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Frontiers of Physics

Simulation of EOM-based frequency-chirped laser slowing of MgF radicals

Kang Yan, Ruoxi Gu, Di Wu, Jin Wei, Yong Xia, Jianping Yin

Published Dec 19, 2021• 12 citations
Publisher

Abstract

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.

DOI
10.1007/s11467-021-1137-y

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•Jul 1, 2017•0 citations
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 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.
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.
A novel cryogenic MgF molecular beam, characterized by high flux and exceptional stability, has been successfully generated within a helium buffer gas environment. This achievement is facilitated by the innovative use of an in-cell stepper motor, which continuously rotates the sample rod during laser ablation. Through meticulous optimization of the ablation laser energy, the position of the ablation spot, and the gas flow rate, among other critical parameters, the resulting MgF beam exhibits a remarkable forward velocity of 209 m/s and an impressive brightness of approximately 1.36 × 1012 molecules per pulse per steradian per internal state. Subsequent attempts at one-dimensional Doppler cooling of the MgF beam have been made, with theoretical calculations closely aligning with experimental outcomes. These findings demonstrate a significant compression in the transverse spatial distribution of the molecular beam, from 7.8 to 6.5 mm, and a substantial cooling of the transverse temperature, from 8.1 to 5.6 mK. This work lays a crucial foundation for the advancement of molecular slowing and magneto-optical trapping techniques for MgF molecules.
Achieving laser cooling of molecules necessitates the establishment of a closed optical cycling transition. In contrast to atoms, molecules exhibit additional vibrational and rotational structures, which must be carefully addressed-alongside hyperfine splittings-when designing the laser frequency scheme for efficient optical cycling. In this work, we investigated optical cycling in MgF molecules on the laser cooling transition, namely [Formula: see text] transition between the electronic ground state ([Formula: see text]) and the electronic excited state ([Formula: see text]). The ground state comprises four hyperfine levels, of which two are unresolved within the excited-state linewidth; the two hyperfine levels in the excited state are also unresolved. Consequently, three laser frequencies suffice to address all transitions. This was realized by generating three independently tunable frequency components using acousto-optic modulators (AOMs). With optimized detunings, power ratios, and total beam power, simultaneous application of all three frequency components increased the total number of scattered photons by up to [Formula: see text] relative to the sum of the individual single-frequency signals. Applying a tilted magnetic field to remix the dark Zeeman states increased the photon yield by an additional factor of [Formula: see text], leading to an overall enhancement of about sevenfold. These results provide quantitative benchmarks for MgF optical cycling and practical guidance for future molecular slowing and magneto-optical trapping experiments.
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.