Atom manipulation using atomic de Broglie waves
J. Fujita a,*, F. Shimizu b
a NEC Fundamental Research Laboratories, 34 Miyukigaoka, Tsukuba 305-8501, Japanb Institute for Laser Science and CREST, University of Electro-Communications, Chofu-shi, Tokyo 182-8585, Japan
Abstract
We demonstrated several techniques to manipulate laser-cooled Ne atoms interferometrically by using a silicon nitride film with
holes and electrodes. Laser-cooled neon atoms passed through a computer-generated through-hole binary hologram and generated
an atomic image on a substrate. The hologram can be designed to provide a spherical phase correction, where the reconstructed
pattern is focused on the substrate at a finite distance from the hologram. A resolving power over 150 was achieved. This type of
holographic manipulation can be further developed extended to reconstruct gray-scale patterns, which can be used to deposit a
relief-like 3D atomic pattern on surfaces. Unlike photons, atoms interact with electric, magnetic, and optical fields. This enables a
holographic atomic-wave manipulation to perform functions that are difficult for a light wave. We also demonstrated using a Stark
shift induced by an external electric field to switch and modify atomic patterns in real time. We also discuss how to develop reflective
interferometric devices by using quantum reflection.
# 2002 Elsevier Science B.V. All rights reserved.
Keywords: Strak shift; Atom; Quantum reflection
1. Introduction
Manipulating neutral atoms is not an easy subject
because their interaction with external fields is relatively
weak. In the past only the deflection of atomic beams in
an inhomogeneous magnetic field was achieved. How-
ever, the development of laser cooling atoms has
changed this situation considerably. Slow atoms change
their trajectory even with a weak force. In the last 15
years various manipulation techniques have been devel-
oped that use electric, magnetic, microwave, and optical
fields. The first interferometric manipulation of atoms
was demonstrated by Gould et al. [1], who diffracted a
sodium atomic beam through a transmission-type grat-
ing made of a silicon nitride film with regularly spaced
slits. Similar experiments were conducted by several
groups by using a standing wave of coherent light.
Carnal et al. [2] constructed the Fresnel lens for use as a
more general purpose atom�/optical element; however,
its efficiency was not proven sufficient for practical
application. We developed the most general technique to
manipulate neutral atoms interferometrically by using a
binary hologram made of a thin film. This paper
describes various holographic atom manipulation tech-niques that we developed in the last 5 years [3�/6]. We
also discuss a new type of surface reflection that can be
applied to reflective interferometric elements [7].
2. Holographic manipulation of atoms
Holography is a simple but powerful technique to
manipulate atomic waves. An atomic wave is trans-
mitted through the hologram, which encodes the
amplitude and the phase of the wave to produce a pre-designed pattern of the atoms on a screen distant from
the hologram. The screen can be any curved surface.
With an appropriately designed hologram transmission
function, the information of each point in the atomic
image on the screen can be spread over the entire
hologram, which makes the reconstructed image im-
mune to local defects of the hologram. When the
hologram is illuminated by a time-independent atomicbeam emitted from a point source, the amplitude of the
atomic wave on the screen G (X , Y ) is obtained by
integrating the product of the hologram transmission
* Corresponding author. Tel.: �/81-298-50-1185; fax: �/81-298-56-
6139
E-mail address: [email protected] (J. Fujita).
Materials Science and Engineering B96 (2002) 159�/163
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PII: S 0 9 2 1 - 5 1 0 7 ( 0 2 ) 0 0 3 1 0 - 0
function T (x , y) and the accumulated phase along the
classical path of the atom from the source to the screen
f(X ; Y ; x; y)� gclassical path
p
hdl
over the hologram coordinates (x , y). The transmission
function T (x , y) is obtained by solving the integralequation.
G(X ; Y )�g T(x; y)exp(�if)dxdy
When the distances from the source to the hologram
and from the hologram to the screen are large compared
with the hologram and screen sizes, f can be expanded
in power series of X , Y , x , and y and approximated
with their quadratic function. Then, T (x , y ) is obtainedsimply by a Fourier transformation of G (X , Y ) multi-
plied by a spherical phase factor, which can be
calculated by an FFT algorithm.
