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Contemporary Physics, 2001, volume 42, number 2, pages 77± 95
Prospects for atom interferometry
R. M. GODUN, M. B. D’ ARCY, G. S. SUMMY and K. BURNETT
Atom interferometers were ® rst realized ten years ago, and since then have evolved from
beautiful demonstrations of quantum physics into instruments at the leading edge of
precision measurement. In this article we trace the development of atom interferometry,
looking at how the physical principles have been put into practice to achieve ground-breakin g
experiments. We also discuss new atom optical techniques that are becoming available and
anticipate the ways in which the consequent improvements will provide new opportunitie s in
metrology and the study of fundamental physics.
1.
Introduction
consider new techniques and experiments for the future in
sections 6 and 7.
Wave-like behaviour of both light and matter has been one
of the most important areas of study in physics since the
beginning of the twentieth century. A crucial aspect of this
behaviour is the ability of waves to exhibit interference
eŒects. These eŒects were ® rst understood in the early
nineteenth century through the work of Young [1] and
Fresnel [2] with light. Over the past hundred years light
interferometers have evolved into powerful measuring
devices with a wide range of application s including
measurement of rotations, accelerations, distances and
spectra. In the 1920s de Broglie [3] showed that matter
also had an associated wave-like character which immediately provided the possibility of performing analogou s
experiments with particles. This has led to the development
of atom interferometry which is now a very active area of
research.
In this review, we explain the physics behind atom
interferometers and discuss the measurements that they can
make. Throughout , we draw analogie s with light and so it is
useful to begin our discussion in section 2 with a
description of a light interferometer. In section 3 we will
move on to consider the requirements of a generic atom
interferometer and in section 4 we will look at the details of
some speci® c atom interferometers. These have already
achieved measurements with a sensitivity equal to the
world’ s best optical interferometers. We will review the
current limitations to these instruments in section 5 and
2.
Interferometry basics
Interferometers are devices that use the interference of
waves to make measurements. To do this, an incident wave
must be split into several components that travel along
diŒerent paths and are recombined at the point where
interference is to be observed. The most commonly
encountered example of an interferometer uses light. In
this case, the manipulatio n of the waves is achieved with
simple mirrors and beam splitters as shown in ® gure 1. The
beam travelling towards the detector has an electric ® eld
that is a superposition of those from the two arms, E1 and
E2 . These have the same amplitude, E0 , and since the path
lengths are x1 and x2 , the resultant electric ® eld is given by
Etotal ˆ E1 ‡ E2
ˆ E0 ‰exp …ikx1 † ‡ exp …ikx2 †Š
ˆ E0 exp …ikx1 †…1 ‡ exp ‰ik…x2 ¡ x1 †Š†
ˆ E0 exp …ikx1 †‰1 ‡ exp …iU†Š ,
where k is the wavelength of the light ( ˆ 2p /k where k is the
wavelength of the light) and Uˆ k(x2 ¡ x1 ) is the phase
diŒerence between the two superposing waves. The
intensity recorded by the detector, Ito ta l , is given by
Itotal / jEtotal j2
/ E20 j1 ‡ exp …iU†j2
Author’s address: Clarendon Laboratory, Department of Physics,
University of Oxford, Parks Road, Oxford OX1 3PU, UK.
Contemporary Physics ISSN 0010-7514 print/ISSN 1366-581 2 online
http://www.tandf.co.uk/journals
DOI: 10.1080 /0010751011004720 1
Ó
/ 2E20 ‰1 ‡ cos …U†Š
2001 Taylor & Francis Ltd
R. M. Godun et al.
78
Figure 1.
waves.
A Mach ± Zehnder light interferometer where the beam splitters and mirrors separate and recombine the paths of the light
In the situation pictured above, the two paths are the
same length and so the interfering waves will add together
in phase with each other, that is Uˆ 0. The detector will
record a spot of bright light resulting from this constructive
interference. If, however, the path length diŒerence is
changed, the phase diŒerence between the superposing
waves, U, will vary. The detector will then record the
intensity of the light as varying between bright and dark,
giving rise to a set of interference fringes as shown by the
solid line in ® gure 2. To look at just one of many examples
of how this device can be useful, we consider how the
Mach ± Zehnder interferometer in ® gure 1 can be used as an
instrument for measuring rotations. The principle is the
same as that of a Sagnac interferometer which is described
in [4]. Suppos e that the device is subjected to a rotation
about an axis perpendicular to the page. When stationary,
the light waves from the two interferometer arms add
together in phase, as described above. When the instrument
is rotating, however, the two paths to the detector acquire
an additional phase diŒerence, D U, proportional to the rate
of rotation. The resulting interference pattern seen at the
detector is then
Itotal / 2E20 ‰1 ‡ cos …U ‡ D U†Š ,
and will be oŒset from the stationary interferometer fringes
by D U, as shown by the dotted line in ® gure 2.
The phase shift due to rotation at angular velocity X is
given by
D Ulight ˆ
4p
X
kc
A,
…1†
Figure 2. The solid line shows the interference fringes as the
phase diŒerence between the two interfering waves is scanned in
a stationary interferometer. The dotted line shows the same scan
for a rotating interferometer. The phase oŒset from the
stationary interferometer’s fringes is D U.
where k and c are the wavelength and speed of the light and
A is the area enclosed by the two paths of the interferometer. A measurement of the phase shift D U and a
knowledge of k and A allow the rate of rotation X to be
determined. The device can therefore be used as a
gyroscope with a sensitivity which depends on how
precisely the resulting interference fringes allow D U to be
measured.
