated radicals for low-velocity applications which are of interest in, e.g., molecule trapping and cold-collision studies.
KeywordsCold molecules Molecular beams Stark deceleration Radicals
Translationally cold molecules have become an attractive subject of research in recent years. A number of techniques for the generation of cold molecules has been developed [1–5] among which Stark deceleration is one of the most important [3, 6–8]. This method finds a broad range of applications in spectroscopy [9–12], collision-dynamics studies [13–26] and trap loading experiments [27–33]. The principle of Stark deceleration has been well documented [2, 3], and a number of operation schemes have been developed for the optimization of Stark-decelerated molecular beams in different types of experiments [34–37].
A Stark decelerator employs time-varying inhomogeneous electric fields produced by an array of dipolar electrodes to slow down pulsed beams of polar molecules [3, 6]. When a packet of molecules approaches a set of electrodes, they are switched to high electric potential. Molecules in low-field-seeking Stark states experience a force which reduces their kinetic energy. The voltages on the electrodes are switched off before the molecules reach the maximum of the dipole potential in order to prevent their re-acceleration after they have passed the electrodes. This procedure is repeated at every pair of electrodes along the decelerator until the molecules have reached their target velocity at the exit of the assembly.
The final velocity of the packet of molecules is controlled by a parameter referred to as phase angle Φ 0 which corresponds to a scaled position of a “synchronous molecule” at which the high voltages on the electrodes of the decelerator are switched. Successful deceleration of the molecules to the target velocity requires careful coupling of the molecular cloud into a stable phase-space volume determined by the phase angle [34, 36, 38]. Successful coupling requires prior knowledge of the initial velocity of the molecular package and the incoupling time, i.e., the time required for the molecules to fly from their point of generation to the entrance of the Stark decelerator. Efficient coupling will lead to an optimized beam density after Stark deceleration .
In this tutorial paper, we give a comprehensive introduction on how to optimize an experiment to achieve a maximum density of Stark decelerated radicals at low velocities. Such optimizations are of particular interest for trapping experiments [27, 28, 30, 33] and low-energy scattering [39, 40] applications. As an example, we focus on the generation of beams of OH (hydroxyl) radicals widely used in Stark deceleration experiments [27, 33]. The present paper is organized as follows. We start by introducing our source for the generation of high-density molecular beams of radicals and discuss relevant parameters of this source. We then discuss procedures for optimizing the number densities of molecules after Stark deceleration and how to to improve the signal-to-noise ratio of the experiment.
A Stark deceleration experiment is preceded by the formation of a molecular beam of vibrationally and rotationally cold polar molecules. The number density of molecules exiting the Stark decelerator critically depends on the initial phase-space distribution and evolution of the expanding gas pulse. In turn, these properties strongly depend on the properties of the gas nozzle used and its operation conditions. A wide variety of valves exists. In another tutorial article of the present series, Vogels et al.  have reviewed the suitability of different beam sources for Stark deceleration in the context of collision experiments.
The pinhole discharge is based on the design of Lewandoski et al. . OH radicals are formed by dissociation in a plasma generated from H2O seeded in a noble gas. Depending on the choice of noble gas, molecular beams in different velocity regimes can be produced. For our Stark decelerator, Kr and Xe yield beams of sufficiently low initial velocity enabling the generation of high-density OH beams at low final velocities.
The discharge strikes through the expanding gas cloud in between two electrodes. Maximum efficiency for OH generation was found when applying a negative voltage to the outer electrode while keeping the inner electrode grounded, such that the current of electrons flows against the direction of the expansion. Typical discharge potentials amount to −900 V with a duration of around 30 μs. The velocity of the thus generated molecular beam of radicals was found to depend on the time delay between opening the valve and striking the discharge. We attribute this observation to changes in the gas dynamics by generating the plasma in different regions of the gas pulse. By changing this delay, the beam velocity can be fine-tuned on the level of a few percent, which is useful to optimize the coupling efficiency into the Stark decelerator (see “Velocity spread and spatial spread of the radical beam” section below for a more detailed discussion).
Characteristics of the molecular beam of OH radicals generated by discharging H2O in different carrier gases
Ground state population
670.5 ± 6.3
9.8 ± 0.5
3.0 ± 0.6
483.5 ± 5.0
13.1 ± 0.6
2.9 ± 0.6
385.1 ± 4.0
9.2 ± 0.8
0.9 ± 0.2
In this section, we give a detailed account on optimization procedures for the generation of cold and dense radical beams using a Stark decelerator. The goal is to optimize the number of radicals decelerated to velocities below 50 m/s. We categorize our optimization procedure into two classes. Class I optimization comprises all the parameters resulting in an increased number density of the decelerated radical package which is important for utilizing the Stark deceleration technique for further applications. This includes optimizing the radical source as well as the operation of the Stark decelerator. Class II optimization seeks to increase the signal-to-noise ratio of the experiment and thus improve the duty cycle.
