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Towards supersolids of laser-cooled dipolar molecules

Phillip Groß

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Quantum gases of diatomic molecules are many body systems that offer unprecedented control over their intrinsic long and short range interactions. This is due to the unique nature of the interactions between molecules, which can be much stronger than those in magnetic atoms and which can be tuned independently through external electromagnetic fields. As a result, diatomic molecules enable both the exploration of novel supersolid states and the creation of dipole dominated and self assembled quantum solids. The molecular properties and internal structure of calcium monofluoride (CaF) make it a promising candidate molecule for the realization of several kinds of strongly correlated quantum systems, such as strongly dipolar Bose Einstein condensates, quantum crystals and arrays of molecules in optical tweezers. This dissertation summarizes the first steps towards the realization of such systems using directly laser cooled CaF molecules. The two major experimental steps which are summarized in this thesis are cryogenic buffer gas cooling and transversal laser cooling of CaF molecules. For the first achievement, cryogenic buffer gas cooling, it is important to observe that CaF molecules are radicals and therefore do not exist in a stable gas phase. As a result, the production of a beam of molecules requires a cryogenic buffer gas cell setup, in which the molecules are produced via laser ablation of a solid precursor target. Two different kinds of ablation target are used to produce a molecular beam. The first is a pellet of a mixture of CaF2/BaF2. The second is a calcium metal target in addition to sulfurhexafluoride gas, which acts as a fluorine donor. The metal target is found to be the much more stable molecule production method, and the buffer gas cooling setup produces a bright and slow beam of molecules with a flux of around 1011 - 1013sr-1 molecules in the ground state of the laser cooling cycle. The second achievement is a significant improvement of the techniques for laser cooling of the resulting molecular beam. Notably, trapped cold gases of directly laser cooled molecules have not reached the quantum degenerate regime yet, but this milestone is within reach. In our experiment we aim to improve the loading of the magneto optical trap from the laser slowed beam, as this has been the most inefficient step in previous experiments with CaF. Our approach is to collimate the molecular beam through transversal laser cooling on the 𝑋 - 𝐴 transition. Due to the angular momentum structure of the type-II cooling transition, Doppler cooling forces in molecules are typically accompanied by sub Doppler Sisyphus heating forces and vice versa. This has made the collimation of molecular beams difficult in previous experiments, because efficient Doppler cooling over a large velocity range is perturbed by the appearance of sub Doppler heating forces at low transversal velocities. Here, we present a new way to address the hyperfine structure in the molecules using carefully chosen laser sidebands, which overcomes this limitation. The sideband spectrum of the cooling laser consists of one strong sideband with ≈ 80% of the laser power addressing a single hyperfine state and several weaker sidebands which repump population from the other hyperfine states. Depending on the detuning of the cooling laser, the strong sideband generates sub Doppler cooling forces on the 𝑋2Σ+(𝐹 = 2) - 𝐴2Π1/2 (𝐹 = 1) or the 𝑋2Σ+(𝐹 = 1+) - 𝐴2Π1/2 (𝐹 = 0) transition. The measured transversal density profiles of the molecular beam suggest that, for certain detunings of the cooling laser, both mechanisms lead to forces that counteract the molecular motion, leading to the simultaneous appearance of Doppler and sub Doppler cooling. This result is contrary to the conventional tendency of type II systems, where sub Doppler cooling forces are usually opposed by Doppler heating forces. The observed behavior is supported by numerical simulations of the laser cooling forces and molecular trajectories based on the optical Bloch equations. Overall, the results highlight the importance of a well tailored cooling laser sideband structure for molecular laser cooling to control the interplay between both cooling mechanisms. Through the collimation of the molecular motion towards the capture region of a magneto-optical trap, the transversal cooling of the molecular beam with simultaneous Doppler and sub-Doppler cooling forces should enable a more efficient trap loading. The experimental results presented here therefore form the basis for future experiments on laser slowing, magneto optical trapping and evaporative cooling towards Bose Einstein condensation or the loading of large optical tweezer arrays of cold CaF molecules.

