Lee96

August 1, 1996 / Vol. 21, No. 15 / OPTICS LETTERS 1177
Single-beam atom trap in a pyramidal
and conical hollow mirror
K. I. Lee, J. A. Kim, H. R. Noh, and W. Jhe
Department of Physics, Seoul National University, Seoul 151-742, Korea
Received January 29, 1996
We present a novel and simple magneto-optical trap in pyramidal and in conical hollow mirrors, using a single
beam. A diode laser having modulation sidebands at microwaves is used for cooling, trapping, and repumping
of rubidium atoms in a vapor cell. When the laser is circularly polarized and sent into the hollow region,
three pairs of counterpropagating beams are automatically produced therein that have the same polarization
configuration as that of a conventional six-beam magneto-optical trap. The f luorescence by the trapped
atoms and its mirror image are observed simultaneously. This system may be useful for atom-manipulation
applications such as gravitational atom traps and atom waveguides. © 1996 Optical Society of America
In the past decade there have been many advances
in laser cooling trapping of neutral atoms with a
frequency-stabilized semiconductor laser. 1 Among
the exciting developments has been the discovery
of sub-Doppler cooling in both optical molasses and
the magneto-optical trap (MOT). 2 Many novel techniques
have been demonstrated that produce samples
of laser-cooled atoms, but the MOT is being widely
used in many applications such as studies of cold
collisons, high-resolution spectroscopy, and nonlinear
optics. 3 Recently Bose–Einstein condensation was
also observed with the MOT as a precooled atom
source. 4
The MOT is a spontaneous-force optical trap consisting
of a spatially nonuniform magnetic field and three
orthogonal pairs of counterpropagating laser beams
having opposite angular momentum. In a cookbooktype
study that describes how to build a conventional
six-beam vapor-cell MOT 5 the authors discussed how
to set the proper circular polarizations of the three
incident beams. In the MOT the orientations of the
respective polarizations are determined by the orientation
of the magnetic-field gradient coils. The longitudinal
beam that propagates through the cell along
the coil axis should have opposite circular polarization,
whereas the two transverse beams that propagate
perpendicular to the axis should have the same circular
polarization, as shown in Fig. 1(a). A straightforward
way to obtain such a polarization configuration
would be to use six commercial quarter-wave plates,
but a cheaper option would be to replace the three retro
quarter-wave plates with three retroref lecting rightangle
mirrors.
In this Letter we present a novel and simple
vapor-cell MOT in pyramidal and in conical hollow
mirrors. The experimental configuration is shown
in Fig. 2. For the laser source we use a frequencymodulated
diode laser with its microwave sideband
used for hyperfine repumping. 6,7
In this setup a
single wide laser beam is incident upon the entire hollow
region, in which three sets of counterpropagating
beams are automatically produced. With respect to
their polarization configurations, let us first consider
the simple case of Fig. 1(b), in which the longitudinal
cross section of the pyramidal and the conical mirror is
shown. When the incident laser is s polarized, each
ref lection from the two sides of the mirror generates
two counterpropagating transverse beams with opposite
polarizations. Moreover, a retroref lected beam
is generated as a result of the two ref lections of the
incident beam by the two sides, and its polarization
Fig. 1. (a) Polarization configurations for a conventional
six-beam MOT having three pairs of counterpropagating
beams. (b) Polarization configurations in a pyramidal (or
conical) hollow mirror, when a single circularly polarized
light beam is incident. Note that laser configurations
similar to those in (a) are automatically produced in our
novel system so that atoms can be trapped.
0146-9592/96/151177-03$10.00/0 © 1996 Optical Society of America

1178 OPTICS LETTERS / Vol. 21, No. 15 / August 1, 1996
Fig. 2. Experimental setup. A single diode laser, which
is frequency stabilized and frequency modulated at
2.91 GHz, is used to trap 85 Rb atoms. The pyramidal or
conical mirror is placed inside a glass-cell vacuum chamber,
and a movable anti-Helmholtz coil is used for trapping.
becomes opposite that of the incident beam. Therefore
at any point in the pyramidal hollow region there
always exist three pairs of counterpropagating beams
with the same polarization configuration as in a
conventional MOT. On the other hand, for the conical
hollow there exist innumerable concentric pairs of
counterpropagating beams in the transverse plane.
Note that, in our traps, a single incident laser beam
automatically produces all the necessary polarizations
and directions for the ref lected beams to realize the
MOT. Consequently, only one quarter-wave plate
suffices, and splitting of a laser into three pairs is not
required.
