Internal-state thermometry by depletion spectroscopy in a cold guided beam of formaldehyde

We present measurements of the internal state distribution of electrostatically guided formaldehyde. Upon excitation with continuous tunable ultraviolet laser light the molecules dissociate, leading to a decrease in the molecular flux. The population of individual guided states is measured by addressing transitions originating from them. The measured populations of selected states show good agreement with theoretical calculations for different temperatures of the molecule source. The purity of the guided beam as deduced from the entropy of the guided sample using a source temperature of 150K corresponds to that of a thermal ensemble with a temperature of about 30 K

Continuum limit of self-driven particles with orientation interaction

We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator

Cold guided beams of water isotopologs

Electrostatic velocity filtering and guiding is an established technique to produce high fluxes of cold polar molecules. In this paper we clarify different aspects of this technique by comparing experiments to detailed calculations. In the experiment, we produce cold guided beams of the three water isotopologs H2O, D2O and HDO. Their different rotational constants and orientations of electric dipole moments lead to remarkably different Stark shift properties, despite the molecules being very similar in a chemical sense. Therefore, the signals of the guided water isotopologs differ on an absolute scale and also exhibit characteristic electrode voltage dependencies. We find excellent agreement between the relative guided fractions and voltage dependencies of the investigated isotopologs and predictions made by our theoretical model of electrostatic velocity filtering.Comment: 14 pages, 13 figures; small changes to the text, updated reference

Velocity-selected molecular pulses produced by an electric guide

Electrostatic velocity filtering is a technique for the production of continuous guided beams of slow polar molecules from a thermal gas. We extended this technique to produce pulses of slow molecules with a narrow velocity distribution around a tunable velocity. The pulses are generated by sequentially switching the voltages on adjacent segments of an electric quadrupole guide synchronously with the molecules propagating at the desired velocity. This technique is demonstrated for deuterated ammonia (ND$_{3}$), delivering pulses with a velocity in the range of $20-100\,\rm{m/s}$ and a relative velocity spread of $(16\pm 2)\,$ at FWHM. At velocities around $60\,\rm{m/s}$, the pulses contain up to $10^6$ molecules each. The data are well reproduced by Monte-Carlo simulations, which provide useful insight into the mechanisms of velocity selection.Comment: 8 pages, 6 figure

Solutions to Maxwell's Equations using Spheroidal Coordinates

Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be defined in a form which is directly reminiscent of the Laguerre-Gaussian solutions to the paraxial wave equation in optics. Expressions for the Cartesian derivatives of the scalar spheroidal wave functions are derived, leading to a new set of vector solutions to Maxwell's equations. The results are an ideal starting point for calculations of corrections to the paraxial approximation

Electrostatic extraction of cold molecules from a cryogenic reservoir

We present a method which delivers a continuous, high-density beam of slow and internally cold polar molecules. In our source, warm molecules are first cooled by collisions with a cryogenic helium buffer gas. Cold molecules are then extracted by means of an electrostatic quadrupole guide. For ND$_3$ the source produces fluxes up to $(7 \pm ^{7}_{4}) \times 10^{10}$ molecules/s with peak densities up to $(1.0 \pm ^{1.0}_{0.6}) \times 10^9$ molecules/cm$^3$. For H$_2$CO the population of rovibrational states is monitored by depletion spectroscopy, resulting in single-state populations up to $(82 \pm 10)$.Comment: 4 pages, 4 figures, changes to the text, updated figures and reference

Doppler-Free Spectroscopy of Weak Transitions: An Analytical Model Applied to Formaldehyde

Experimental observation of Doppler-free signals for weak transitions can be greatly facilitated by an estimate for their expected amplitudes. We derive an analytical model which allows the Doppler-free amplitude to be estimated for small Doppler-free signals. Application of this model to formaldehyde allows the amplitude of experimentally observed Doppler-free signals to be reproduced to within the experimental error.Comment: 7 pages, 7 figures, 1 table, v2: many small improvements + corrected line assignmen

Sisyphus Cooling of Electrically Trapped Polyatomic Molecules

The rich internal structure and long-range dipole-dipole interactions establish polar molecules as unique instruments for quantum-controlled applications and fundamental investigations. Their potential fully unfolds at ultracold temperatures, where a plethora of effects is predicted in many-body physics, quantum information science, ultracold chemistry, and physics beyond the standard model. These objectives have inspired the development of a wide range of methods to produce cold molecular ensembles. However, cooling polyatomic molecules to ultracold temperatures has until now seemed intractable. Here we report on the experimental realization of opto-electrical cooling, a paradigm-changing cooling and accumulation method for polar molecules. Its key attribute is the removal of a large fraction of a molecule's kinetic energy in each step of the cooling cycle via a Sisyphus effect, allowing cooling with only few dissipative decay processes. We demonstrate its potential by reducing the temperature of about 10^6 trapped CH_3F molecules by a factor of 13.5, with the phase-space density increased by a factor of 29 or a factor of 70 discounting trap losses. In contrast to other cooling mechanisms, our scheme proceeds in a trap, cools in all three dimensions, and works for a large variety of polar molecules. With no fundamental temperature limit anticipated down to the photon-recoil temperature in the nanokelvin range, our method eliminates the primary hurdle in producing ultracold polyatomic molecules. The low temperatures, large molecule numbers and long trapping times up to 27 s will allow an interaction-dominated regime to be attained, enabling collision studies and investigation of evaporative cooling toward a BEC of polyatomic molecules

Measurement of the lifetime of Pb52+^{52+}, Pb53+^{53+} and Pb54+^{54+} beams at 4.2 MeV per nucleon subject to electron cooling

By measuring the lifetime of stored beams, the recombination of the ions with cooling electrons was investigated. Rates found are larger than expected for radiative electron capture and significantly higher for Pb53+ than for Pb54+ and Pb52+. These results are important for the design of the lead ion injection system for the Large Hadron Collider and for recombination theories