Optimizing the radical source for Stark deceleration
As Stark decelerators rely on conservative forces, the phase-space volume of the molecule packets cannot be compressed and the decelerator can only preserve the phase-space density of the initial molecular beam. This underlines the necessity to optimize conditions at the source as much as possible to maximize the number density of molecules decelerated to the target velocity. The first step in class I optimization is to optimize the radical source. There are several parameters relating to the initial molecular beam which are relevant for Stark deceleration experiments, primarily its mean velocity v, its velocity spread Δ v (expressed as the full-width-at-half-maximum (FWHM) of the velocity distribution), its longitudinal spatial spread Δ x and its initial radical density n after exiting the valve. These parameters are strongly correlated with each other. It is often difficult or even impossible to tune only one parameter without changing one or all of the others. This imposes challenges to experimentalists, and compromises have to be made to maximize the beam density after deceleration.
Velocity of the radical beam
Generally, higher initial beam velocities demand for higher phase angles Φ 0 when targeting a specific final velocity after Stark deceleration [3, 7]. In turn, high phase angles result in a reduced phase-space acceptance of the decelerator leading to reduced number densities at the exit of the decelerator . It is thus advantageous to start with a molecular beam which is as slow as possible. In our experiment, mean velocities were measured by correlating different longitudinal valve positions to maxima in the corresponding time-of-flight (TOF) profiles of the OH radicals.
The velocity of a radical beam can be coarse-tuned by using different carrier gases. In a previous study , we showed that OH beam velocities around 670 m/s, 485 m/s and 385 m/s can be obtained with Ar, Kr and Xe as carrier gases in our discharge source. Note that the carrier gas also influences the properties and plasma chemistry of the discharge and therefore the density of radicals produced. Ar and Kr beams resulted in similar OH densities, but with Xe the radical density was found to be a factor of 2 to 3 lower (see Table 1). Furthermore, by tuning the delay between striking the discharge relative to opening the valve, the velocity of the radical beam can be fine-tuned at the cost of decreasing the beam density  (see also Fig. 5 below).
The velocity of the molecular beam in a Stark deceleration experiment should be chosen according to the specifications of the Stark decelerator. The decelerator in our experiment consists of 124 stages composed of pairs of rods of 3 mm diameter separated by 5 mm (center-to-center distance). The distance between two adjacent stages is 5.5 mm. The typical operating voltage applied to the deceleration stages amounts to ±10 kV. This configuration provides a maximum deceleration energy of 1.4 cm −1 per stage for OH molecules. Given this number, the maximum initial velocity of OH molecules is limited to ≃500 m/s if a target velocity of 35 m/s is to be reached. This restriction excludes the use of Ar as carrier gas in our case.
As already discussed in Ref. , using Kr as carrier gas yields an initial OH beam density a factor 2 to 3 lager than with Xe. The higher initial density for OH in Kr compared to Xe can be seen by comparing the TOF profiles obtained in guiding mode (i.e., Φ 0=0°) displayed as insets in Fig. 3. As Xe carrier gas produces a lower initial OH beam velocity, the same target velocities as with Kr can be achieved with smaller phase angles. The lower phase angles compensate the initially lower density of OH in a Xe beam so that the radical densities achieved after deceleration are similar to those achieved with Kr. Hence, employing Kr or Xe makes no significant difference in terms of optimizing the radical density at low velocities. One notices that our initial OH beam velocities are higher than one would expect, e.g., from the results of Ref. . This is attributed to different gas dynamics in the valve caused by the discharge and the fact that the valve warms up to about 40°C during operation.
Velocity spread and spatial spread of the radical beam
As can be seen in Fig. 4 a, the spatial spread of the initial beam determines the number of adjacent stable phase-space volumes (defined by the periodicity of the Stark decelerator) into which the molecule cloud will couple. The coupling into several phase-space volumes results in side peaks around the central peak in the TOF profiles, as observed in the first column. Those side peaks have different velocities compared to the main peak. As the spatial spread increases from 10 mm to 30 mm, the intensity ratio of the main peak and the side peak decreases, and more side peaks appear . This effect can be observed when the simulations are running in both guiding and decelerating mode. A large spatial spread is not necessarily detrimental to the deceleration experiments, depending on the intended application. For example, in spectroscopic measurements and trap loading experiments the side peaks will not cause problems as often one of the peaks can be selected. On the other hand, in collision experiments each of the transported molecule packets may contribute to the collision process, which complicates the interpretation of the results. It has to be noticed that at low final velocities, the intensity of the side peaks is not increasing symmetrically when increasing the spatial spread. The peaks pertaining to higher velocities increase in intensity more markedly than those at low velocities, because molecules with lower velocities are stopped and reversed in the decelerator.
