Stark Deceleration Research Articles

Efficient transfer of population between rotational levels in deuterated ammonia using THz transitions

We demonstrate the efficient transfer of population between rotational levels of ND 3 using a commercially available table-top THz source. We use a Stark decelerator to prepare a packet of para- ND 3 molecules in the 1 1 − upper inversion component of the rotational ground state, and induce the 2 1 + ← 1 1 − electric dipole allowed transition both in the presence of an electric field and under field free conditions. Using THz chirps to address all hyperfine components, transfer efficiencies up to 87% are reached, limited by the power of the THz source. Population transfer from the 1 1 − to the 2 1 − level is demonstrated either by driving directly the 2 1 − ← 1 1 − transition in a field, or by a 1 1 − → 1 1 + → 2 1 − double-resonance excitation scheme. In addition, we present a novel method to produce packets of ND 3 ( 1 1 − ) with pure M J = 0 or | M J | = 1 character using the Stark decelerator, and a method to probe the M J composition of a packet of molecules using THz excitation.

Electrostatic trapping vibrationally excited Rydberg NO molecules

Nitric oxide (NO) molecules travelling in pulsed supersonic beams have been laser photoexcited to long-lived Rydberg states in series converging to the lowest lying, , and first excited, , vibrational states in the ground electronic state of NO. After excitation, the molecules were decelerated in the travelling electric traps of a chip-based Rydberg–Stark decelerator. Deceleration to rest in the laboratory-fixed frame of reference allowed subsequent electrostatic trapping before in situ detection by pulsed electric field ionisation. The decay rates of the molecules from the traps were measured for states with principal quantum numbers between 32 and 48. Comparison of the corresponding trap decay time constants, ranging from 245 to s for states with , with those recorded for molecules in states with , allowed bounds to be placed on the vibrational autoionisation rates of the ℓ-mixed Stark states prepared in the experiments of Hz.

Efficient transfer of inversion doublet populations in deuterated ammonia using adiabatic rapid passage

We demonstrate the efficient transfer of population from the upper to the lower inversion level within the rotational ground state of para-ND. A packet of ND molecules is velocity controlled and state selected using a Stark decelerator, and subsequently transferred with efficiency using the principles of adiabatic rapid passage. Transitions are induced using microwave chirps both under zero-field conditions as well as in the presence of an electric field to probe -resolved transition efficiencies. Simulations of the transfer efficiencies based on the von Neumann equation, taking all hyperfine transitions into account, showed excellent agreement with experimental observations.

Correlated rotational excitations in NO-CO inelastic collisions.

We present a joint experimental and theoretical study of rotationally inelastic collisions between NO (X2Π1/2, ν = 0, j = 1/2, f) radicals and CO (X1Σ+, ν = 0, j = 0) molecules at a collision energy of 220 cm-1. State-to-state scattering images for excitation of NO radicals into various final states were measured with high resolution by combining the Stark deceleration and velocity map imaging techniques. The high image resolution afforded the observation of correlated rotational excitations of NO-CO pairs, which revealed a number of striking scattering phenomena. The so-called "parity-pair" transitions in NO are found to have similar differential cross sections, independent of the concurrent excitation of CO, extending this well-known effect for collisions between NO and rare gas atoms into the realm of bimolecular collisions. Forward scattering is found for collisions that induce a large amount of rotational energy transfer (in either NO, CO, or both), which require low impact parameters to induce sufficient energy transfer. This observation is interpreted in terms of the recently discovered hard collision glory scattering mechanism, which predicts the forward bending of initially backward receding trajectories if the energy uptake in the collision is substantial in relation to the collision energy. The experimental results are in good agreement with the predictions from coupled-channels quantum scattering calculations based on an ab initio NO-CO potential energy surface.