Until the 1920s, no one had ever considered making such
interferometers with matter sources because the wave-like
nature of matter was not known. All this changed in 1924
Prospects for atom interferometry
when de Broglie postulated that any particle with
momentum, p, should have an associated wavelength,
kd B , related through his renowned equation
kdB ˆ
phase shift is given by equation (1). If, however, an
interferometer of equivalent area is built using matter
waves then the measured phase shift will be
4p
X
A
kdB v
kc
ˆ
D Ulight
kdB v
mc2
ˆ ±
D Ulight ,
hx
h
,
p
where h is Planck’ s constant. Typical de Broglie wavelengths for atoms at room temperature are about 1000
times smaller than wavelengths of visible light, making it
di cult to detect eŒects related to this wave-like nature.
Nevertheless, experimental evidence of matter waves came
just three years later in 1927 when Davisson and Germer [5]
demonstrated electron diŒraction from a crystal lattice. The
wave nature of atoms was ® rst observed in 1930 by
Estermann and Stern who diŒracted helium atoms from
single crystal surfaces of NaCl [6]. Neutron matter waves
were later observed in the 1940s through re¯ ection [7],
diŒraction [8] and interference [9] of neutron beams.
With the ability to manipulate electron, neutron or atom
waves it should then be possible to build matter wave
analogues of light interferometers, but how do atoms
compare with electrons and neutrons for use in interferometry? Atoms have larger masses and hence smaller de
Broglie wavelengths (for a given velocity) than electrons
and neutrons and this makes atom interferometry technically much more di cult. However, it is advantageou s to
use atoms rather than electrons or neutrons for several
reasons. Firstly, atomic sources are readily available and
atoms can be precisely controlled by electromagnetic ® elds
acting on their internal states. This control is essential to be
able to guide the matter waves around precise paths.
Although electrons are also readily availabl e and can be
manipulated easily, their electric charge results in interactions both with other electrons and with stray external
® elds. This leads to unwanted phase shifts in an electron
interferometer. Neutrons have the advantage over electrons
that they do not interact electromagnetically with each
other; however, they are not as useful as atoms because
they do not interact with applied electric ® elds. Additionally, neutron sources could not be incorporated into a
table-top experiment.
Atom interferometers also have several advantages over
light interferometers. The range of physical phenomena
which can be probed by matter interferometers goes
beyond the possibilitie s available to light interferometers.
For example, properties of the particles themselves such as
electric polarizabilitie s or collision cross-sections can be
probed. Gravitationa l interactions can also be explored
since the interfering waves have mass. Additionally , atom
interferometers have the potential to measure phase shifts
much more accurately than light interferometers. Consider
once again the example of a rotating Mach ± Zehnder
interferometer. If the interfering waves are light, then the
79
D Uatom ˆ
…2†
where kd B is the de Broglie wavelength and v is the atomic
speed. The ratio of the measured phase shifts in the matter
and light interferometers is therefore mc2 / ±hx , where m is
the particle mass in a matter interferometer and x is the
light frequency in an optical interferometer. This ratio
suggests that atom interferometers could make measurements with 101 1 times more accuracy than light interferometers. These huge gains have yet to be realized as
atom interferometers have not achieved areas or particle
¯ uxes comparable with light interferometers. However, the
® eld of atom interferometry is still developing and the
techniques are rapidly improving.
3.
Designing an atom interferometer
Just as with light interferometers, the key components of
atom interferometers are the source and the elements to
manipulate the waves such as the mirrors and beam
splitters. Let us begin by considering the source.
In light optics, lasers are the ideal source for many
interferometry experiments because they have large coherence lengths, are well collimated and have a high photon
¯ ux. The coherence length is the maximum distance along
the wave over which the phase at all points has a well
de® ned relationship. Two points separated by more than
this distance will not have a ® xed phase relationship
between them and interference cannot be observed with a
detector which has a response time longer than the time
scale of the phase ¯ uctuations. Larger coherence lengths
therefore allow larger path diŒerences between the interferometer arms before the interference fringes start to
disappear. The fringes in ® gure 2, for example, would wash
out after fewer periods if the coherence length of the source
were smaller. For accurate measurements of the phase shift,
D U, it is desirable to take readings over as many fringes as
possible and therefore a large coherence length is required.
High photon ¯ ux also improves the sensitivity of an
interferometer as it increases the signal-to-nois e ratio in the
interference fringes. The lower the noise in the results, the
more accurately the phase of the interference fringes is
de® ned and the more precisely D U can be measured.
In atom optics, there are two main choices of atomic
source: atom beams and cold atom clouds. Atom beams are
R. M. Godun et al.
80
created, in general, by allowing atoms to emerge from a
hole in an oven. The ¯ ux of detected atoms is typically
109 atom s¡1 . This is much higher than the ¯ uxes
attainabl e with cold atom clouds, typically about
10 7 atom s¡ 1 . Using atom beams in interferometry therefore
gives better signal-to-nois e ratios and can increase the
precision of a phase shift measurement. Beam experiments
also allow continuous measurement which can be useful for
some interferometer applications . Cold atom clouds such as
those from magneto-optic traps (MOTs) [10] or Bose ±
Einstein condensates (BECs) [11], on the other hand, have
much narrower momentum distribution s than beams. The
eŒect of a momentum distribution in an atomic source is
analogous to that of a frequency distribution in a light
source. The narrower the distribution, the larger the
coherence length. The relationship between the momentum
spread, D p, in an atomic source and the coherence length,
D x, is given by
D xD p
±h .
