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Laser Cooling and Trapping
Cooling Atoms With Light
Scattering (Radiative) Force
dp h p ˆ
F
A
dt
c
Velocity Change
• The momentum
transfer during
absorption will cause
the atoms to change
velocity
• The photon frequency
must be
approximately equal
to the atoms’
resonance frequency
h
v
cm
1
2
Doppler Shift
• The required frequency is
dependent on the atoms’
velocity due to Doppler shifts
• For atoms heading into the
laser beam, the photons are
blue-shifted, while for atoms
moving with the laser, the
photons are red-shifted.
• As atoms slow, the Doppler
shift and thus the required
frequency changes
• Only atoms moving toward the
laser will be slowed; thus, two
counterpropagating beams are
needed (in 1D)
v
D
c
Dipole Forces
• When δ>>γd, spontaneous
emission may be less frequent
than stimulated emission. The
dipole force is the force arising
from stimulated emission
• The light shift is the Stark shift
due to the electromagnetic
wave’s electric field
• In a standing light wave, the
light shift varies sinusoidally.
Atoms are excited by one
beam and stimulated into
emission (thus slowing them)
by the other
Dipole Forces (cont)
p
s0 d
2
2 1s0 D
d
2
2
H *
0
2
ls
2
2
2
p
s0
2
2
2 ps0
ls
4
8
Fx
I x
8Is
2
d
Dipole Optical Traps
• For a Gaussian beam, the2
r
d I0 r w
transverse force is F 4 I w 2 e
s
0
• At sufficiently large detuning,
atoms will spend little time in the
longitudinally repelled state, thus
atoms will be trapped both
transversely and longitudinally
• Trap depth is proportional to the
square of the beam’s waist width
0
2
Optical Traps – Scattering Force
• Six
counterpropagating
lasers can be used to
trap atoms
• Optical Earnshaw
theorem precludes
such a trap from
being stable so long
as the trapping force
is proportional to light
intensity
P 0
F 0
F nˆ dS F dV 0
S
V
Optical Molasses
Magnetic Trapping/Cooling
• Laser cooling can only cool up to a
certain limit. Below it, purely
magnetic traps are necessary
• With a positive magnetic moment,
the atom is forced toward higher
potentials (high-field seekers); with a
negative moment, the atom is forced
toward low potentials (low-field
seekers)
F B
Magnetic Traps – Quadrupole Trap
• Field at the center is zero,
and will trap low-field
seekers
• Time varying magnetic
fields cause state
changes, transforming
the atom from a low-field
to a high-field seeker,
thus causing losses
through the zero point of
the field. Loss rate is
approximately hN/2πml2
B 2 4z 2
Magnetic Traps – TOP trap
• A rotating uniform
field is superimposed
on the quadrupole
field, changing the
location of the zero
point faster than the
atoms can respond
• The field rotates at a
frequency ωb, chosen
to be smaller than the
Larmor frequency
U b
2
2 / b
0
U(t)dt Bb
Bg2
4Bb
2
8z 2 ....
Magnetic Traps – Ioffe trap
• Another possibility to
avoid holes: use a
trap with a nonzero
minimum
• The bars create a
local minimum at the
center and transverse
confinement U A r l P z
2 2
B(, , z) 3A 3z, 0, A1 3A 3 z
2
2
2 2 C 2 2
2i
* 2i
B A1 3A3 z
U
Ce C e
2 2A1
2
2
l
l
C 3A1A 3
Magnetic-Optical Trap (MOT)
• A MOT uses a combination of
lasers and magnetic fields to
trap and cool atoms
• At z>0, the transition frequency
to the m=-1 frequency
approaches the laser
frequency; atoms moving to
the left have a higher
probability of absorbing a
photon from the beam
propagating to the left, moving
them to the center
• The net force is approximately
linear, of the form F=-kz
• Many variations
Mirror MOT
• Two lasers are
reflected off a mirror
• For an atom in the
path of the beam,
each of these lasers
serves as two
counterpropagating
lasers
• MOT uses four lasers
in total
Doppler Limit
• As the velocity of
atoms decrease, so
does the cooling rate
• At the Doppler
temperature, random
momentum kicks
caused by photon
emission counteract
further cooling
TD
2k B
Sisyphus Cooling
• For two lasers with
perpendicular linear
polarization, the magnitude of
the electric field potential
varies sinusoidally, with
maxima and minima having a
periodicity of λ/8.
• Atoms must traverse an
increasing potential until
reaching the “hilltop” (where
the polarization is circular, with
alternating polarization), where
they are pumped into the other
sublevel
• Thus, the atoms keep loosing
kinetic energy
Limit of laser cooling
• All methods involve the
absorption and emission
of photons by atoms.
• At very low temperatures,
the “kick” caused to an
atom by photon emission
is large enough relative to
the atom’s velocity to
prevent cooling.
• The minimal temperature
is known as the recoil
limit.
Tr
h
m
2
Evaporative Cooling
• Evaporative cooling involves cooling an
ensemble of trapped particles by allowing the
higher-energy particles to escape from the trap.
• Mutual collisions cause the remaining particles
to achieve a new, lower mean temperature.
• The trap depth is further reduced, allowing the
particles at the high-energy end of the new
distribution to escape, and the process repeats.
• Inelastic collisions may cause the atom to shift to
a non-trapped state; thus, the lower cooling limit
is dependent on the ration of elastic to inelastic
collisions.
Evaporative Cooling (cont)
Further Reading
•
•
•
•
Metcalf, H.J, van der Straten, P. (2003) Laser
Cooling and Trapping of Neutral Atoms,
Journal of the Optical Society of America B,
volume 20, 887
BGU Atom Chip group’s site
(http://www.bgu.ac.il/atomchip/)
Nobel Prize site (physics, 1997)
(http://nobelprize.org/physics/laureates/1997/in
dex.html)
University of Colorado’s Physics 2000 site
(http://www.colorado.edu/physics/2000/bec/las
cool1.html)