Formation of high-density cold molecules via electromagnetic trap

Preparation and control of cold molecules are advancing rapidly, motivated by many exciting applications ranging from tests of fundamental physics to quantum information processing. Here, we propose a trapping scheme to create high-density cold molecular samples by using a combination of electric and magnetic fields. In our theoretical analysis and numerical calculations, a typical alkaline-earth monofluoride, MgF, is used to test the feasibility of our proposal. A cold MgF molecular beam is first produced via an electrostatic Stark decelerator and then loaded into the proposed electromagnetic trap, which is composed of an anti-Helmholtz coil, an octupole, and two disk electrodes. Following that, a huge magnetic force is applied to the molecular sample at an appropriate time, which enables further compressing of the spatial distribution of the cold sample. Molecular samples with both higher number density and smaller volume are quite suitable for the laser confinement and other molecular experiments such as cold collisions in the next step.

Multipole-moment effects in ion-molecule reactions at low temperatures: part II - charge-quadrupole-interaction-induced suppression of the He+ + N2 reaction at collision energies below kB·10 K.

We report on an experimental and theoretical investigation of the He+ + N2 reaction at collision energies in the range between 0 and kB·10 K. The reaction is studied within the orbit of a highly excited Rydberg electron after merging a beam of He Rydberg atoms (He(n), n is the principal quantum number), with a supersonic beam of ground-state N2 molecules using a surface-electrode Rydberg–Stark decelerator and deflector. The collision energy Ecoll is varied by changing the velocity of the He(n) atoms for a fixed velocity of the N2 beam and the relative yields of the ionic reaction products N+ and N2+ are monitored in a time-of-flight mass spectrometer. We observe a reduction of the total reaction-product yield of ∼30% as Ecoll is reduced from ≈kB·10 K to zero. An adiabatic capture model is used to calculate the rotational-state-dependent interaction potentials experienced by the N2 molecules in the electric field of the He+ ion and the corresponding collision-energy-dependent capture rate coefficients. The total collision-energy-dependent capture rate coefficient is then determined by summing over the contributions of the N2 rotational states populated at the 7.0 K rotational temperature of the supersonic beam. The measured and calculated rate coefficients are in good agreement, which enables us to attribute the observed reduction of the reaction rate at low collision energies to the negative quadrupole moment, Qzz, of the N2 molecules. The effect of the sign of the quadrupole moment is illustrated by calculations of the rotational-state-dependent capture rate coefficients for ion–molecule reactions involving N2 (negative Qzz value) and H2 (positive Qzz value) for |J, M〉 rotational states with J ≤ 5 (M is the quantum number associated with the projection of the rotational angular momentum vector J⃑ on the collision axis). With decreasing value of |M|, J⃑ gradually aligns perpendicularly to the collision axis, leading to increasingly repulsive (attractive) interaction potentials for diatomic molecules with positive (negative) Qzz values and to reaction rate coefficients that decrease (increase) with decreasing collision energies.

An Alternative Operation Scheme to Improve the Efficiency of a Stark DeceleratorSupported by the National Key R&D Program of China (Grant No. 2019YFA0307701), the Science Challenge Project (Grant No. TZ2018005), and Jilin University.

A Stark decelerator can slow down polar molecules to very low velocities. When the velocities are very low, the number of cold molecules obtained is very small. In order to obtain a higher quantity of cold molecules, inspired by the work of Reens et al. [Phys. Rev. Res. 2 (2020) 033 095], we propose an alternative method of operating a Stark decelerator. Through the trajectory simulation of OH molecules in the decelerator, we find that the number of cold molecules can be greatly increased by one order of magnitude at both low and high final velocities on a Stark decelerator consisting of around 150 electrodes. This development is due to the improved longitudinal and the transverse focusing property provided by the new switching schemes and the high-voltage configurations on the decelerator unit.

Deceleration and Trapping of SrF Molecules.