In a MOT, the momentum distribution width after laser
cooling is typically 10 ±hk, where k ˆ 2p /k and k is the
wavelength of the light cooling the atoms. This leads to a
coherence length k/10. A BEC is much colder and the
extremely narrow distribution gives a coherence length at
least an order of magnitude larger. Atomic beams, on the
other hand, have much smaller coherence lengths, typically
100 to 1000 times less than cold atom clouds and so their
path diŒerences cannot be as large. It is quite common,
however, to operate atom interferometers in a con® guration with zero path length diŒerence. To create the
interference fringes, the relative phase, U, between the
interfering waves must then be scanned in some way other
than altering the path length. Examples of how this relative
phase can be changed are given later. The coherence length
is then no longer an important characteristic and so it is not
immediately obvious why cold atoms might be useful.
However, narrower atomic momentum distribution s have
two further advantages . The ® rst is that the atom cloud
expands more slowly. This is useful because if the atoms
move apart too quickly, they might move out of the beam
splitting interaction regions and be lost from the experiment. Atoms in cold clouds can therefore remain together
for longer, allowing the interferometer paths to be traced
out over a longer time. This can lead to an increased
sensitivity in certain types of experiment, examples of which
will be seen in section 4. The second advantag e of colder
atoms is that some beam splitting mechanisms are
momentum dependent and hence have a more uniform
eŒect on narrower momentum distributions . This produces
an improvement in the contrast of the interference fringes
and so any oŒset phases, D U, can be more precisely
determined. Some further points to consider when choosing
an atomic source are that the vacuum systems for cold
atom experiments can be much more compact than in beam
experiments. This is because atoms in a beam travel much
faster and cover greater distances in the time of the
interferometer, typically up to several metres, whereas cold
atoms will only travel a few millimetres. Apart from the
technical convenience of smaller experiments, they are also
more stable over time allowing more accurate measurements to be made. In general, the relative importance of the
diŒerent source characteristics will depend largely on what
is to be measured.
Having chosen an appropriate source of matter waves,
they need to be manipulated with the analogues of mirrors
and beam splitters. The mirrors and beam splitters which
are used to de¯ ect light cannot be used for atoms and new
elements must be designed. Material diŒraction gratings
can, however, be used in atom optics in exactly the same
way as they are used in light optics [12]. An incident matter
wave will be diŒracted into a variety of orders, some of
which can be selected out to create an interferometer, as
shown for example in ® gure 3. If the detector records the
number of atoms emerging from the third grating in the
direction shown, then interference fringes will be seen as the
phase diŒerence between the two paths is changed. This is
done by translating the third grating along its length.
The material gratings used in atom optics, however,
usually require smaller periodicities than those used in light
optics because of the small de Broglie wavelengths of
atoms. Apart from the di culty in the fabrication of such
small structures, these beam splitters have the disadvantag e
that they block a large portion of the atoms, reducing the
signal. This can also lead to clogging of the small apertures
after prolonged use.
Atoms have internal structure, however, and this allows
the creation of many additiona l types of mirrors and beam
splitters that make use of an atom’ s interaction with
electromagnetic ® elds. Consider the example shown in
® gure 4. An atom initially in its ground state exposed to
light can absorb a photon and undergo a transition into an
excited state. The absorption of the photon will cause the
atom to recoil with velocity ±hk/m, where k ˆ 2p /k, k is the
wavelength of the absorbed light and m is the mass of the
atom. In this way the light acts as a type of `mirror’ ,
de¯ ecting atoms into a diŒerent momentum state with unit
probability. Note that it is not a mirror in the conventiona l
sense as the angle of incidence does not necessarily equal
the angle of re¯ ection. If, however, the probabilit y of
absorbing the photon is between zero and one, the atom
will be left in a superposition of the ground and excited
states, each with diŒerent momenta. The components of
the atom in the two states will then spatially separate from
one another and can become the two interferometer arms.
The light in this con® guration has behaved as a beam
splitter.
Prospects for atom interferometry
81
Figure 3. A Mach ± Zehnder style interferometer where the beam splitters are diŒraction gratings which separate and recombine the
paths of the atomic matter waves.
The crucial attribute of any mirror or beam splitter in an
atom interferometer is that it must not disturb the phase of
the matter wave; it must be what is known as `coherent’.
Any disruption to the phase relationship between the two
interferometer arms will result in destruction of the
interference fringes. The example in ® gure 4 would therefore be useless if the atom were to decay out of the excited
state by spontaneous emission. This would produce a
random phase shift, due to the momentum change with
random direction and timing, which would destroy the
phase relationship between the two interferometer arms.
The beam splitter depicted in the ® gure above could only be
used, therefore, in the case of an atom with a metastable
excited state so that spontaneous decay is unlikely to occur
during the time of the experiment [13]. Similarly, the light
itself must not impart random phase shifts onto the atoms.
The light beam must therefore have a long coherence
length, such as that provided by a laser.
For atoms without a metastable excited level, a second,
counter-propagatin g laser beam can be used in addition to
the ® rst to cause the atom to return to a ground level (not
necessarily the same level as initially ) by stimulated
emission. The atom gains a further velocity recoil in the
process and is left in a state from which spontaneous decay
cannot occur. Since the absorption and emission process
relies on stimulated transitions , coherence is preserved
between the interferometer arms. A Raman transition is a
speci® c example of this and is shown in ® gure 5.
