Chap——9

average force that slows the atom down.
The magnitude of this scattering force equals the rate at which the absorbed photons impart momentum to the atom :
Figure(c) shows a real solenoid the field changes gradually.
9.2.1 Chirp cooling
The laser frequency was changed to keep track of the Doppler shift as the atoms slowed down.
Atoms in a gas move in all directions and to reduce their temperature requires laser cooling in all three directions by the configuration of three orthogonal standing waves .
Chapter 9 Laser cooling and trapping
Contents
• • • • • • • • • • 9.1 The scattering force 9.2 Slowing an atomic beam 9.3 The optical molasses technique 9.4 The magneto-optical trap 9.5 Introduction to the dipole force 9.6 Theory of the dipole force 9.7 The Sisyphus cooling technique 9.8 Raman transitions 9.9 An atomic fountain 9.10 Conclusions
The trace shows the experimentally observed fluorescence from the atoms as the laser frequency was scanned over a frequency range greater than the initial Doppler shift of the atoms in the atomic beam .
Fscatt＝( photon momentum ) x ( scattering rate ) The scattering rate (9. 2)
Rscatt
2 2 2 2 2 2 2 4
(9 .3)
The frequency detuning from resonance
The idea that radiation has momentum ( and energy ) which follows from the conservation of momentum that when an object absorbs radiation its momentum changes. The force equals the rate at which the light delivers, therefore radiation of intensity I exerts a force on area A given by
amax
Fmax k r M M 2 2
d dv a dt dx
(9 .5)
the atom decelerates at a rate (9 .6)
Integration gives the velocity as a function of distance
William Phillips and co-workers used the ingenious method shown in figure.
The atomic beam travels along the axis of a tapered solenoid, the Zeeman effect of the varying magnetic field perturbs the atomic energy levels is that the transition frequency matches a constant laser frequency.
(a) “optical molasses “is the name given to the laser cooling technique that uses the configuration of three orthogonal pairs of counter-propagating laser beams along the Cartesian axes. ( b ) The laser beams are derived from the same laser and have a frequency that is slightly below the transition frequency between the two atomic levels 1 and 2.
9.3 The optical molasses technique
In an atomic beam the collimation selects atoms moving in one direction that can be slowed with a single laser beam.
To compensate for the change in Doppler shift as the atoms slow down from V0 to the chosen final velocity, the frequency shift caused by the Zeeman effect needs to obey the condition
0 k
The Rabi frequency and saturation intensity are related by
I I sat 22 2
so that
Fscatt
I I sat k 2 1 I I sat 4 2 2
(9 .4)
For an atom of mass M this radiation force produces a maximum acceleration that we can write in various forms as
B0
B
h0
(9.12)
Generally , it is more useful to leave the atoms with a small velocity so that they travel out of the tapered solenoid to a region where experiments , or further cooling , can be performed.
0
B B( z )

kv
(9.10)
Hence we find from eqn 9.9 that the required magnetic field profile is
z 12 B( z ) B0 (1 ) Bbias L0
For , where
(9.11)

(c) A stationary atom in a pair of counter-propagating laser beams experiences no resultant force because the scattering is the same for each laser beam , but for a moving atom.
From eqns 9.7 and 9.8 we see that during constant deceleration the velocity at distance z from the starting point is giv0
(9 .9)
Figure (a) shows the field profile for ω≈ω0 and Bbias≈0，so that the maximum field at the entrance to the solenoid is about B0. Figure (b) shows the field profile for a different choice of Bbias that requires a lower magnitude of the field .
This imbalance in the forces arising from the Doppler shift can be written as
Fmolasses Fscatt ( 0 k ) Fscatt ( 0 k ) F F Fscatt ( 0 ) k Fscatt ( 0 ) k F (9.15) 2 k
Frad
IA c
(9.1)
Lasers produce well-collimated monochromatic beams of light that can slow atoms in an atomic beam
Each absorbed photon gives the atom a kick in the direction opposite to its motion and spontaneously-emitted photons go in all directions, so that the scattering of many photons gives an
2az
2 0 2
(9 .7)
Hence the stopping distance is
L0

2 0
(9 .8)
amax
9.2 Slowing an atomic beam
The two pioneering laser cooling experiments used different methods to compensate for the change in Doppler shift as the atoms slowed down.
This Doppler shift brings the light closer to resonance with the atom and thereby increases the rate of absorption from this beam. This leads to a resultant force that slows the atom down. Expressed mathematically, the difference between the force to the right and that to the left is
The Nobel Prize in Physics 1997
Steven Chu
Claude Cohen-
William D. Phillips
Tannoudji
For development of methods to cool and trap atoms with laser light
9.1 The scattering force