We report on the electrostatic trapping of neutral SrF molecules. The molecules are captured from a cryogenic buffer-gas beam source into the moving traps of a 4.5-m-long traveling-wave Stark decelerator. The SrF molecules in X^{2}Σ^{+}(v=0,N=1) state are brought to rest as the velocity of the moving traps is gradually reduced from 190 m/s to zero. The molecules are held for up to 50ms in multiple electric traps of the decelerator. The trapped packets have a volume (FWHM) of 1 mm^{3} and a velocity spread of 5(1) m/s, which corresponds to a temperature of 60(20)mK. Our result demonstrates a factor 3 increase in the molecular mass that has been Stark decelerated and trapped. Heavy molecules (mass>100 amu) offer a highly increased sensitivity to probe physics beyond the standard model. This work significantly extends the species of neutral molecules of which slow beams can be created for collision studies, precision measurement, and trapping experiments.

Velocity-tunable beam of continuously decelerated polar molecules for cold ion-molecule reaction studies.

Producing high densities of molecules is a fundamental challenge for low-temperature, ion-molecule reaction studies. Traveling-wave Stark decelerators promise to deliver high density beams of cold, polar molecules but require non-trivial control of high-voltage potentials. We have overcome this experimental challenge and demonstrate continuous deceleration of ND3 from 385 to 10m/s, while driving the decelerator electrodes with a 10 kV amplitude sinewave. In addition, we test an alternative slowing scheme, which increases the time delay between decelerated packets of ND3 and non-decelerated molecules, allowing for better energy resolution of subsequent reaction studies. We characterize this source of neutral, polar molecules suitable for energy-resolved reaction studies with trapped ions at cold translational temperatures. We also propose a combined apparatus consisting of the traveling-wave decelerator and a linear ion trap with a time-of-flight mass spectrometer and discuss to what extent it may achieve cold, energy-resolved, ion-neutral reactions.

Detection and manipulation of the transverse motion of neutral molecules in a Stark decelerator

By enabling precise control over longitudinal velocity of neutral molecules, Stark deceleration has become an important tool for studying cold molecular collisions. However, the information about transverse motion is often hard to extract and to some extent beyond control. Here we demonstrate a new experimental approach that allows us to observe the transverse phase-space distribution of molecules within a Stark decelerator. The transverse dynamics can be tracked along the decelerator, which can be used to measure the initial transverse phase-space distribution of the molecules. The observed frequency of the transverse oscillations agrees well with the one determined from electric field distribution. Thermalization of the molecules at the decelerator entrance must be accounted for in our Monte Carlo simulations of the molecules dynamics to reach agreement with experimental data. We introduce two approaches of manipulating transverse modes. In the first method, a free-flight pulse is introduced to achieve a short phase-space stretching, an equivalent technique to delta kick cooling [Phys. Rev. Lett. 78, 2088 (1997)]. In the second mode we enforce phase-space rotation by varying the applied voltage. Both modes allow us to manipulate the transverse phase-space distribution and, in particular, allow us to tune (in a well-controlled way) the anisotropy of the phase-space distribution.

A supersonic laser ablation beam source with narrow velocity spreads.

A supersonic beam source for SrF and BaF molecules is constructed by combining the expansion of carrier gas (a mixture of 2% SF6 and 98% argon) from an Even-Lavie valve with laser ablation of a barium/strontium metal target at a repetition rate of 10 Hz. Molecular beams with a narrow translational velocity spread are produced at relative values of Δv/v = 0.053(11) and 0.054(9) for SrF and BaF, respectively. The relative velocity spread of the beams produced in our source is lower in comparison with the results from other metal fluoride beams produced in supersonic laser ablation sources. The rotational temperature of BaF is measured to be 3.5 K. The source produces 6 × 108 and 107 molecules per steradian per pulse in the X2Σ+ (ν = 0, N = 1) state of BaF and SrF molecules, respectively, a state amenable to Stark deceleration and laser cooling.

Quantum-state-dependent decay rates of electrostatically trapped Rydberg NO molecules.