The frequency diŒerence between the two laser beams is
set to x 1 3 so that the atom can undergo a simultaneous
two-photon transition between the ground states j1i and
j3i, gaining momentum kicks from the absorption and
emission of the photons equal to ±h (k1 ¡k2 ). If the two laser
beams are counter-propagating , then k1 . ¡k2 and the
atoms receive a momentum of 2±hk. In this way, atoms
in states j1i and j3i can be given diŒerent momenta and will
Figure 4. An atom in one of its ground states (thick lines) can
absorb a photon and be transferred into one of its excited states
(thin lines). The atom gains momentum from the photon and is
de¯ ected in a way similar to re¯ ection from a mirror.
Figure 5. Atoms in state j1i will undergo a simultaneous twophoton Raman transition to state j3i when the frequency
diŒerence between the laser beams is equal to x 1 3 . The transition
proceeds via a virtual level shown by the dotted line which is a
large detuning, D , from the excited state j2i. This ensures a
minimization of loss through spontaneous decay.
82
R. M. Godun et al.
separate spatially from one another if given su cient time.
The large detuning, D , of the laser beams from the
transition into state j2i reduces the probabilit y of this
excited state becoming populated. This in turn inhibit s
spontaneous decay, as required to preserve the coherence
between the two interferometer arms. Note that if the two
counter-propagatin g laser beams are of the same frequency,
then they create a standing wave. In this case the
momentum kicks described above can also be considered
as the result of the atoms being diŒracted by an optical
diŒraction grating formed from the standing light wave.
A useful feature of these Raman transitions is that they
can be used either as `mirrors’ or `beam splitters’ ,
depending on how long the light is applied. If the atoms
are in state j1i when the light is ® rst applied, they will be
transferred into state j3i as described above. Once in state
j3i, however, if the light is still applied they will be
transferred back into state j1i by the reverse process. The
atoms will continue to oscillate between states j1i and j3i
for as long as they are exposed to the light. To use the
Raman transition as a mirror, the light must be applied for
the correct length of time for all the atoms to go from one
ground state to the other. They will then all receive the
same momentum kick and be de¯ ected equally. An
exposure to the laser beams with frequency, intensity and
pulse length to cause such a complete transfer between
states is known as a p pulse. To act as a beam splitter, the
process should create a superposition of states with
diŒerent momenta. This is accomplished by exposing the
atoms to the light for only a fraction of the time required
for a complete transfer. If the frequency, intensity and pulse
length of the laser light are such that the atom is left in an
equal superposition of these states, then the laser beams are
said to create a p /2 pulse.
Light has proved to be the most widely used mechanism
for creating mirrors and beam splitters for atoms because
of the relative ease with which the necessary optical
potentials can be realized. There are also many other ways
in which electromagnetic ® elds can be used to manipulate
the momentum and position of atoms. Examples include
atomic mirrors which use either a static magnetic ® eld [14]
or an evanescent light wave [15] to provide a repulsive
potential which re¯ ects atoms. Another example is the use
of magnetic ® elds from current carrying wires [16]. We will
examine some of these techniques later in section 6.
Having seen that many mirrors and beam splitters rely
on manipulatin g the atoms’ internal states, it is important
to examine how these processes can be used to build an
interferometer. Consider the interferometer in ® gure 6,
where the beam splitting mechanism is Raman pulses and
the atom is always in its ground states j1i and j3i (the
excited state j2i is not depicted). Notice that the middle two
beams form a p pulse and hence act as mirrors, while the
® rst and last pairs of laser beams create p /2 pulses, thus
acting as beam splitters. The paths are separated according
to the momentum associated with the atoms’ internal state
and when they are recombined the populatio n amplitudes
of the two states superpose to give
jW ifinal ˆ aj1i ‡ b j3i .
The values of a and b can be calculated by tracing the
amplitude s through the interferometer. For the case of the
p /2 ± p ± p /2 pulse sequence depicted in ® gure 6, the state
amplitude s in the superposition are shown in ® gure 7 at
each stage of the interferometer.
Each time an atom changes state after a photon
interaction, the phase of the light, U1 , is imprinted on the
new state. In the case of emission, the new state receives
‡U1 and for absorption, it receives ¡U1 . Thus for a Raman
pulse which involve s an emission and an absorption from
two separate beams, the phase change on the new state is
governed by the relative phase of those two beams. Let the
relative phases be U1 , U2 and U3 for the p /2, p and p /2
pulses respectively. The ® nal amplitudes in the two states
are then found to be
¡1
exp ‰i…U2 ¡ U1 †Š…1 ‡ exp ‰i…U3 ¡ 2U2 ‡ U1 †Š†
2
¡i
bˆ
exp …¡iU2 †…1 ¡ exp ‰¡i…U3 ¡ 2U2 ‡ U1 †Š† ,
2
aˆ
which lead to the ® nal population s of
Pop 1 / jaj2
/
1
‰1 ‡
2
2
/
1
2 ‰1
Pop 1 / jb j
cos…U3 ¡ 2U2 ‡ U1 †Š
…3†
¡ cos…U3 ¡ 2U2 ‡ U1 †Š
…4†
By keeping U1 and U2 ® xed and by scanning U3 , familiar
cosine interference fringes may be seen if the population of
atoms in a particular internal state is detected. This is an
example of the way in which the phase shift between the
two interferometer arms may be changed while the path
lengths are kept equal. We will refer to this type of
interferometer as an internal state interferometer since the
interference is between the populatio n amplitudes in the
internal states.
4.
Interferometers as instruments
The ® rst detailed design for an atom interferometer was
patented in 1973 by Altshuler and Frantz [17]. There then
followed an eighteen year delay before one was achieved
experimentally. The main problem was the design and
fabrication of the coherent beam splitters and mirrors. For
beam splitters relying on light, advancements in the ® eld of
laser technology helped enormously as `oŒthe shelf’ lasers
Prospects for atom interferometry
83
Figure 6. An internal state interferometer where the beam splitters separate and recombine the paths according to the internal atomic
state. The detection records the population of atoms in a particular internal state.