Conversely, the effect of velocity spread is shown in Fig. 4 b. An increasing velocity spread will not only change the ratio between the main peak and the side peaks, but also significantly decreases the total number density of molecules transported through the decelerator. In general, in a deceleration experiment the molecular beam will fly freely over a certain distance before it is coupled into the Stark decelerator. In our experiment, the distance between the valve and the decelerator across two vacuum chambers separated by a skimmer amounts to a total of 232 mm. After this free flight, the finite velocity spread has effectively enlarged the spatial spread thus diluting the beam before entering the decelerator.
Optimized operation of the Stark decelerator for low-velocity applications
The optimal operation of a Stark decelerator depends on its application and different schemes have been proposed [34–37, 46]. In a typical Stark deceleration experiment, a high voltage (HV) pulse sequence to be applied to the electrodes is devised according to a chosen “synchronous velocity v s ” and the target velocity after deceleration. This synchronous velocity v s is chosen from the velocity distribution of the molecular beam (not necessarily but often corresponds to the maximum of the beam profile). When a package of molecules with the synchronous velocity v s arrives at the entrance of the Stark decelerator, the calculated HV pulse sequence is applied. Part of the molecular package within the stable phase-space volume of the decelerator is slowed down to the final velocity. It is critical that the high voltage pulse sequence is applied to the Stark decelerator at the exact time when the molecule package arrives at the Stark decelerator to maximize the incoupling efficiency. The precise determination of the incoupling time t incoupling , i.e., the time delay between the generation of the pulsed beam and the coupling into the Stark decelerator, is thus crucial to a successful deceleration experiment.
A detailed protocol to determine the incoupling time has been given by Vogels et al. . In our experiments, we first determine the mean velocity and the velocity spread of the OH beam as described in “Velocity of the radical beam” and “Velocity spread and spatial spread of the radical beam” sections. The incoupling time can be estimated by the relation t incoupling = L/v s , where L is the distance between the valve and the Stark decelerator, and v s is a chosen synchronous velocity which, in this case, is identical to the mean velocity of the molecular beam. Subsequently, we operate the Stark decelerator in guiding mode, i.e., with phase angle Φ 0 = 0°. The incoupling time is fine-tuned until a symmetric TOF profile as shown in Fig. 3 is achieved. t incoupling can further be tuned by optimizing the slow-molecule yield at running the Stark decelerator at higher phase angle, i.e., low final velocity. In our experiment, we chose a final velocity at around 35 m/s to determine t incoupling . The TOF profile in guiding mode and the TOF profile at low final velocity are then compared with simulations. Once the experimental TOF profiles are well reproduced by the simulations, t incoupling is fixed.
In our case, the distance L det between the exit of the Stark decelerator and the detection point amounts to 11.5 mm. An uncertainty Δ L det in L det of 1 mm will give an uncertainty of 2 μs in the TOF for a velocity of 470 m/s and 28 μs for a velocity of 35 m/s, respectively. The measurement uncertainty for L det is less than 1 mm. Thus, as a rule of thumb, we assume that the discrepancy between experimental and simulated TOF traces should be smaller than 2 μs for the guiding profile and 20 μs for low final velocity profile.
Once t incoupling is set, the density of decelerated molecules can further be optimized by selecting different synchronous velocities v s from the velocity distribution of the molecular beam. In general, v s does not have to be the same as the mean velocity v mean of the beam. Under the premise of keeping the final velocity fixed, choosing a lower synchronous velocity v s allows to operate the decelerator at lower phase angles. This results in a larger addressable phase-space volume for deceleration and leads to an improved deceleration efficiency.
If, however, v s deviates too much from v mean , then the density of the molecule package coupled into the Stark decelerator will decrease substantially from the maximum value as sparser sections of the gas pulse are sampled. This suggests that there is an optimal value of v s for an optimal operation of the experiment.
To illustrate this point, we selected various initial velocities within the velocity profile as synchronous velocities v s and decelerated the molecules down to 35 m/s. In this experiment, the OH molecules were seeded in Kr yielding a beam of mean velocity v mean = 470 m/s and a velocity spread (FWHM) of about 20%.