DOI
10.18419/opus-18093

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Quantum gases of diatomic molecules are many body systems that offer unprecedented control over their intrinsic long and short range interactions. This is due to the unique nature of the interactions between molecules, which can be much stronger than those in magnetic atoms and which can be tuned independently through external electromagnetic fields. As a result, diatomic molecules enable both the exploration of novel supersolid states and the creation of dipole dominated and self assembled quantum solids. The molecular properties and internal structure of calcium monofluoride (CaF) make it a promising candidate molecule for the realization of several kinds of strongly correlated quantum systems, such as strongly dipolar Bose Einstein condensates, quantum crystals and arrays of molecules in optical tweezers. This dissertation summarizes the first steps towards the realization of such systems using directly laser cooled CaF molecules. The two major experimental steps which are summarized in this thesis are cryogenic buffer gas cooling and transversal laser cooling of CaF molecules. For the first achievement, cryogenic buffer gas cooling, it is important to observe that CaF molecules are radicals and therefore do not exist in a stable gas phase. As a result, the production of a beam of molecules requires a cryogenic buffer gas cell setup, in which the molecules are produced via laser ablation of a solid precursor target. Two different kinds of ablation target are used to produce a molecular beam. The first is a pellet of a mixture of CaF2/BaF2. The second is a calcium metal target in addition to sulfurhexafluoride gas, which acts as a fluorine donor. The metal target is found to be the much more stable molecule production method, and the buffer gas cooling setup produces a bright and slow beam of molecules with a flux of around 1011 - 1013sr-1 molecules in the ground state of the laser cooling cycle. The second achievement is a significant improvement of the techniques for laser cooling of the resulting molecular beam. Notably, trapped cold gases of directly laser cooled molecules have not reached the quantum degenerate regime yet, but this milestone is within reach. In our experiment we aim to improve the loading of the magneto optical trap from the laser slowed beam, as this has been the most inefficient step in previous experiments with CaF. Our approach is to collimate the molecular beam through transversal laser cooling on the 𝑋 - 𝐴 transition. Due to the angular momentum structure of the type-II cooling transition, Doppler cooling forces in molecules are typically accompanied by sub Doppler Sisyphus heating forces and vice versa. This has made the collimation of molecular beams difficult in previous experiments, because efficient Doppler cooling over a large velocity range is perturbed by the appearance of sub Doppler heating forces at low transversal velocities. Here, we present a new way to address the hyperfine structure in the molecules using carefully chosen laser sidebands, which overcomes this limitation. The sideband spectrum of the cooling laser consists of one strong sideband with ≈ 80% of the laser power addressing a single hyperfine state and several weaker sidebands which repump population from the other hyperfine states. Depending on the detuning of the cooling laser, the strong sideband generates sub Doppler cooling forces on the 𝑋2Σ+(𝐹 = 2) - 𝐴2Π1/2 (𝐹 = 1) or the 𝑋2Σ+(𝐹 = 1+) - 𝐴2Π1/2 (𝐹 = 0) transition. The measured transversal density profiles of the molecular beam suggest that, for certain detunings of the cooling laser, both mechanisms lead to forces that counteract the molecular motion, leading to the simultaneous appearance of Doppler and sub Doppler cooling. This result is contrary to the conventional tendency of type II systems, where sub Doppler cooling forces are usually opposed by Doppler heating forces. The observed behavior is supported by numerical simulations of the laser cooling forces and molecular trajectories based on the optical Bloch equations. Overall, the results highlight the importance of a well tailored cooling laser sideband structure for molecular laser cooling to control the interplay between both cooling mechanisms. Through the collimation of the molecular motion towards the capture region of a magneto-optical trap, the transversal cooling of the molecular beam with simultaneous Doppler and sub-Doppler cooling forces should enable a more efficient trap loading. The experimental results presented here therefore form the basis for future experiments on laser slowing, magneto optical trapping and evaporative cooling towards Bose Einstein condensation or the loading of large optical tweezer arrays of cold CaF molecules.