For further simplification of our setup we used a
compact extended-cavity diode laser that is frequency
stabilized by optical feedback from a diffraction grating
and frequency-modulated by a direct microwave
modulation of the bias current with commercial
yttrium iron garnet tuned oscillators. 7 Using the
single diode laser with microwave sidebands provides
much simplicity and controllability of the trapped
atoms in the MOT. For instance, we recently achieved
simultaneous trapping and spatial separation of the
two stable Rb isotopes in the MOT. 7
The schematic of the laser setup is shown in
Fig. 2. The carrier frequency of the diode laser was
red detuned to the 5S1/2, F 3 ! 5P3/2, F 0 4 cooling
transition of 85 Rb, and the modulation sideband at
2.91 GHz was tuned to the 5S1/2, F 2 ! 5P3/2,
F 0 3 line to prevent the atoms from accumulating
in the F 2 ground state. The power of the incident
laser beam was 6.5 mW, and its diameter was 2.1 cm,
so that the entire hollow region of the pyramidal
(1.7 cm 3 1.7 cm at the entrance) or the conical (2-cm
diameter at the entrance) mirror is illuminated.
We made the pyramidal hollow mirror system by gluing
four identical triangular Al-coated mirrors together
onto an Al block, as shown in Fig. 1. The angle between
the two facing mirrors was adjusted to be near
90 ± . We found that the relative phase change between
s- and p-polarization components of the incident beam
resulting from ref lection by an Al-coated mirror at an
incidence angle of 45 ± is less than 2p60 and the relative
intensity change between the two components is
4.6%. 8 Thus the resulting contamination of the polarization
of the incident circularly polarized laser
turns out to be less than 1%. Moreover, the power loss
of the light owing to ref lection from the metallic mirror
is less than 12% (the ref lectivity of the Al mirror
is greater than 88% at a 45 ± incidence angle). 9 These
imperfections in the intensity imbalance and the polarization
contamination are known to be negligibly
small, 5 so that the trap characteristics of our simple
MOT are not greatly affected. We also made a simple
conical mirror system, using an Al solid block that was
carefully polished after machining. However, it was
difficult to make the conical surface optically f lat, and
therefore the retroref lecting beams were rather scattered
and distorted. Note that using dielectric coated
mirrors will minimize the imperfections so that the
trap performances of the present pyramidal and conical
MOT will undoubtedly be improved. (We caution that
there can be significant differences in the ref lectance
of s- and p-polarized light with dielectric coated mirrors,
depending on the coating parameters.)
The pyramidal or the conical hollow mirror is
placed inside a parallelepiped glass cell (dimensions,
2.75 cm 3 2.75 cm 3 5cm) that is glued to a commercial
glass–metal tube. The laser beam impinges
upon the hollow mirror region through the glass-plate
window, and the f luorescence from the trapped atoms
is observed through the same window with a CCD
camera or a photomultiplier at a slightly oblique
angle. An anti-Helmholtz coil (4 cm in diameter and
separation) is placed along the laser beam direction
outside the glass cell, producing a linear field gradient
of 10 Gcm at 1 A. It is mounted upon an x–y
translator so that the field-minimum position, where
the atoms are trapped, can be easily changed in the
hollow region.
In Fig. 3 a CCD image of the f luorescence by the
trapped atoms in the pyramidal hollow mirror and
its descriptive schematic are presented. The atom
f luorescence is shown as a bright spot on the righthand
side. Note that the f luorescence shown on the
left-hand side is the mirror image that is due to
ref lection of the atom f luorescence by the rear mirror.
By moving the field-minimum position of the magnetic
coil within the hollow region we could freely move the
trapped atoms therein. However, we could not see the
trapped atoms at the center and near the side edges
of the pyramid because of light scattering and mirror
imperfections.
We measured the number of trapped atoms by detecting
the trap f luorescence with a photomultiplier tube
(Hamamatsu R928). Under our optimized experimental
conditions of 7.2-Gcm magnetic-field gradient and
13-MHz red detuning, corresponding to 22.2G for the
given trapping laser intensity of 1.9 mWcm 2 (0.6% of
the carrier intensity for the repumping sideband) in
the hollow region (1.7 cm 3 1.7 cm at the entrance),
we estimate the number of the trapped atoms to be
1.2 3 10 7 after careful calibration of the detection
efficiency. The loading time was measured to be
400 ms at a nominal vapor pressure of 10 29 Torr, and
the size of the trap cloud was measured to be 0.7 mm
(FWHM) with a CCD array.

Fig. 3. Fluorescence by the trapped 85 Rb atoms in the
pyramidal hollow mirror trap is shown as a bright spot on
the right-hand side of the photograph and is indicated by
the arrow in the schematic. The bright spot on the lefthand
side is its mirror image resulting from the ref lection
of the atom f luorescence by the rear mirror.