In all experiments described below the atomic point
source was metastable neon atoms in the 1s3 state, which
were obtained from a tight magneto�/optical trap of
neon atoms in the 1s5 state by optical pumping. The
typical source diameter was 100 mm, and the tempera-ture was 200 mK. The hologram was a 100-nm thick
silicon nitride membrane with holes, which functioned
as a binary amplitude hologram. The screen was a
micro-channel plate (MCP) detector equipped with
fluorescent plate that detected individual atoms with a
30-mm two-dimensional spatial resolution. The source,
the hologram, and the MCP were aligned along a
vertical line to minimize the non-axially symmetricaberration caused by gravity acceleration (Fig. 1).
In the actual experiment the pattern of the hologram
was obtained by using the following method. First,
relevant areas of both the hologram and the image plane
were divided into 2N by 2N square pixels. The amplitude
of the image G (Xm , Yn ) at each pixel point (m , n ) was
the product of the square root of the intensity of the
designed pattern and a random phase factor ex-
p(ifrand(m , n)). The random phase factor disperses the
information on each pixel point of the screen over the
entire hologram. This is equivalent to making the object
optically diffusive. Next, T was calculated by Fourier
transformation using an FFT algorithm. Finally, the
complex amplitude T (xj, yk) at each hologram pixel was
approximated by a set of binary values to determine the
hole pattern (Fig. 2). Since this procedure produced an
amplitude hologram, the image was always accompa-
nied by a conjugate image and a pattern of the non-
diffracted beam. The latter typically had the shape of the
hologram area. The conjugate image was focused on a
plane above the hologram and was usually out-of-focus.
Since we divided the hologram plane with a regularly
spaced mesh, theoretically, nearly identical three-images
sets appeared repeatedly on the image plane. The actual
number of sets reconstructed on the screen depended on
the angular diveregence of the atoms diffracted from the
hologram, which was inversely proportional to the size
of the hole.
In the first atom holography experiment [3], the
complex number T (xj, yk) was expressed by holes 1/4
of the pixel length dpx. As a result, four image sets with
approximately equal intensity appeared on the screen.
To concentrate nearly all atoms to a single set requires
setting the hole length dh equal to that of the pixel. To
achieve this, each complex number T (Xj, Yk) must be
approximated by either 1 or 0. The simplest coding
method that satisfies this requirement is to set a thresh-
old tth. The holes open on the pixels that satisfy the real
part of T larger than tth, RT (xj, yk)�/tth. The choice of
tth changes the ratio of the open area to that of the entire
hologram. In the following examples the ratio was
typically 20%.
Figs. 3 and 4 show holographically reconstructed
atomic patterns with the parameter dh�/dpx. In both
Fig. 1. Schematic diagram of experimental setup. The atomic source,
hologram, and screen of micro-channel-plate (MCP) were placed
vertically. Fig. 2. Scanning electron microscope image of a part of the hologram.
J. Fujita, F. Shimizu / Materials Science and Engineering B96 (2002) 159�/163160
examples the number of pixels along a 2N line was 1024.
Note that, once the geometry of the optics and N were
fixed, the size of the image, and therefore, the theoretical
resolution was determined by the length dpx�/dh. We
expected the image ‘NEC’ to achieve the best resolution
(Fig. 3). We chose dpx�/400 nm to match the spatial
resolution of the MCP. The distance from the source to
the hologram and from the hologram to the MCP were
40 and 42 cm, respectively. The black square in the
middle of the figure was generated by the non-diffracted
beam. The conjugate image was out-of-focus and spread
out all over the screen. The resolution of the image was
65 mm, which agreed approximately with the value
expected from the resolution of the MCP and the size
of the atomic source. The hologram for Fig. 4 was
designed to obtain a better resolving power and
constructed the image ‘atom-Ne-c’. To spread atoms
over the entire MCP surface a smaller pixel with dpx�/
100 nm was used. Consequently, the hologram size and
the non-diffracted pattern decreased, and a slightly
blurred conjugate image appeared in the lower half of
the figure.
A binary hologram does not restrict reconstructing a
binary pattern. A continuous tone image can be
constructed as well, simply by using a continuous
amplitude for G (X , Y ). However, the number of atoms
required to construct a gray-tone pattern is much larger
than that for a binary pattern. We thus need to increase
the flux of the atomic beam or the area of the hologram.
