We describe the statistical mechanics of a new method to produce very cold atoms or molecules. The method results from trapping a gas in a potential well, and sweeping through the well a semi-permeable barrier, one that allows particles to leave but not to return. If the sweep is sufficiently slow, all the particles trapped in the well compress into a very cold gas. We derive analytical expressions for the velocity distribution of particles in the cold gas, compare these results with numerical simulations, and discuss limitations on reduction in energy due to imperfections of the barrier.
We describe the statistical mechanics of a new method to produce very cold atoms or molecules. The method results from trapping a gas in a potential well, and sweeping through the well a semi-permeable barrier, one that allows particles to leave but not to return. If the sweep is sufficiently slow, all the particles trapped in the well compress into a very cold gas. We derive analytical expressions for the velocity distribution of particles in the cold gas, compare these results with numerical simulations, and discuss limitations on reduction in energy due to imperfections of the barrier.
PACS. 32.80.Pj – Optical cooling of atoms; trapping. PACS. 33.80.Ps – Optical cooling of molecules; trapping. Abstract. – We describe the statistical mechanics of a new method to produce very cold atoms or molecules. The method results from trapping a gas in a potential well, and sweeping through the well a semi-permeable barrier, one that allows particles to leave but not to return. If the sweep is sufficiently slow, all the particles trapped in the well compress into an arbitrarily cold gas. We derive analytical expressions for the velocity distribution of particles in the cold gas, and compare these results with numerical simulations. Introduction. – Evaporative cooling was originally suggested as a means to achieve Bose-Einstein condensation in atomic hydrogen [1–3]. Its application to magnetically trapped alkali atoms [4,5] culminated in the first observation of Bose–Einstein condensation in atomic vapors [6–8]. Since then it has been the essential process by which to obtain degenerate quantum gases. Nevertheless it has shortcomings. The main two are
The ability to cool and trap atoms has revolutionized atomic and ultra-cold physics. Molecular physics is currently undergoing a similar transformation. This thesis aims to research a general cooling method that will be applicable to wide range of molecular and atomic species and other particles. We studied the dynamics of molecules in optical fields, focusing in particular on exploring the molecular self-organisation phenomena in optical cavities to cool molecular ensembles to sub-mK temperatures. Firstly, the general model of cavity cooling from atoms to molecules and the dynamics of a particle in a single cavity mode were discussed. We extended the existing cooling scheme for two-level atoms to an ensemble of multi-level molecules. Then we studied the spatial dynamics of molecules in the new parameter conditions, focusing in particular on exploring the molecular self-organisation phenomena in optical cavities to cool molecular ensembles to sub-mK temperatures. The scheme complements well with our present experimental work on the deceleration and focusing of cold molecules and can extend our present capability to simultaneously cool and trap a large cold molecular ensemble. For simulation of a large ensemble of molecules, we proposed a new statistical model based on the Boltzmann equation beside the traditional discrete model and studied two solution methods. The comparison of the theory and numerical simulations between discrete model and statistical model showed a good agreement, which validated this new model. We then explored the scaling laws with a view to the self-organization and cooling of a large ensemble of species. We studied the cooling of a CN molecular cloud of the density 10/cm, with an initial temperature at 10 mK in an optical cavity. We found that more than a third of the molecules are stably trapped by the intracavity field and the final temperature is below 1mK. We discussed the scaling laws in the case when a large ensemble of species is involved. Finally we argue that cavity cooling using a far
Slowing down atoms using laser cooling, together with techniques like magnetic trapping and evaporative cooling, has led to numerous exciting results over the last decade [1], with the realization of Bose-Einstein condensation as the most spectacular achievement [2]. Laser-cooling schemes are applicable to atoms since closed multilevel systems can be realized and many consecutive absorptionemission cycles can be induced. This leads to a significant momentum transfer from the photons of the laser to the atom, resulting in a change of the velocity of the atom. There currently is a great interest in producing cold molecules for the study of cold molecule-molecule collisions, molecular quantum collective effects, Doppler-free spectroscopy, frequency standards, as well as many other applications already realized for atoms [3]. Slowing down of neutral molecules, a prerequisite for being able to trap them, has proven to be considerably more difficult to be achieved, however. The above-mentioned laser-cooling scheme cannot be applied to slow down molecules as no simple closed-level systems can be found; the unavoidable off-resonant radiative decay of molecules from the excited state to other vibrational levels in the electronic ground state hampers efficient momentum transfer [4]. Once molecules are present at sufficiently low kinetic energies, below a fraction of a cm21, they can be trapped in various ways. Trapping of neutral molecules in inhomogeneous magnetic [3] and electric fields [5] and trapping based on the use of evanescent fields close to the dielectricvacuum interface have been proposed [6]. It has also been suggested that extremely high laser powers might be used to induce a dipole moment in polarizable molecules, leading to trapping of these molecules in the laser beam [7]. Other methods to produce slow molecules have been put forward and have recently been successfully applied to produce the first samples of trapped molecules. By injecting molecules in a cold buffer gas, sufficiently low kinetic energies of the injected molecules can be obtained after thermalization that they can subsequently be trapped in an inhomogeneous magnetic field. This has recently been demonstrated for CaH injected in 3He buffer gas at temperatures of around 0.3 K [8]. Associative collisions between ultracold trapped atoms [9] have proven to be
Abstract Many areas of physics—precision measurements, quantum information, and physical chemistry, to name a few—are starting to benefit from the enormous advantages offered by cold and ultracold polar molecules. Molecules have more states, more interactions, and more chemical properties compared to atoms, which make them exciting to study but difficult to tame. In particular, the powerful techniques of atomic laser cooling cannot be naïvely applied to molecules due to their complicated structure. Developments over the past few years have made directly laser cooled and trapped molecules a reality, and now much effort is focused on making these samples larger, denser, and colder—an important step to realizing many of their exciting applications. A careful experimental and numerical study by Truppe et al (2017 New J. Phys. 19 022001 ) demonstrates a significant improvement and advance in understanding of one of the most limiting steps in laser cooling and trapping of molecules—slowing them from a molecular beam to a near-standstill, with small enough kinetic energy that they can be loaded into a trap.