Nitric oxide (NO) molecules travelling in pulsed supersonic beams have been prepared in long-lived Rydberg–Stark states by resonance-enhanced two-colour two-photon excitation from the X 2Π1/2 (v′′ = 0, J′′ = 3/2) ground state, through the A 2Σ+ (v′ = 0, N′ = 0, J′ = 1/2) intermediate state. These excited molecules were decelerated from 795 ms−1 to rest in the laboratory-fixed frame of reference, in the travelling electric traps of a transmission-line Rydberg–Stark decelerator. The decelerator was operated at 30 K to minimise effects of blackbody radiation on the molecules during deceleration and trapping. The molecules were electrostatically trapped for times of up to 1 ms, and detected in situ by pulsed electric field ionisation. Measurements of the rate of decay from the trap were performed for states with principal quantum numbers between n = 32 and 50, in Rydberg series converging to the N+= 0, 1, and 2 rotational states of NO+. For the range of Rydberg states studied, the measured decay times of between 200 μs and 400 μs were generally observed to reduce as the value of n was increased. For some particular values of n deviations from this trend were seen. These observations are interpreted, with the aid of numerical calculations, to arise as a result of contributions to the decay rates, on the order of 1 kHz, from rotational and vibrational channel interactions. These results shed new light on the role of weak intramolecular interactions on the slow decay of long-lived Rydberg states in NO.

Experimental and theoretical investigation of resonances in low-energy NO-H2 collisions.

The experimental characterization of scattering resonances in low energy collisions has proven to be a stringent test for quantum chemistry calculations. Previous measurements on the NO-H2 system at energies down to 10 cm-1 challenged the most sophisticated calculations of potential energy surfaces available. In this report, we continue these investigations by measuring the scattering behavior of the NO-H2 system in the previously unexplored 0.4 cm-1-10 cm-1 region for the parity changing de-excitation channel of NO. We study state-specific inelastic collisions with both para- and ortho-H2 in a crossed molecular beam experiment involving Stark deceleration and velocity map imaging. We are able to resolve resonance features in the measured integral and differential cross sections. Results are compared to predictions from two previously available potential energy surfaces, and we are able to clearly discriminate between the two potentials. We furthermore identify the partial wave contributions to these resonances and investigate the nature of the differences between collisions with para- and ortho-H2. Additionally, we tune the energy spreads in the experiment to our advantage to probe scattering behavior at energies beyond our mean experimental limit.

A superconducting Fabry–Perot cavity for trapping cold molecules

A superconducting Fabry–Perot microwave cavity for a molecular trap was designed, constructed and characterized. The cavity was designed to create intense microwave fields that are sufficient to trap cold polar molecules by the AC Stark force. By coating the mirror surfaces with a superconducting material, an unloaded quality factor of up to 1.1 × 106 at 24.087 GHz was achieved at a temperature of 2.24 K. The field strength of 1.06 MV m−1 obtained for a TEM02 transverse mode with an input power of 10 W is sufficiently intense to trap ammonia molecules at a temperature of 85 mK, which is achievable by a conventional Stark molecular decelerator. We have also implemented an ion optics assembly for sensitive detection of molecules inside the microwave cavity by resonance enhanced multi-photon ionization.

A velocity map imaging apparatus optimised for high-resolution crossed molecular beam experiments

We present the design of a Velocity Map Imaging apparatus tailored to the demands of high-resolution crossed molecular beam experiments employing Stark or Zeeman decelerators. The key requirements for these experiments consist of the combination of a high-relative velocity resolution for large ionisation volumes and a broad range of relatively low lab-frame velocities. The SIMION software package was employed to systematically optimise the electrode geometries and electrical configuration. The final design consists of a stack of 16 tubular electrodes, electrically connected with resistors, which is divided into three electric field regions. The resulting apparatus allows for an inherent velocity blurring of less than for NO ions originating from a ionisation volume, which is negligible in a typical crossed beam experiment. The design was recently employed in several state of the art crossed-beam experiments, allowing the observation of fine details in the velocity distributions of the scattered molecules.