Figure 7. The boxes give the amplitudes of the components in states j1i and j3i after each pulse of light. Every time one state is
transferred into another, the relative phase of the laser beams in the Raman pulses (U1 ,U2 ,U3 ) is imparted to the new state, along with an
additional phase of ¡p / 2.
R. M. Godun et al.
84
could be purchased at a variety of wavelengths . The ® rst
demonstration of a beam splitter was in 1985 by Moskowitz
et al. [18] using lasers to create standing waves which acted
as diŒraction gratings for atoms. Alternative beam splitters,
using material gratings , relied on advancements being made
in nanofabricatio n technology to produce gratings with a
su ciently small periodicity to act as a beam splitter for the
atom waves. Such nanofabricate d structures were used in
1991 by Carnal and Mlynek [19] and Keith et al. [12] to
create the world’ s ® rst atom interferometers. With the
experimental advances in the ® eld of atom optics [20,21]
and, in particular, the development of diŒerent coherent
beam splitting mechanisms, other interferometers rapidly
followed [22 ± 27].
It is only ten years since the ® rst atom interferometer was
built and there are many atom interferometers throughout
the world with numerous diŒerent con® gurations. More
signi® cantly, there are new experiments and proposals
being frequently reported. Why is there still such interest?
The answer lies in the fact that atom interferometry has
gone beyond the `proof of principle’ stage and is ® nding
many application s as an approach to measurement. With
the techniques for atom interferometry developing all the
time, there is much potential for improved instruments in
the future.
As an overview of the range of application s of atom
interferometers, a summary is given of some of the physical
phenomena which have already been measured.
4.1.
The MIT group
The ® rst example of an interferometer that we will examine
was used in 1995 to measure directly the electric polarizability of sodium atoms [23] at the Massachusetts Institute
of Technology. This experiment is the only one to date
which has permitted a physical barrier to be placed between
the two arms of an interferometer.
The de® nition of electric polarizability , a, is given by
U ˆ ¡a
e2
,
2
where U is the Stark potential felt by the atoms when an
electric ® eld, e, is applied. The experiment therefore
consisted of exposing atoms in one path to an electric ® eld
and ® nding the potential energy shift by measuring
the resulting phase shift of the interference fringes,
D Uˆ ¡Us / ±h, where s is the time for which the atoms
experience the interaction. The design was based on a
Mach ± Zehnder interferometer as pictured in ® gure 8. The
beam splitting mechanism consisted of material gratings
which diŒracted the atomic matter waves into diŒerent
orders which gave rise to the separated paths. The de
Broglie wavelength of the sodium atoms was only 17 pm
and so a nanofabricatio n process was used to produce
gratings with a period of just 200 nm.
A beam of the sodium atoms was split and recombined
with three of these gratings. To observe interference fringes,
the third grating was translated along its length. This
allowed the separated paths to be recombined with a phase
shift which varied according to the grating’ s position. To
allow the electric ® eld to be applied to only one
interferometer arm without aŒecting the other, a thin
metal foil was inserted between the two arms, directly after
the second diŒraction grating. At this point in the
interferometer, the two atomic beam widths were 40 l m
(FWHM) and the beam centres were separated by 55 l m.
This was just enough separation to allow a 10 l m thick foil
to be inserted. The thin foil was stretched to try and remove
wrinkles but it nevertheless cast a 20 ± 30 l m shadow on the
Figure 8. The atom interferometer at MIT, using nanofabricated diŒraction gratings as the beam splitters. The interaction region
consists of a metal foil held symmetrically between two side electrodes, allowing an electric ® eld to be applied to one arm only.
Prospects for atom interferometry
detector due to remaining imperfections. It was important
for the atoms to have as long an interaction time with the
electric ® eld as possible to give a large phase shift and hence
increased sensitivity. The interaction region was therefore
made 10 cm long. Any longer than this would have led to
serious clipping of the atomic beam by the foil.
The interferometer was able to measure phase shifts to a
precision of 10 mrad when averaged over 1 min of data
taking. The reference phase was taken as the position of the
interference fringes when no electric ® eld was applied to the
atoms. This phase was found to drift by about 1 rad h¡ 1 so
it was measured frequently to try and reduce errors.
External vibrations also had to be overcome to allow the
interferometer to perform at the required sensitivity. Other
sources of error arose from uncertainty in the velocity
distribution of the atomic beam, and the geometry of the
interaction region.
The results of these measurements gave the atomic
polarizabilit y with an error of just 0.3% , an order of
magnitude improvement on previous direct measurements.
It is important to have precise data on atomic polarizabilities as they allow determinations of many atomic
properties such as dielectric constants and refractive
indices, van der Waals forces between two polarizable
systems and Rayleigh scattering cross-sections. This experiment was the ® rst implementation of an atom interferometer as a measurement tool.
4.2.
Atomic clock
The primary frequency standard which is created for
atomic clocks uses the physics of an internal state atom
interferometer. Precise time and time interval data are
needed for many application s including telecommunications networks, electricity generation, computer network
synchronizatio n and navigation . Calibration laboratorie s
are constantly striving for a more precise de® nition and
realization of the second. The second is currently de® ned as
the duration of 9192 631 770 periods of the radiation in the
transition F ˆ 3 ! F ˆ 4 in the ground state of the caesium
atom. An atomic clock can therefore be made by creating a
frequency standard based on this atomic transition and
using it as a reference to give `ticks’ to determine the speed
of a clock.