Laser cooling and trapping are central to modern atomic physics. It has been roughly three decades since laser cooling techniques produced ultracold atoms, leading to rapid advances in a vast array of fields and a number of Nobel prizes. Prior to the work presented in this thesis, laser cooling had not yet been extended to molecules because of their complex internal structure. However, this complexity makes molecules potentially useful for a wide range of applications. The first direct laser cooling of a molecule and further results we present here provide a new route to ultracold temperatures for molecules. In particular, these methods bridge the gap between ultracold temperatures and the approximately 1 kelvin temperatures attainable with directly cooled molecules (e.g. with cryogenic buffer gas cooling or decelerated supersonic beams). Using the carefully chosen molecule strontium monofluoride (SrF), decays to unwanted vibrational states are suppressed. Driving a transition with rotational quantum number R=1 to an excited state with R'=0 eliminates decays to unwanted rotational states. The dark ground-state Zeeman sublevels present in this specific scheme are remixed via a static magnetic field. Using three lasers for this scheme, a given molecule should undergo an average of approximately 100,000 photon absorption/emission cycles before being lost via unwanted decays. This number of cycles should be sufficient to load a magneto-optical trap (MOT) of molecules. In this thesis, we demonstrate transverse cooling of an SrF beam, in both Doppler and a Sisyphus-type cooling regimes. We also realize longitudinal slowing of an SrF beam. Finally, we detail current progress towards trapping SrF in a MOT. Ultimately, this technique should enable the production of large samples of molecules at ultracold temperatures for molecules chemically distinct from competing methods.
Ultracold molecules can be used for a diverse set of exciting applications including controlled quantum chemistry, probes of physics beyond the standard model, simulation of many-body quantum systems and quantum information processing. However their rich internal structure makes the required control of their motional and internal states difficult. In the last decade, the field has made rapid progress on developing techniques for producing, cooling and trapping molecules and, whilst challenges remain, many of these applications are now being realised. This thesis presents my work on laser cooling and coherent control of calcium monofluoride (CaF) molecules. We load molecules into a three-dimensional magneto-optical trap (MOT), the first such trap for CaF and the second for any molecule. The MOT contains around 2×10⁴ molecules with an initial temperature of 12 mK. Lowering the laser intensity brings the temperature of the MOT down to 960 μK. To further cool the molecules we load them into a blue-detuned optical molasses, cooling them to 5.4(7) μK. This temperature is ~40 times below the Doppler limit and corresponds to a typical molecule moving at only a few times the single-photon recoil velocity. We optically pump the molecules into a single Zeeman sub-level and coherently transfer them between rotational states using microwave radiation. We load the molecules into a magnetic trap where they remain confined for about 5 s, the lifetime being limited by vibrational excitation due to room-temperature blackbody radiation. We show how to prepare the trapped molecules in a coherent superposition of two rotational states, and how to maintain this coherence for long periods, up to 6.4(8) ms. Detailed simulations of the remaining decoherence mechanisms suggest that it is possible to extend this to more than a second by compressing the sample to a smaller size, and using a magnetic trap geometry where the direction of the field is nearly uniform across the trapping volume. Finally we explore theoretically how Raman sideband cooling can be applied to molecules in optical tweezer traps, potentially providing a route to full quantum control.
