Buffer Gas Cooling of atomic and molecular beams

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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 and T’ is the temperature of the buffer gas and
initial temperature of the species.

(')/
T T T

 
2
( )/2
Mm mM

 
Basic idea


Then we can get the differential form of this equation:





Solve this equation,give the results:





In order to promise that thermalization goes well, the
minimum density should be


.

( )/
l l
dT TT

 
/('/1)exp(/)1
l
TTTT l

  
16 3
10
cm

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

about



16 3
1.2 10
cm


Effect of buffer
-
gas density

For an effusive flow at Temperature T, the flux is


the oven orifice surface area, the Rb number density in the

Oven, is the average Rb velocity

Therefore in the absence of buffer gas the Rb beam intensity is


, L is the distance between the oven orifice and the cell

aperture. Due to the existence of buffer gas,


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 ,


is the cell aperture surface area.







0 0 0 0,
1
4
n v A
 
0 0
8/
B
v kT M


0
0
2
2
I
L



0
exp[ ]
c He
I I n

 
0
A
0
n


He
n
in c c
N I A

.
exp[ ]
in
Rb He He
NNAn Bn
 
 
c
A
2/3 1
0
3
He
V nv
 


2/3 1
0 0
3
c
A AIVv



Effect of buffer
-
gas density

The measured optical density


The

The value of B corresponds to


,assuming

Is consistent with estimates for

the pumping speed for He

within the region shielded by

the charcoal cup.




/( )exp[( )]
Rb He He
DNVanc bnc

:
max 16 3
1.110
He
n cm

  
/20
He He
n n

2
1,1
cm nm

 
Effect of Oven Temperature

Condition:cell temperature 4.2K

He buffer
-
gas number density


D can be well fitted

by


The Rb flux could be further

increased by increasing the oven

temperature.!


16 3
1.2 10
cm


0
1/2
0'0
() (')
TT
DT PTT



 
2.5/
Ktorr


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 ,buffer
-
gas density


oven temperature


Several effects contribute to the total

linewidth, such as pressure, intensity,

and Doppler broadening

4.3 0.1
K

270 10
C

o
16 3
1.510
cm


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


Using


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

a distance assuming a Rb
-
He cross section


at ,this is consistent with the observations:

the probed region is about 10mm downstream from the cell

entrance where we find the Rb atoms thermalized.




4.3 0.3
K

/('/1)exp(/)1
l
TTTT l

  
N
He
N
L
n


2
0.5
nm


0.2
N
L cm

16 3
10
He
n cm


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.