The simplest way to ® nd the frequency would be to scan
a microwave frequency source over the line and detect
when the atoms undergo the transition with the highest
probability. A much more accurate technique, however, is
to use Ramsey’ s method of separated oscillatory ® elds [28]
which is illustrated in ® gure 9. Since this is the method used
in an atomic clock, we will now look in detail at how the
internal states are manipulated. The two states involve d are
the magnetically insensitive m ˆ 0 components of the
hyper® ne levels, F ˆ 3 and F ˆ 4 in the ground state of
85
caesium. The beam splitting mechanism is a pulse of
microwaves at frequency, x , close to the transition
frequency from F ˆ 3 to F ˆ 4. Atoms in the F ˆ 3 level
are exposed to a p /2 pulse of these microwaves, which have
a frequency, intensity and pulse length such that the atomic
wavefunction is `split’ into an equal superposition of the
F ˆ 3 and F ˆ 4 levels. This is similar to the p /2 pulse
described in relation to the Raman pulses in ® gure 5. The
diŒerence, however, is that the microwaves transfer the
atoms directly from one ground state to the other with a
single photon. The microwaves have a frequency of
101 0 Hz, about four orders of magnitude less than the
optical frequencies required in the Raman transition. This
means that the momentum transferred to the atoms on
absorption of a microwave photon is negligible . The
components in the two internal states therefore remain
spatially overlapped throughout the clock sequence. After a
time T, a second p /2 pulse of microwaves is applied which
recombines the components in the two levels. The ® nal
population in each individual state depends on the relative
phase, U, between the atomic states and the microwaves at
the time of the second pulse.
We now consider the origin of this relative phase, U.
During the time between pulses, T, a phase diŒerence
evolves between the F ˆ 3 and F ˆ 4 atomic levels,
Ua t ˆ x 0 T, due to their energy diŒerence, ±hx 0 . The
microwaves at frequency x also evolve a phase in the time
interval so that Um w ˆ x T. If the microwave frequency is
such that Um w ˆ Ua t after the time interval, then the second
p /2 pulse will add to the ® rst, producing the overall eŒect of
a p pulse and transfer all the atoms into the F ˆ 4 level. If,
however, Um w and Ua t become p radians out of phase
during the time interval, then the second p /2 pulse will
cancel the eŒect of the ® rst and all the atoms will be
returned to F ˆ 3. As the phase diŒerence Uˆ Um w ¡Ua t
varies, the population in each of the internal states will be
seen to oscillate. This phase diŒerence can be controlled by
scanning the microwave frequency, x , since Uˆ (x ¡x 0 )T.
A fringe pattern will then be formed, such as that shown in
® gure 10, if the population of atoms in the F ˆ 4 level is
detected.
The fringes are essentially the cosine pattern which we
saw earlier, but with a modulating envelope. The origin of
this extra modulation arises from the fact that as the
microwaves are detuned further from resonance, the atoms
are less and less likely to make a transition into the F ˆ 4
level and the signal falls oΠto zero. The shape of the
envelope is what would be seen if only one of the p /2 pulses
of microwaves were applied. The advantage of the
separated oscillatory ® eld method is that it sets up fringes
which have a much narrower width than that created by a
single pulse. This allows x 0 to be found much more
precisely. The longer the time interval between the two
pulses, T, the more critically the microwave frequency, x ,
86
R. M. Godun et al.
Figure 9. The manipulation of the internal atomic states with two p /2 microwave pulses separated by a time, T. The ® rst pulse places
the atom in an equal superposition of the two states. The second pulse alters the superposition according to the relative phase, U, between
the atomic states and the microwaves.
must match the atomic transition frequency, x 0 . Hence the
width of the fringes decreases as 1/T so that increasing the
time between the pulses allows a reference source to be
locked to the central frequency more precisely.
Experimentally, the regions where the microwaves are
applied to the atoms will be ® xed in space and so the pulse
interval, T, will depend on the speed of the atoms between
these regions. Cold atoms with slower speeds will therefore
give the longest pulse separation times and hence the most
precisely de® ned reference frequency. An additiona l technique which can be used to increase the pulse separation
time is to launch the atoms in a so-called fountain
arrangement as shown in ® gure 11. The atoms pass through
a microwave cavity once on their way up, and again on
their way down. Times between the pulses can then
approach 1 s with a fountain height of 1 m. An extra
advantag e of passing the atoms through the same micro-
wave cavity twice is that this eliminates many systematic
eŒects.
Figure 12 shows the real set-up of just such a caesium
fountain at the National Physical Laboratory, Teddington, UK. The vacuum system in which the atoms are
launched is on the right of the picture and the optics and
electronics which control the atoms are towards the left.
These new experiments are a long way beyond the simple
pendulum which acts as the frequency standard in a
grandfathe r clock. The accuracy and stability, however,
are similarly far removed. Currently, clocks making use of
the frequency standard derived from atomic fountains can
achieve an accuracy of one part in 101 5 with a stability of
one part in 101 6 by averaging results over a day [29]. The
dominant factors limiting the accuracy arise from
uncertainties in the frequency shift induced by cold
inter-atomic collisions and the ac Stark shift induced by
Prospects for atom interferometry
87
Figure 10. Interference fringes in the population of atoms in
the F ˆ 4 ground state of caesium as the frequency of the
microwaves is scanned. The middle of the central fringe is
precisely the transition frequency, x 0 , which is to be found.
blackbody radiation. For more information on errors,
see [30].
4.3.