Laser cooling and trapping in a magneto-optical trap (MOT) have been essential to the success of cold atom physics in the last decades. Recently, the application of the same techniques to molecules has begun. The complexity of even a simple diatomic molecule makes laser cooling difficult, but promises new applications in many areas of research. In this thesis I describe the development of the first three-dimensional MOT of calcium fluoride (CaF) molecules. First, a cryogenic buffer gas source was set up, producing a pulsed beam of 9.3*10^10 molecules per steradian per pulse with forward velocities around 170 m/s. A similar source for very large molecules was set up during a 5 month internship at the University of Vienna. Next, the molecular pulse was slowed down to the capture velocity of a MOT using chirped laser slowing, resulting in about 7*10^5 CaF molecules passing through the typical MOT volume of 1 cm^3 at velocities of 15+-5 m/s. A new deceleration method, called Zeeman-Sisyphus deceleration, was also investigated. In this method molecules move through a spatially varying magnetic field and are optically pumped between low- and high-field seeking states in such as a way that they are always losing kinetic energy. The method promises to deliver more slow molecules because the molecules are guided transversely as they are decelerated. A small prototype was built and the optical pumping step was tested successfully. Finally, 7.6*10^3 CaF molecules were trapped in a MOT and cooled to a temperature of 8.5 mK. The radial trap frequency is 2 pi*130 Hz and the damping constant is beta=9.5*10^2 s^-1. The lifetime is about 100 ms and depends strongly on the scattering rate. This MOT is an an ideal starting point for a wide range of new experiments with ultracold molecules.
Ultracold polar molecules have emerged as promising platforms for quantum simulation, quantum information science, precision measurements of fundamental symmetry violations, and quantum chemistry. Over the past decade, rapid progress in direct laser cooling of molecules has enabled new capabilities such as magneto-optical traps (MOTs), sub-Doppler cooling, and optical dipole traps (ODTs), expanding the quantum toolbox with ultracold molecules of complex internal structures and strong dipolar interactions. This thesis presents the design, construction, and operation of an experiment on ultracold strontium monofluoride (88Sr19F) molecules, demonstrating state-of-the-art techniques for molecular laser cooling and trapping. The apparatus integrates a broad range of technical sub-systems, including cryogenics, ultra-high vacuum, optics, electronics, and automated laboratory control software. SrF molecules produced in a slowed cryogenic buffer gas beam are captured into a dual-frequency MOT. Subsequent Λ-enhanced gray molasses cooling reduces the molecule temperature to as low as 5 μK. A novel blue-detuned MOT is also implemented to further compress the molecular cloud, increasing the density by a factor of ∼ 400. At this high density, SrF molecules are efficiently loaded into an ODT, a tight, conservative trap with long lifetimes. Population transfer between different rotational levels is achieved via optical pumping and coherent microwave control, yielding ∼ 0.8 ms coherence time in Rabi oscillation and ∼ 90 % transfer efficiency. This thesis also describes the development of an ultracold rubidium (87Rb) atom experiment, in which a loading rate of ∼ 10^10 atoms/s into a radio-frequency (RF) MOT is demonstrated. A modular two-dimensional MOT serves as the Rb source and can be seamlessly integrated into the SrF apparatus, opening the possibility for future studies of co-trapping and sympathetic cooling of SrF molecules with atoms. The results presented in this thesis establish an experimental foundation for exploring new frontiers in ultracold molecular physics.
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.
Potential wide-ranging scientific applications, spanning fundamental physics to quantum engineering, has led to significant efforts in controlling molecules at the quantum level. The rich internal structure of molecules, that gives rise to these desirable properties also complicates the task of controlling such species. Over the past decade, our ability to produce, control, and detect molecules has advanced tremendously with direct laser-cooling and magneto-optical trapping of diatomic molecules realized by several groups around the world. In this thesis, we describe the creation of the first RF MOT of CaF, which at the time of the writing of this thesis, remains the largest and densest molecular MOT. New laser cooling techniques for molecules are demonstrated, allowing laser cooling of molecules to 4 uK, 50 times colder than the Doppler limit. Optical trapping of these molecules is also achieved, which, in combination with in-trap laser cooling increased the density of trapped molecules by five orders of magnitude compared to the density in the MOT. We developed methods to cool and detect single molecules with high fidelity, which aided us in the creation of an optical tweezer array of single, ultracold CaF molecules. The densities of molecules (10^12 cm^-3) attained inside the tweezer traps also enabled us to observe both light-assisted and ground state collisions of laser cooled molecules, for the first time. The phase space density within the merged tweezers reached 5x10^-4, 10 orders of magnitude larger than the initial MOT. We implemented internal quantum state control of the molecules and dynamical control of the tweezers to build a platform for exploring state-selective ultracold quantum chemistry.