When the image size is fixed, the pixel size dpx is also
fixed. Therefore, the number of pixels in a line increases
with the size of the hologram. This problem can be
solved by increasing the array size in the FFT calcula-
tion. Alternatively, if it increasing the resolving power isnot required, smaller-sized hologram patterns can be
pasted in a two-dimensional array to produce a big
hologram. Not all patterns need to be calculated
independently, because the translational shift of the
hologram position causes an identical phase shift for all
pixels.
Fig. 5 shows the atomic image constructed by using
this method. The figure is a part of the photograph ofMichelangelo’s statue ‘Juliano de Medici’. The unit
hologram has the lengths 2N �/1024 and dpx�/200 nm.
Sixteen units were tiled in a 4�/4 array forming a big
0.8�/0.8-mm hologram. The pattern contains 6�/106
atoms accumulated in 2 h.
3. Phase control using Stark effect
Atoms interact with external fields including electric,
magnetic, and off-resonant optical ones. These fieldscause phase shifts to the atomic waves passing through
the interaction region. A phase hologram can be
constructed that uses phase shift caused by interaction
with these fields. A phase hologram has in principle a
much higher efficiency than an amplitude one, whose
efficiency cannot exceed 10%. However, a phase holo-
graphy for atoms that has as high a quality as an optical
one is unlikely to be developed in near future, becausetargeting individual hologram pixels independently by
using an external field is extremely difficult. Never-
theless, the phase control by an external field can be
utilized for specific atom-manipulation functions. Figs.
6 and 7 show an example in which two patterns were
switched by changing the condition of electric field. In
addition, multiple exposure, a common technique used
in optical holography, was applied. When a randomphase factor was multiplied with the image amplitude
jG (Xm , Yn)j to calculate the hologram pattern, as in the
previous section, every part of the hologram recon-
structed the same intensity pattern jG j2. This not only
Fig. 3. Reconstructed image of ‘NEC’.
Fig. 4. Reconstructed image of ‘atom ne f ’.
Fig. 5. Reconstructed image of ‘Juliano de Medici’.
J. Fujita, F. Shimizu / Materials Science and Engineering B96 (2002) 159�/163 161
applies to connected areas but also for sets of randomly
selected hologram pixels. Therefore, several patterns can
be encoded on a single hologram if the random phases
for the different patterns are not correlated. Interference
between the patterns is washed out to produce an
uniform background.
Fig. 6 shows the schematics of the phase-controlled
hologram. The 0.5 mm wide electrodes were deposited in
parallel onto the silicon nitride film with a 1 mm
periodicity. The hologram pattern was then encoded
by opening holes in the 0.5-mm wide gaps between the
electrodes. Each electrode was randomly connected to
one of two terminals. When a finite potential was
applied between the two terminals, atoms that passed
through half of the gaps (gaps A) felt the electric field
and caused a phase shift on their wavefunction, while
for the remaining gaps (gaps B) the wavefunction was
not affected. We encoded two patterns, ‘f ’ and ‘p ’, on
the hologram with two different conditions. For pattern
‘f ’ a hole was opened on the pixels that satisfy RT �/0
in all gaps. For pattern ‘p ’ a hole was opened on gap-A
pixels satisfying RT B/0, and on gap-B pixels satisfying
RT �/0. The reconstructed image is shown in Fig. 7. In
the upper image the potential between the two terminals
was zero. The pattern ‘f ’ was reconstructed on the
screen, because the coding formula was the same as thatfor the standard hologram. For pattern ‘p ’ the con-
tributions from gaps A and B were canceled because the
hologram amplitude in the open pixels had opposite
signs. When the potential to produce a p phase shift in
the A gaps was applied, the situation was reversed. In
the lower image the pattern ‘p ’ was reconstructed
because the phase shift of p for the holes in gap A
reversed the sign of the wavefunction when the atompassed through a hole, and all contributions added to
the construction.
4. Quantum reflection
We conducted several atom-manipulation experiment
that used binary transmission type holograms. Although
this technique can be used for general manipulation, the
thin film lacks the stability of an interferometric device
with a short wavelength. A device can operate morestably if a solid surface is used as an interferometric
element. So far, however, solid surfaces have not been
used as a coherent reflectors of atomic waves. An atom
near the surface is accelerated by attractive van der
Waals potential, its de Broglie wavelength shrinks
within the classical atomic size, and it hits the repulsive
wall generated by electrons near the solid surface. Since
no solid surface is flat within the atomic scale over amacroscopic distance, the colliding atom loses coher-
ence, even when it is scattered elastically. When the
velocity of the colliding atom is very small the situation
is different. The atom feels the van der Waals potential
sufficiently steep, causes impedance mismatch and is
reflected back long before it hits the repulsive wall. This
reflection is similar to the one of an optical wave at a
refractive-index step. Since the atom sees the surfacefrom a certain distance, the roughness of the surface is
averaged, and the reflection becomes highly coherent.