The Stanford group
Perhaps the most exciting possibilitie s oŒered by atom
interferometry are in precision measurement and this has
been the centrepiece of this group’ s research. One of their
atom interferometers is based on a fountain of cold caesium
atoms, similar to the atomic clock. The key diŒerence is the
use of optical Raman pulses instead of microwaves to
manipulate the superposition of internal states, thus
creating a spatial separation between the two interferometer arms. A schematic of the apparatus is shown in
® gure 13. The instrument has been used to make measurements of the Earth’s gravitational acceleration, g, in 1991
and subsequent years [31]. The result has been a value of g
with an accuracy equivalent to that attainable from falling
corner cube experiments [32], currently among the most
sensitive gravimeters in the world. The interferometer is
precise enough to show variations in g due to tidal eŒects
over the period of a day.
Due to the diŒerent momenta imparted by the Raman
pulses, the internal states trace out diŒerent trajectories in
the fountain, one reaching a greater height than the other,
as shown in ® gure 14. Note that an additional p pulse is
therefore needed at the top of the trajectory to impart
momentum so as to ensure that the paths are brought back
to spatially overlap at the last p /2 pulse. To see the
Figure 11. The basic principle of an atomic fountain for a
primary frequency standard. The atoms start in one state and are
exposed to a p / 2 pulse of microwaves, placing them in an equal
superposition of both internal states as they are launched
upwards. On their way back down, they are exposed once again
to a p /2 pulse of microwaves. The resulting superposition of
states depends on the relative phase accumulated between the
atoms and microwaves as outlined in ® gure 9.
interference fringes, the relative phase of the Raman beams
in the last p /2 pulse, U3 , is scanned. The ® nal atomic
population s in the two states at the end of the interferometer sequence are therefore given by equations (3)
and (4), but due to gravity there is an additiona l phase
oŒset [33],
D U ˆ kR
gT 2 ,
where kR ˆ k1 ¡k2 is the eŒective wavevector of the Raman
transition (with magnitude k1 ‡k2 . 2k, g is the acceleration
due to gravity and T is the time between each of the pulses
in the p /2 ± p ± p /2 sequence. From measurements of this
phase oŒset, a value for g can be found.
The origin of this gravitationa l phase shift can be seen in
simple terms by considering the relative phase between the
atoms and the light at the time of each pulse. An atom at
rest would see x T/2p oscillation s of an applied ® eld in a
time T. If the atom moves a distance D z in the same
direction as the light, however, it will see kR D z/2p fewer
88
R. M. Godun et al.
Figure 12. The atomic caesium fountain used to create the primary frequency standard at the National Physical Laboratory, UK. The
photograph shows the optics and electronics on the left which control the atoms in the vacuum chamber on the right. [We thank
D. Henderson for allowing us to reproduce this photograph from NPL, Teddington, UK.]
oscillation s in the same time. The atomic phase therefore
keeps a count of how many periods of the light ® eld the
atom has moved across. The applicatio n of the ® rst Raman
pulse causes the two components of the superposition to
separate from one another whilst travelling upwards. At the
time of the second pulse, both components are in new
positions in the light ® eld and consequently experience
diŒerent phase shifts. Therefore, although the ® rst two
Raman pulses are applied with the same relative phase
(U1 ˆ U2 ˆ 0), the phases imprinted onto the atoms are
diŒerent. Between the second and third Raman pulses,
there is a further change in relative position and hence
another phase shift. In the absence of gravity, these
accumulated phases in the ® rst and second halves of the
p /2 ± p ± p /2 sequence cancel each other out. In the presence
of gravity, however, the fountain trajectories are asymmetric as shown in ® gure 14 and there is an overall phase
oŒset in the ® nal interference fringes. In eŒect, the
interferometer measures the diŒerence between the foun-
tain trajectories against the very accurate ruler created by
the light wave.
The most challengin g part of this experiment has been to
minimize the random and systematic errors. The largest
random errors are due to vibrations and rotations of parts
of the apparatus. Systematic eŒects in the instrument
include uncertainty in the rf phase shift, the Coriolis eŒect,
the wavelength of the caesium D1 transition to which the
frequencies of the Raman lasers are referenced, the laser
lock oŒset, gravity gradients, ac Stark shift and precise
pulse timings. Nevertheless, the resulting interferometer is
accurate enough to allow phase shifts 10 mrad to be
detected, leading to a value of g accurate to one part in 10 9 .
4.4.
The Yale group
Atom interferometers based on the analogu e of optical
Mach ± Zehnder interferometers, as described in section 1,
can be used to make very accurate gyroscopes. Sensitive
Prospects for atom interferometry
89
Figure 14. A schematic of the fountain trajectories traced out
by the diŒerent components of the atomic superposition in the
Stanford interferometer. Time increases towards the right.
Figure 13. The Stanford atom interferometer, using a MOT of
cold caesium atoms launched into a fountain trajectory with
Raman beams providing the beam splitting mechanism.
rotation measurements are required in navigation, geophysical studies and can even be used to make tests of general
relativity.
The Yale group have used their atom interferometer to
measure the Earth’ s rotation rate from 1996
onwards [34,35]. The interferometer consists of a horizontally propagatin g atomic caesium beam which is manipulated with transverse Raman pulses, like that shown in
® gure 6. As mentioned before, rotations introduce phase
shifts in the interference fringes proportiona l to the rate of
rotation, X , given by equation (2)
D Uatom ˆ
4p
X
kv
A,
where k is the atom’s de Broglie wavelength and v its
velocity. We see that the phase shift is also proportiona l to
A, the area enclosed by the interferometer. Thus larger area
interferometers make more sensitive gyroscopes. The
reason for using atomic beams rather than cold atoms in
this experiment is therefore to make the enclosed area as
large as possible, 22 mm2 in this case. From accurate
measurements of the phase shift, the Earth’s rate of
rotation has been determined with a short term sensitivity
comparable with that of the best active ring laser
gyroscopes [36,37].
