Buffer Gas Cooling of atomic and molecular beams by tm8v5N1D

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									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 cm3
      .
                  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 xe 
 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
                     
           10c
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 01 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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