The reflectivity increases as the normal incident velocity
of the atom decreases and converges to unity at zero
velocity. This reflection is called quantum reflection,
and its existence was verified experimentally in the
Fig. 6. Design of electrode array for random phase distribution.
Fig. 7. Pattern switching by changing electric-field conditions. (a) f
pattern appeared at a 0-biased voltage, and switched to (b) p pattern
when the electrode was biased at 0.78 V.
Fig. 8. SEM image of brazed grating. The width of the top surface is
40 nm.
J. Fujita, F. Shimizu / Materials Science and Engineering B96 (2002) 159�/163162
reflection of metastable neon atoms from a silicon and
glass surfaces by one of the authors [7].
Although the coherent quantum reflection can be
used, in principle, as a reflective element for atoms, the
velocity required to obtain a significant reflectivity is so
small that it excludes practical applications on earth,where the gravity accelerates atoms to a higher velocity
in a short distance. We recently found that the
reflectivity improved drastically if a ridged surface is
used instead of a flat one. Fig. 8 shows an example of
the surface structure used to enhance the reflectivity.
The silicon surface was modified to form a grating
structure that has a periodic array of roof shaped ridges
with a narrow top. In this example the periodicity of theridge was 10 mm and the width of the top of the ridge
was approximately 40 nm. Metastable neon atoms were
sent at a small angle to the surface perpendicularly to
the direction of the ridge. The reflectivity was measured
as a function of the incident angle. Fig. 9 shows the
reflectivity for two samples with a ten (squares) and a
100 mm (triangles) periodicity together with the reflec-
tivity of a flat surface (solid line). The longitudinalvelocity of the atom was 3 m s�1, and, therefore, 30-nm
s�1 the normal- incident velocity corresponded to the 10
mRad incident angle. The reflectivity at this angle was
more than 102 times larger than that for a flat surface.
The drastic improvement resulted from a distinctive
characteristic of the quantum reflection. The reflectivity
is higher if the van der Waals constant is smaller,
because the atom approaches the surface more closely,feels a steeper potential slope, and experiences a larger
impedance mismatch. The constant is proportional to
the density of the solid near the surface. The grating
structure is affected in the same way, because the
colliding atom interacts with the solid only on a small
fraction of the entire surface. This justification breaks
down when the atom approaches the surface more
closely than the turning point of the van der Waals
potential. This distance is typically a few nm. We believe
the reflectivity can still be improved by an order ofmagnitude by using a grating with a smaller periodicity.
Such structures should be applicable to stable reflective
mirrors, beam splitters, and holograms.
5. Conclusion
We have demonstrated several holographic techni-
ques that use a transmissive thin film binary hologram
for atomic beam manipulation. We also demonstrated
new type of reflection that can be used for atom optical
elements.The authors thank Shinji Matsui, Makoto Morinaga
and Tetsuo Kishimoto for contributions in the early
stage of our research on atom holography. This work
was partly supported by a Grant in Aid for Scientific
Research (11216202) from the Ministry of Education,
Science, Sports and Culture.
References
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[2] O. Carnal, et al., Phys. Rev. Lett. 67 (1991) 3231.
[3] J. Fujita, et al., Nature 380 (1996) 691.
[4] M. Morinaga, et al., Phys. Rev. Lett. 77 (1996) 802.
[5] T. Kishimoto, et al., Jpn. J. Appl. Phys. 38 (Pt. 2) (1999) L683.
[6] J. Fujita, et al., Phys. Rev. Lett. 84 (2000) 4027.
[7] F. Shimizu, Phys. Rev. Lett. 86 (2001) 987.
Fig. 9. Reflectivity obtained by grating of 10 mm pitch (squares) and that of 100 mm pitch (triangle). Solid line shows the reflectivity by flat Si surface.
J. Fujita, F. Shimizu / Materials Science and Engineering B96 (2002) 159�/163 163
