Buffer Gas Cooling of atomic and molecular beams Wenhan Zhu Princeton University 11/06/2007 Basic idea The technique relies on thermalization of the species-to-be-trapped via collisions with a cold buffer gas, which serves to dissipate the translational energy of the atoms or molecules. Assuming elastic collision between two mass points, m (buffer gas atom) and M (species-to-be- trapped). Considering momentum and energy conservation, we will have: T ( ' ) T T/ ( )/ m M 2 2M m T and T’ is the temperature of the buffer gas and initial temperature of the species. Basic idea Then we can get the differential form of this equation: dl (l ) T T/ T Solve this equation,give the results: T / p / ( T e lT ' T 1 (/)1 )xl In order to promise that thermalization goes well, the minimum density should be 1016 cm3 . Advantage 1. It is very versatile and applicable to any atom or molecule, since it only relies on elastic scattering cross section. 2. Cooling of the translational degrees of freedom in the buffer gas is accompanied by efficient rotational cooling. Limitation • Since the relationship of Temperature and Density, this puts a lower limit on the temperature of the buffer gas, it can be as low as 240mK! Experiment Apparatus Generation&Introduction 1. laser ablation: An intense laser pulse illuminates a solid precursor target causing evaporation and fragmentation of the precursor molecules. (a)it usually lacks specificity and unwanted species including clusters often form as by-product. (b)the yield of the molecules of interest per ablation pulse is limited and hard to predict. (c)bring additional heat into the cryogenic cell 2. capillary filling: a thin capillary connects the low temperature buffer gas cell with a room-temperature gas supply, and molecules driven into the cell due to supply pressure. Generation&Introduction This method only have very limited applications since only stable molecules with high vapor pressures can survive the trip along a thin cold channel without condensing or recombining. 3.A novel loading technique:molecular beam loading. A molecular from a room temperature source is injected into a cryogenic buffer gas cell, this loading technique is quite mature and it is also possible to remove unwanted byproducts in the beam by introducing standard electrostatic or magnetic filters. Effect of buffer-gas density The loading process is sensitive to the density of the buffer gas. 1.Density too low: molecules are not thermalized 2.Density too high: (a)the molecules will thermalize too close to the cell entrance and will stick to the front cover. (b)Also, the buffer gas will scatter the molecules and diminish their flow into the cell. Effect of buffer-gas density The dependence of the number density of the Rb atoms loaded into the buffer-gas cell on the buffer-gas density. The absorption signal, which is proportional to the Rb number density, is measured at the center of the cell. The peak is 1 .2 m3 about 1 0 c 16 Effect of buffer-gas density 1 For an effusive flow at Temperature T, the flux is 0 n0 v0 A0, 4 A0 the oven orifice surface area, n0 the Rb number density in the kT is Oven, v 8B 0/ M the average Rb velocity 0 Therefore in the absence of buffer gas the Rb beam intensity is I 0 , L is the distance between the oven orifice and the cell 2 L 0 2 c I xe aperture. Due to the existence of buffer gas, I e [ n 0 p H ] nHe is the average He number density, the effective length over which scattering occurs, the Rb-He scattering cross section.The. number of thermalized Rb atoms in the cell is given By N i e pn ]Nin Ic A R NA b n, e n [ H H x B e c 3 2 H Ac is the cell aperture surface area. A 3cIV301 V/3 ne 01 A 2 v 0 / v Effect of buffer-gas density The measured optical density : R Na c b c / ( n e ( x H] p e D V H) [ n ) b e 10c The n 11 a mx 6 1 3 He . m The value of B corresponds to n e /n e 2 ,assuming 1 , 1m H H 0 c n 2 m Is consistent with estimates for the pumping speed for He within the region shielded by the charcoal cup. Effect of Oven Temperature Condition:cell temperature 4.2K He buffer-gas number density 1 6c D can be well fitted 2 3 . 0 m 11 () '( 2 by D TTTT / T P 0 '1 0 0 ) 2 Kt r .5 / or The Rb flux could be further increased by increasing the oven temperature.! Thermalization The thermalization was determined from the measured absorption line Shapes, this graph shows the sample spectra of Rb in the cell with and without buffer gas. The temperature of cell 4.3 0.1K,buffer-gas density 1 06c oven temperature 2 01 oC 1 .5 m3 1 7 0 Several effects contribute to the total linewidth, such as pressure, intensity, and Doppler broadening Thermalization For the Rb atoms in the buffer-gas cell, the Doppler broading is in fact an accurate measure of the atom’s temperature. The Rb temperature obtained from the fit is 4.3 0.3K Using T / p / ( T e lT ' T 1 (/)1)xl In order for the Rb temperature to fall within 5% of T=4K, the Rb atoms have to undergo about 100 collisions. In the course of the thermalization, the Rb atom will move over N a distance LN assuming a Rb-He cross section 0 n 2.5 m nHe L 0 c at ne 06c ,this is consistent with the observations: N .2 m H m 1 3 1 the probed region is about 10mm downstream from the cell entrance where we find the Rb atoms thermalized. Summary Buffer-gas cooling is a very simple and versatile technique, it is based on the thermalization of the species and the buffer-gas. The fundamental limitation lies in the relationship of the temperature and number density of the buffer gas. In the experiment, the Rb atoms are cooled to the expected temperature and the behaviour of thermalization agree with the simulation quite well.
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