Note that, in a typical MOT, 3 3 10 7 atoms
were trapped with a similar microwave-modulated
diode laser (2.2% of the carrier for the sideband), 6
and 4 3 10 7 atoms were also typically trapped (with
7-mW power and a 1.5-cm-wide beam) with a separate
repumping laser. 5 Therefore our smaller number of
trapped atoms may be attributed not only to the fact
that the volume of the laser-overlap region (i.e., the
volume of the pyramidal hollow), which determines
the capture velocity and thus the number of trapped
atoms, 5 is six times smaller than that of the typical
MOT but also to the smaller intensity of the repumping
laser. A detailed numerical analysis will be needed for
quantitative comparison and is now under way.
In addition to the pyramidal trap, we also trapped
atoms in the hollow region of a cone-shaped mirror
(axicon mirror) system. In this case there are no edge
problems as there were with the pyramidal trap, and
trapping is possible near the symmetric mirror axis.
The polarization configurations are also automatically
satisfied, as in the case of the pyramidal trap. Moreover,
the cooling and trapping forces are present in all
the radial directions at a given position along the mirror
axis, so that the optical forces are expected to be
enhanced compared with those of the pyramidal trap.
Note that a similar mirror, but with a much larger hole
near the apex, was used to focus an atomic beam passing
through the hole by the two-dimensional optical
dipole forces. 10 We observed the f luorescence by the
trapped atoms in the conical hollow, using the same
single-diode-laser system as in the pyramidal case.
The exact number and the dimensions of the trapped
cloud were, however, difficult to measure because the
image was somewhat distorted, mainly as a result of
the roughness of the conical surface.
August 1, 1996 / Vol. 21, No. 15 / OPTICS LETTERS 1179
Because of its simplicity and controllability the
single-beam atom trap realized in a pyramidal or conical
hollow region may be ideal for other elaborate experiments
such as those involving atom waveguides 11,12
or gravitational atom traps. 13,14 A similar pyramidal
or conical hollow system using uncoated mirrors can
also be employed for cooling and trapping resulting
from evanescent waves near the surface for the possible
realization of Bose–Einstein condensation, as
suggested in Ref. 13. Since it offers much convenience
and f lexibility in the manipulation of trapped atoms
within the interesting hollow region, our novel and
simple single-beam MOT can easily be used as a precooled
funneled atom source for these experiments,
which are currently under way.
The authors acknowledge helpful discussions with
Y.-Z. Wang. This study was supported by the Korean
Science and Engineering Foundation, the Il-Ju Cultural
Foundation, and the Ministry of Education.
References
1. C. Monroe, W. Swann, H. Robinson, and C. Wieman,
Phys. Rev. Lett. 65, 1571 (1990).
2. E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D.
Pitchard, Phys. Rev. Lett. 59, 2631 (1987).
3. J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J.
Kimble, Phys. Rev. Lett. 66, 3245 (1991).
4. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E.
Wieman, and E. A. Cornell, Science 269, 198 (1995).
5. C. E. Wieman, G. Flowers, and S. Gilbert, Am. J.
Phys. 63, 317 (1995); K. Lindquist, M. Stephens, and
C. Wieman, Phys. Rev. A 46, 4082 (1992).
6. C. J. Myatt, N. R. Newbery, and C. E. Wieman, Opt.
Lett. 18, 649 (1993); P. Feng and T. Walker, Am. J.
Phys. 63, 905 (1995).
7. H. R. Noh, J. O. Kim, D. S. Nam, and W. Jhe, Rev. Sci.
Instrum. 67, 1431 (1996).
8. D. R. Lide, ed., Handbood of Chemistry and Physics,
74th ed. (CRC, Boca Raton, Fla., 1994), Chap. 12.
9. M. Born and E. Wolf, Principles of Optics, 5th ed.
(Pergamon, Oxford, 1975).
10. V. I. Balykin and A. I. Sidorov, Appl. Phys. B 42, 51
(1987).
11. W. Jhe, M. Ohtsu, H. Hori, and S. R. Friberg, Jpn.
J. Appl. Phys. 33, L1680 (1994); H. Ito, K. Sakati, T.
Nakata, W. Jhe, and M. Ohtsu, Opt. Commun. 115, 57
(1995).
12. M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson,
C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 75,
3253 (1995).
13. J. Söding, R. Grimm, and Yu. B. Ovchinnikov, Opt.
Commun. 119, 652 (1995).
14. J. P. Dowling and J. Gea-Banacloche, Phys. Rev. A 52,
3997 (1995).