Theoretical Studies On The Adiabatic And Evaporative Cooling Of Polar Molecules In A Novel Electrostatic Trap

In recent years, cold and ultracold molecules have wide and important applications in the fields of quantum computation and simulation, cold collisions and chemistry, cold molecule spectroscopy and precise measurements for fundamental constants, the parity violation and electron’s electric-dipole moment, and so on. Therefore, many approaches have been developed to prepare cold or ultracold molecules, such as laser-cooled-atom association methods, Feshbach resonance, buffer-gas cooling and velocity filtering, electrostatic or optical Stark deceleration, magnetic Zeeman slowing, and other cooling methods, for example sympathetic cooling, evaporative cooling, opto-electric cooling and laser cooling. And many physical teams have carried out a lot of active attempts and explorations to prepare and manipulate cold molecules with electrostatic trap. In this paper, we focus on the electrostatic trapping cold molecules, and the applications of cold molecules in trapping depth, such as adiabatic cooling and evaporative cooling.Firstly, we introduce a novel scheme to confine cold molecules with electrostatic trap. It is composed of two charged disks with drilled holes in the centers. When the two disks are applied with equal voltages, we derive the distributions of the electric field strength between the disks in the Cartesian coordinate system. To verify the accuracy of our analytical solutions, we calculate the contour distributions by a commercial finite-element software (Maxwell), which are nearly consistent with the numerical ones within the radius of 5 mm. What’s more, we study the dependences of the electric field on the radius R0 and the distance d between the two disk centers and we find when R0/d=0.5, the effective well depths in the x, y, and z directions are nearly the same. By calculating the trap depth of electric field and the temperature of cold molecules from the Stark decelerator, comparing with the first-order derivative of the electrostatic field and the Stark gradient force on ND3 molecules, we find that our proposed novel electrostatic trap scheme can be used to trap cold ND3 molecules in the gravity field.Then, we propose the loading and trapping schemes of cold molecules in our double disk electrostatic field. By changing the voltages applied to the left and right disks, U1 and U2, the shapes of the electric field are different, so we can realize the loading and trapping effectively. When U1= 30 kV and U2=50 kV, the electric field strength is increased along the loading direction, then the ND3 molecules in weak field seeking (WFS) states will be decelerated under the gradient forces of electric field. Once the ND3 molecules move to the center, we quickly change the voltage of left disk to U1= 50 kV, then resulted electric field will have the minimum in the center and larger value in the farther, so the cold molecules will be trapped in the center. And we analyze the dependences of the loading efficiency on the central velocity Vy0 of the incident molecular beam and the loading time tload and find that when Vy0= 12 m/s and tload= 1.27 ms, we can achieve the highest loading efficiency of cold molecules with about 95%. In comparison with the initial and final velocity distributions of cold ND3 molecules, we find that the velocity in the loading direction is obviously decreased and the final 3D temperature of the trapped molecules is about 28.8 mK.Afterward, we study the adiabatic cooling of ND3 molecules in the electrostatic trap depth. In the first, we develop a new analytical model to study the adiabatic cooling of cold molecules in a linear trap, and derive some corresponding analytical solutions. Then we use the Monte Carlo simulations of adiabatic cooling of ND3 molecules in our linear trap considering the elastic collisions among molecules to study the number change of molecules in the linear trap. We find when the molecular loss is less than 10%, the voltage is decreased from 50 kV to 25 kV. To test whether the molecules in the linear trap are cooled adiabatically, we simulate the 3D temperature change of molecules with the decrease of voltages and find that when the voltage is decreased from 50 kV to 25 kV, the 3D temperature of molecules will decrease from 25 mK to 15 mK. And the simulated results are consistent with the calculated one according to the analytical solutions, which shows our proposed new trap scheme can be used to study the adiabatic cooling of cold polar molecules by lowering trap potential depth.Finally, we study the evaporative cooling of ND3 molecules in the electrostatic trap depth. We propose the analytical solutions with respect to the linear electrostatic trap, and derive the temperature change of molecules with the decrease of voltages. Then, we make a contrast between the simulated result and the calculated ones and find when the voltage is less than 10 kV, the both are consistent, that is the molecules experience the evaporative cooling. In the end, we simulate and analyze the middle process. There are both adiabatic cooling and evaporative cooling inside, with only different proportions.