Abstract We propose a scheme for dual-species deceleration and trapping of a cold atom–molecule mixture by a frequency chirping stimulated force. We study the stimulated force exerted on MgF and Rb using optical Bloch equations based on a direct numerical solution for the time-dependent density matrix. We analyze the relationship between the frequency chirping rate and the number of MgF molecules and Rb atoms. In addition, we study the dynamical process of molecular deceleration and the effect of transverse diffusion. Monte–Carlo simulations show that buffer-gas-cooled MgF and Rb beams, with initial velocities of 200 m/s and 130 m/s respectively, can be decelerated to less than 10 m/s. This is achieved with laser powers of as low as 357 mW for MgF and 10 mW for Rb per traveling wave. The rapid deceleration minimizes molecular loss due to transverse diffusion during the deceleration process. The estimated number of molecules that can be trapped in a magneto-optical trap (MOT) is about 9.0 × 106, which is an order of magnitude larger than the number of MgF molecules decelerated by the spontaneous radiation force. The results offer a promising starting point for further studies of sympathetic cooling.
Abstract We propose a scheme for dual-species deceleration and trapping of a cold atom–molecule mixture by a frequency chirping stimulated force. We study the stimulated force exerted on MgF and Rb using optical Bloch equations based on a direct numerical solution for the time-dependent density matrix. We analyze the relationship between the frequency chirping rate and the number of MgF molecules and Rb atoms. In addition, we study the dynamical process of molecular deceleration and the effect of transverse diffusion. Monte–Carlo simulations show that buffer-gas-cooled MgF and Rb beams, with initial velocities of 200 m/s and 130 m/s respectively, can be decelerated to less than 10 m/s. This is achieved with laser powers of as low as 357 mW for MgF and 10 mW for Rb per traveling wave. The rapid deceleration minimizes molecular loss due to transverse diffusion during the deceleration process. The estimated number of molecules that can be trapped in a magneto-optical trap (MOT) is about 9.0 × 106, which is an order of magnitude larger than the number of MgF molecules decelerated by the spontaneous radiation force. The results offer a promising starting point for further studies of sympathetic cooling.
Heavy atoms play a critical role in scientific research and applications by providing a better understanding of fundamental physical phenomena. The use of a slowed atomic beam to extend the interaction time is expected to enhance measurement sensitivity, resolution, and precision. Here, we theoretically demonstrate a rapid and short-distance deceleration of heavy atoms by using a continuous stimulated force with optical phase compensation and frequency chirping. The scheme effectively overcomes the spatial inhomogeneity of the stimulated force on atoms during deceleration. Our approach employs the numerical solutions of the optical Bloch equations for two-level atoms driven by time-dependent fields, and simulates atom trajectories using a three-dimensional Monte Carlo method. Concerning a buffer-gas-cooled radium atom beam with an initial velocity of 130 m/s, from our simulations it can be decelerated to 5 m/s within 5 cm distance using 40 mW laser power, achieving a deceleration force approximately 35 times stronger than the radiation force and covering an effective velocity range over eight times that of the radiation force. In addition, the deceleration of other heavy atoms, such as francium and thallium, also are applicable. This approach offers an efficient tool for rapidly slowing and cooling complex atoms and molecules, facilitating future precision measurements.
Here we propose a scheme to slow MgF molecules by using EOM-based frequency-chirped radiation pressure slowing. The scheme well addresses the need for a rapid chirp rate while light molecules are being laser slowed, whose scattering rate and recoil velocity are large. Two EOMs are used to compensate the rapidly changing Doppler shifts arised from the movement of molecules, and to cover the hyperfine energy structure of MgF, respectively. Based the scattering rate maps calculated from an optical Bloch equation model, individual molecule trajectories are simulated by using a semi-classical three-dimensional Monte Carlo approach. We show how the modulation configuration of EOM and the magnetic field influence the slowing results. The study shows that a cryogenic buffer gas-cooled MgF beam source is possible to be slowed down with a number of ∼ 1.4 × 10 6 −10 7 , and the final forward speed peaks at ∼ 10 m/s near the capture velocity of a molecular MOT.
Abstract We present a theoretical approach to achieve sub-Doppler cooling of magnesium fluoride (MgF) molecules by tuning the AC Stark shift with a blue-detuned laser. We study three blue-detuned magneto–optical trapping (MOT) schemes by using the Bayesian optimization method with the optical Bloch equations. We perform a comprehensive analysis of the relationship between the force in the MOT and the velocities and positions of the MgF molecules. Monte–Carlo simulations show that our MOT schemes can achieve a temperature as low as 28 μK and a density as high as 4.0 × 108 cm−3 at the conditions of a ratio of two laser intensities of 2:7, a detuning of 3Γ and a polarization configuration of σ −–σ +. These results provide a clear way for transferring a large number of MgF molecules into a conservative trap to enhance the subsequent cooling such as evaporative or sympathetic cooling.
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.
Diatomic molecules are promising systems for quantum science applications due to their complex energy structures and strong dipole-dipole interactions. Achieving ultracold temperatures is essential for these applications, but the complexity of molecular energy levels requires precise optimization of experimental parameters for laser slowing and magneto-optical trapping (MOT). Here, we simulate and optimize the complete process of slowing and trapping MgF molecules, from a buffer-gas beam source to MOT capture, using Bayesian optimization. By combining laser slowing and MOT simulations, we identify parameters that maximize the capture velocity and the ratio of trapped molecules. Our results demonstrate a maximum MOT capture velocity of 82.5 m/s, and 28.6% of the molecules that reach the MOT region are trapped under optimal conditions. These findings provide insights into experimental setups for MgF and similar molecules, offering a framework for advancing molecular laser cooling and quantum experiments.
We present the properties of a magneto-optical trap (MOT) of CaF molecules. We study the process of loading the MOT from a decelerated buffer-gas-cooled beam, and how best to slow this molecular beam in order to capture the most molecules. We determine how the number of molecules, the photon scattering rate, the oscillation frequency, damping constant, temperature, cloud size and lifetime depend on the key parameters of the MOT, especially the intensity and detuning of the main cooling laser. We compare our results to analytical and numerical models, to the properties of standard atomic MOTs, and to MOTs of SrF molecules. We load up to molecules, and measure a maximum scattering rate of s −1 per molecule, a maximum oscillation frequency of 100 Hz, a maximum damping constant of 500 s −1 , and a minimum MOT rms radius of 1.5 mm. A minimum temperature of 730 μ K is obtained by ramping down the laser intensity to low values. The lifetime, typically about 100 ms, is consistent with a leak out of the cooling cycle with a branching ratio of about . The MOT has a capture velocity of about 11 m s −1 .