January 10, 2011 / Vol. 9, No. 1 / CHINESE OPTICS LETTERS 010201-1
Maximized cooling efficien cy for a Zeeman slower operating
at optimized magnetic field profile
Zhuanxian Xiong (
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)
1,2
, Yun Long (
999
)
1,2
, Huixing Xiao (
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1,2
, Xi Zhang (
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)
1,2
,
Lingxiang He (
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)
1
, and Baolong L¨u (
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999
)
1∗
1
State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics,
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
2
Graduate University of the Chinese Academy of Sciences, Beijing 100049, China
∗
Corresponding author: baolong lu@wipm.ac.cn
Received June 17, 2010; accepted August 20, 2010; posted online January 1, 2011
We build a Zeeman slower with consecutive coils and use it to load an Yb magneto-optical trap (MOTs).
Cooling efficiency is measured by the fluorescence inten sity of the atomic cloud trapped by the MOT.
An optimized magnetic field p rofile can acquire the maximum cooling efficiency, corresponding to a good
compromise between the smaller magnetic field mismatch and the high capture velocity. Our studies
provide useful information on how the performance of the Zeeman slower can be improved.
OCIS codes: 020.3320, 020.7010, 020.7490.
doi: 10.3788/COL201109.010201.
The Zeeman slower was first developed by Phillips
et al. in 1982
[1]
. It is more effective in creating slow
atomic beams than other methods based on frequency
chirping
[2]
, frequency sweeping
[3]
, broadband lasers
[4−6]
,
and so o n. It has been widely used as a pre-cooling
stage in magneto-optical traps (MOTs). Certain metal
elements employed in optical clocks, such as Sr and
Yb
[7−14]
, which have very low vapor pressures at room
temper ature, cannot be trapp ed dir e ctly by a MOT. In
such a case, a Zeema n-slowed atomic beam is usually
the only choice to obtain a high flux of slow atoms for
subsequent laser co oling. To produce the desired mag-
netic field profile, a tapered coil is normally adopted in
a Zeeman slower
[1,15]
. It needs only one current supply;
however, the magnetic coil requires precise design and
construction for the optimal performance. Recently, a
Zeeman slower based on magnetic dipoles and composed
of an array of compact discrete neodymium magnets was
proposed by Ovchinnikov
[16,17]
. This slower needs no cur-
rent; however, it has the same limitations as the tapered
coils. Dedman et al. performed deta iled theoretical cal-
culations of the magnetic field profile for a slowing light
beam with non-uniform intensity distributions. Gener-
ally, precisely determining the optimal magnetic field
profile is difficult because atomic cooling depends upon
many other factor s, such as the alignment and the spa-
tial distribution of the slowing light beam. A novel type
of Zeeman slower with consecutive coils was first demon-
strated by Harris
[18]
. Although independent current con-
trols for each coil make this system quite complicated, it
is simpler to build. More importantly, it provides flex-
ibility to optimize the magnetic field profile to acquire
maximized cooling efficiency.
In this letter, we inves tig ate how to improve the cooling
efficiency of a Zeeman slower by considering the imperfec-
tion of its magnetic field distribution. We use a Zee man
slower made of consecutive coils to load an Yb MOT . The
cooling efficiency of the Zeeman slower is increased by op-
timizing the magnetic field distribution. We first give a
brief introduction of the principle of a Zeeman slower,
and then provide a description of our Zee man slower, as
well as an analysis to the effect of the magnetic field dis-
tribution. We also present experimental obse rvations to
support our analysis.
In a Zeeman slower, a red-detuned laser beam is guided
to counter-propagate against the atomic beam. A spa-
tially varying magnetic field produces a varying Zeeman
shift to compensa te the changing Doppler shift of the
atoms. The radiation force acting o n an atom is given
by
[15]
F =
¯hkΓ
2
s(z)
1 + s(z) + 4∆
2
eff
/Γ
2
, (1)
where ¯h is the Plank’s constant divided by 2π, k is the
wave vector, Γ is the linewidth of transitio n, s(z) is the lo-
cal saturation parameter along the ax is of Zeeman slower,
and ∆
eff
= δ
0
+ kv(z)–µ
′
B(z)/ ¯h is the effective detuning,
which includes both the Doppler shift and the Zeeman
shift. Here, δ
0
is the laser detuning, v(z) is the velocity
of the atoms, and µ
′
is the magnetic moment. If a moving
atom is in resonance with the slowing laser (i.e., ∆
eff
=
0), the magnetic field distribution B(z) of the Zeeman
slower can be written as
B(z) =
¯h
µ
′
δ
0
+
v(z)
λ
, (2)
where λ is the wavelength of the slowing laser. Accord-
ing to Eq. (1), the maximum deceleration rate a
max
=
¯hk Γ/2m (m is the atomic mass) can only be reached in
the resonant case and at infinite intensity of the laser
light. In practice, only a fraction of the ma ximum decel-
eration rate, a = η a
max
, is used in the design of a slower.
Thus, a higher maximum velocity v
max
requires a higher
peak magnetic field to co mpensa te for the large r Doppler
shift. The dista nce over which slowing takes place is sim-
ply given by L = (v
2
max
− v
2
f
)/(2a), where v
f
is the desired
final velocity at the exit of the slower. The velocity as a
1671-7694/2011/010201(4)
c
2011 Chinese Optics Letters