Figure 6 b shows the combined effect of the initial package density and phase angle on the density of decelerated molecules by choosing different v s values. In the experiment, we decelerate OH molecules down to the same final velocity (35 m/s) from different initial velocity components of the beam. As v s decreases relative to v mean , the density of the decelerated OH beam increases due to the larger phase-space acceptance provided by the lower initial velocity. The density of the decelerated radicals reaches a maximum at v s = 450 m/s. A further decrease of v s also decreases the density of decelerated OH molecules as the gain achieved by using smaller phase angles is not able to compensate the loss in initial beam density. The simulations (lower traces in Fig. 6 b) nicely reproduce the trends we observe in the experiments. Thus, by optimizing the synchronous velocity v s , the density of decelerated OH radicals could be increased by a factor of 2 consistent with previous observations .
Finally, the voltage applied to the Stark decelerator is another parameter which can be tuned to optimize the operation of a Stark decelerator. A typical voltage applied on our Stark decelerator is ±10 kV. Keeping the operation phase angle, higher applied voltage will result in larger phase-space acceptance which increases the number of decelerated molecules. This is true for high final velocities. But for low-velocity applications, especially when the final velocity after deceleration is below 50 m/s, molecules with lower velocities will be stopped and reflected in the Stark decelerator , which causes loss. This is also observed in our experiment. On that note, we always operate our Stark decelerator at ±10 kV.
Optimizing the detection efficiency
For sensitive LIF detection, reducing stray light and increasing the collection efficiency of the fluorescence are essential. In our experiment, molecules are pumped to the first electronically excited state by using transitions in the A 2 Σ +(v=1)←X 2 Π(v=0) band around 282 nm, while fluorescence is collected on X 2 Π(v=1)←A 2 Σ +(v=1) transitions around 313 nm. The emitted off-resonant fluorescence occurs at longer wavelengths and can thus be separated from the excitation wavelength by bandpass optical filters. However, besides stray light at the excitation wavelength also spurious fluorescence originating from the Brewster windows, light baffles or other components in the setup can occur at a similar wavelength as the LIF due to inelastic photon scattering. Therefore, it is advisable to create a transmission window as narrow as possible around the wavelength at which the targeted LIF occurs. To that end, two narrow band pass filters (XHQA313, Asahi Filter and FF01-315/15-25, Semrock) are used in our experiment. At 313 nm, this filter combination provides a transmission of up to 50% centered in a transmission window of 10 nm.
In this tutorial paper, we have discussed the optimization of relevant experimental parameters in order to maximize the beam density of Stark-decelerated radicals for low-velocity applications. Crucial parameters are the carrier gas, the discharge conditions in the radical source, the velocity, velocity spread and spatial spread of the initial molecular beam, the synchronous velocity chosen for coupling the beam into the decelerator and the voltages applied to the Stark decelerator.
Differences between using Kr and Xe as carrier gases in which OH radicals are seeded have been compared. Higher OH densities are initially achieved using Kr, but the Stark decelerator has to be operated at a higher phase angle and therefore lower stable phase-space volume in comparison to Xe. Thus, the radical densities achieved after deceleration proved similar.
The effect of velocity spread and spatial spread of the beam on the final number densities have been discussed. An optimized operation scheme has been found by fixing the discharge delay to the maximum density of the beam profile, thereby minimizing the velocity spread.
The synchronous velocity for operating a Stark decelerator can be tuned within the beam’s velocity profile. By appropriately choosing the synchronous velocity, the number density of the decelerated OH beam can be increased compared to fixing it at the mean velocity of the initial beam. However, there is a trade-off between decreasing the synchronous velocity (and thus increasing the phase-space acceptance of the decelerator) and the loss of beam density by deviating too far from the mean velocity of the beam.
By a careful optimization of the parameters discussed, we were able to achieve OH densities n=(2.3±1.2)×109 cm −3 at a velocity of v=28 m/s, as determined by a calibrated LIF measurement.
In the present paper, we focused on the generation of radicals with final velocities around 30 m/s suitable for trap loading. For even lower target velocities, it has been proven to be advantageous to couple a conventional Stark decelerator (as employed here) with a ring Stark decelerator  which yields an improved deceleration performance for very slow molecules. Such a scheme has been demonstrated in Ref. .
1 We note that these values slightly deviate from the results given in Table 1. The characteristics of the beam slowly vary over time as wear parts such as the spring of the valve and the discharge electrodes age. The experiment thus has to be periodically re-optimized to adapt to changing beam characteristics.
We acknowledge financial support from the Swiss National Science Foundation, grant nr. 200021_156182 and the University of Basel. We thank Claudio von Planta for his contribution in the experiment and in the discussions of the content of the manuscript. We thank D. Wild, Ph. Knöpfel, G. Martin, and N. Janssen for technical support. We also thank Professor S.Y.T. van de Meerakker (Radboud University) for helpful discussions.
DH, SBS and DZ performed the experiments and the simulations and analyzed the data. SW supervised the project. DDZ, DH and SW wrote the manuscript. All authors took part in discussions on the analyses of the data and the content of the manuscript. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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