Cold molecules are an invaluable tool for modern physics. Cold atoms have already revolutionized precision metrology, allowed for spectacular findings in quantum physics and opened the door for the creation and observation of novel states of matter. Cold molecules bring with them additional degrees of freedom which give rise to unique properties that enable new kinds of experiments. For these experiments it is of vital importance to start with a sufficiently large number of cold molecules. There are multiple paths for the slowing and cooling of atoms and most of the slowing techniques utilizing lasers for direct cooling have been transferred to the molecular case with its specific requirements. The Zeeman slowing technique is advantageous for loading a trap with cold particles but had not yet been transferred from atoms to the molecular case. In this thesis I will show the first realization of the Zeeman slowing technique for diatomic molecules. This thesis will discuss several preparatory steps: Our group has had some ideas to collimate the molecular beam with a conical nozzle outlet at the buffer gas cell which I investigated on potassium atoms generated by the ablation of 39K35Cl inside the buffer gas cell. I also realized a fluorescence spectroscopy of the |XΣ1/2, N = 1, v = 0⟩ → |AΠ1/2, N = 0, v = 0⟩ transition in magnetic fields up to 300 G and confirmed simulations regarding our two laser cycling scheme in the Paschen-Back regime by measuring the scattering rate of light on one molecule. Finally, I created pre-cooled 40Ca19F with a forward velocity of around 150 m s−1 from a 40Ca19F2 target with laser ablation inside a cryogenic buffer gas cell. With the Zeeman slowing technique I slowed the molecules down to 25 m s−1, a velocity where trapping can be possible. I have also shown the characteristic compression into specific velocity classes for not yet trappable velocities. Together these two findings demonstrate that molecular Zeeman slowing is possible and a real promising tool for future experiments.
Slowing, cooling, and trapping molecules One of the major achievements in physics during the last two decades of the twentieth century was the ability to cool and trap atoms [1]. Laser cooling can produce previously inconceivable atomic temperatures of less than 1 μK. Atoms with sufficiently low kinetic energy can be trapped in magnetic and optical traps and thus studied for a prolonged time, thereby improving the resolution of spectroscopy by many orders of magnitude as well as reducing Doppler broadening. Furthermore, besides the external degrees of freedom, the internal degrees of freedom of the atoms can also be manipulated, leading to full control of the atoms. One of the holy grails of physics, the achievement of Bose–Einstein condensation in a dilute gas, was achieved mainly because of laser cooling and trapping of atoms. One of the natural extensions of laser cooling and trapping of atoms is the application of the techniques to molecules. Molecules offer a much richer internal structure than atoms, and thus provide extended possibilities to experimentalists. However, atomic laser cooling is based on the repetitive scattering of light and requires a closed, or at least nearly closed, two-level system. Because of the complicated internal structure of molecules, a closed two-level system cannot usually be found because they have many different electronic, vibrational, and rotational states and in general can decay to many different states after absorption of light (see Chap. 16). This requires a complete rethinking of the schemes that are used to cool atoms. Still, because of the extended possibilities cold molecules can offer with respect to cold atoms, there have been a large number of techniques developed to slow, cool, and trap them. These techniques can be divided into two classes, namely direct and indirect cooling. In the first case, molecules at cryogenic or room temperature are directly slowed and cooled. Although many different slowing techniques are used, this chapter focuses on Stark slowing of molecules since it was the first technique developed. Apart from the Stark shift of the molecules, the Zeeman and light shift of molecules can also be used to slow them. The idea behind Stark slowing is to subject the moving molecules to a continuously increasing electric field so that their kinetic energy is converted into potential energy.