Rydberg–Stark deceleration and trapping of helium in magnetic fields

Triplet (S = 1) He Rydberg atoms in supersonic beams with an initial velocity of 350 m s−1 have been decelerated to zero velocity and loaded into an off-axis electric trap in the presence and absence of magnetic fields. Comparing the deceleration efficiencies and the radiative decay of the population of trapped He Rydberg atoms to the (1s)1(2s)1 3S1 metastable level in the two sets of deceleration and trapping experiments revealed that the effects of magnetic fields up to 30 mT are negligible provided that a background dc electric field is maintained in the decelerator. A magnetic quadrupole trap of 30 mT depth corresponds to a He temperature of about 40 mK. The results thus represent an important step towards achieving high densities of cold paramagnetic samples following successive cycles of Rydberg–Stark deceleration, trapping, and radiative decay in overlaid electric and magnetic traps.

Correlations in rotational energy transfer for NO-D2 inelastic collisions.

We present a combined experimental and theoretical study of state-to-state inelastic collisions between NO (X 2Π1/2, j = 1/2, f) radicals and D2 (j = 0, 1, 2, 3) molecules at collision energies of 100 cm-1 and 750 cm-1. Using the combination of Stark deceleration and velocity map imaging, we fully resolve pair-correlated excitations in the scattered molecules. Both spin-orbit conserving and spin-orbit changing transitions in the NO radical are measured, while the coincident rotational excitation (j = 0 → j = 2) and rotational de-excitation (j = 2 → j = 0 and j = 3 → j = 1) in D2 are observed. De-excitation of D2 shows a strong dependence on the spin-orbit excitation of NO. We observe translation-to-rotation energy transfer as well as direct rotation-to-rotation energy transfer at the lowest collision energy probed. The experimental results are in good agreement with cross sections obtained from quantum coupled-channels calculations based on recent NO-D2 potential energy surfaces. The observed trends in the correlated scattering cross sections are understood in terms of the NO-D2 quadrupole-quadrupole interaction.

Beyond the limits of conventional Stark deceleration

Stark deceleration enables the production of cold and dense molecular beams with applications in trapping, collisional studies, and precision measurement. Improving the efficiency of Stark deceleration, and hence the achievable molecular densities, is central to unlock the full potential of such studies. One of the chief limitations arises from the transverse focusing properties of Stark decelerators. We introduce a new operation strategy that circumvents this limit without any hardware modifications, and experimentally verify our results for hydroxyl radicals. Notably, improved focusing results in significant gains in molecule yield with increased operating voltage, formerly limited by transverse-longitudinal coupling. At final velocities sufficiently small for trapping, molecule flux improves by a factor of four, and potentially more with increased voltage. The improvement is more significant for less readily polarized species, thereby expanding the class of candidate molecules for Stark deceleration.

Electrostatic guiding of the methylidyne radical at cryogenic temperatures

We have produced a cryogenic buffer-gas cooled beam of the diatomic molecular radical CH (methylidyne). This molecule is of interest for studying cold chemical reactions and fundamental physics measurements. Its light mass and ground-state structure make it a promising candidate for electrostatic guiding and Stark deceleration, which allows for control over its kinetic energy. This control can facilitate studies of reactions with tuneable collision energies and trapping for precise spectroscopic studies. Here, we have demonstrated electrostatic guiding of CH with fluxes up to 109 molecules per steradian per pulse. Graphical abstract

Ultracold molecular collision dynamics

Ultracold Chemistry Ultracold collision dynamics are of great importance in understanding the quantum nature of chemical interactions, but achieving the ultracold regime for molecules is challenging. Traditional techniques based on alternative routes to assemble the ultracold atomic constituents are only able to produce a type of ultracold molecules that cannot probe state-selective dynamics. Using Stark deceleration and velocity map–imaging techniques, de Jongh et al. achieved the ultracold regime directly for a nitric oxide–helium system and measured the state-to-state cross sections for inelastic scattering with high precision (see the Perspective by Yang and Yang). The observed scattering resonances confirmed high sensitivity to the underlying interaction potential because only the most accurate electronic structure theory could reproduce their structure. Science , this issue p. [626][1]; see also p. [582][2] [1]: /lookup/doi/10.1126/science.aba3990 [2]: /lookup/doi/10.1126/science.abb8020