To achieve such impressive results, there were of course
many engineering di culties which had to be overcome.
Once again, vibrations would be extremely detrimental to
the instrument’s sensitivity and so the whole system was
designed with vibration isolation in mind. The Raman
beam alignment is also very critical and has to be correct to
within 10¡ 4 rad to observe interference fringes at all. The
Raman beams themselves propagate in tubes to reduce
optical phase shifts from air currents.
The short term sensitivity could be further improved by
increasing the atomic ¯ ux as this would give a better signalto-noise ratio. Long term mechanical stability, however, is
much more di cult to achieve in a system such as this
which is over 2 m long. One possible way to reduce the
consequent systematic errors is to create a second
90
R. M. Godun et al.
gyroscope, with an atomic beam counter-propagatin g
relative to the ® rst which uses the same laser beams for
its atom optical elements. The area vectors of the two
gyroscopes will then have opposite signs, as will the
rotational phase shifts. Subtracting the two phase shift
measurements leads to common mode rejection of many
systematic errors which do not reverse sign with the
direction of the atomic beam and thus enhances the
instrument’s long term sensitivity.
In a second and completely separate device, the Yale
group have built a gravity gradiometer [38]. The principle
of this experiment involves simultaneously measuring the
phase shifts due to gravity in two identical interferometers
separated by a height of about 1 m, as shown in ® gure 15.
The diŒerence in the value of g yielded by the two
interferometers then gives the change in gravity over their
separation.
The two interferometers are very similar in design to the
Stanford interferometer. The atomic sources are caesium
MOTs and the beam splitters are vertically propagatin g
Raman pulses. The main diŒerence is that the Yale group
simply allows their atoms to fall, rather than launching
them in a fountain trajectory. The Yale group tested their
system by measuring the gradient of the Earth’ s gravitational ® eld. Two sets of interference fringes were obtained
with signal-to-nois e ratios su ciently high to see phase
shifts between the two fringe patterns of the order of
50 mrad. These measurements yielded a value for the
Earth’s gravity gradient consistent with the expected value,
assuming an inverse square law scaling for g.
Figure 15. A schematic of the gravity gradiometer. Two
interferometer regions, separated by about a metre, detect phase
shifts due to gravity. The diŒerence in their phase oŒsets gives a
measure of the gradient of gravity.
The experiment is designed to reduce systematic eŒects
by having as many elements as possible in common to both
interferometers. These include the Raman and detection
beams which are both vertical. This means that platform
vibration eŒects, likely to be a large source of error in a
single interferometer, can be eliminated when the two
interferometer phase shifts are subtracted from one
another. Data can also be taken with the Raman beam
direction reversed. This changes the sign of the gravitational gradient whilst leaving the sign of the systematic
errors unaŒected. Once the data has been suitably analysed
to remove these eŒects, the main sources of systematic
errors that remain are time-varying magnetic ® elds, ac
Stark shifts from the laser beams and platform rotations.
Nevertheless, the ability to minimize the major error, that
of vibrations, gives a device stable enough to take
measurements over periods of several hours. It has also
led to this instrument being seen as a viable method for
measuring gravity gradients on board a moving platform
such as a ship or aircraft.
5.
Current limits and possible improvements
From the examples we have looked at, it is clear that
external factors, such as vibrations, are a major limitation
to the achievable sensitivities of existing interferometers.
Combinations of passive isolation and active feedback have
been used to reduce vibration eŒects as much as possible.
Passive isolation typically consists of rubber feet under the
apparatus to damp out high frequency vibrations . Active
feedback works by having an accelerometer, such as a light
interferometer, attached to the apparatus. The output
which is produced in response to a vibration can be fed
back to a control device to provide the reverse motion and
compensate the vibration. Such a device responds best to
frequencies in the range 0.2 ± 5 Hz, the region which is most
detrimental to measurements. It is due to these external
factors that both atom and light interferometers currently
have the same precision. In other words, they are both
limited by the same eŒects. If, however, experiments could
be performed in an environment where vibrations are
naturally much less of a problem, then the intrinsic
advantage s of atom interferometers would allow them to
make much more precise measurements than light interferometers. Such an environment might be a satellite in
free-fall around the Earth. It is known that this can be
almost vibration-free and there are currently several groups
working towards putting atom interferometers in space.
Although atom interferometers in a vibration-free
environment would start to out-perform light interferometers, the gain would still not be the 11 orders of magnitude
mentioned in section 3 as being theoretically achievable.
Atom interferometers still have much smaller areas and
particle ¯ uxes than their counterparts in light and this too is
Prospects for atom interferometry
preventing them from attaining their ultimate sensitivity.
The current limits to the area of atom interferometers are
two-fold. First, the atoms cannot simply be made to travel
for longer times to create bigger areas. Since gravity is
always acting on them, after a certain length of time the
atoms would fall out of the regions where the atom optics
takes place. Secondly, the beam splitting mechanisms which
impart momentum to separate one path from the other do
not scale well to higher momenta. For example, applying
two Raman pulses instead of one to impart twice as much
momentum results in a serious loss of e ciency. Hence
there is a limit to the amount of spatial separation which
can be achieved between the interferometer arms. Placing
the atom interferometer in space would be one way to
increase the interferometer’s area because the micro-gravity
environment would allow interaction times to become very
long without the atoms falling out of the experiment. The
limit which would then be reached is that the atomic
distribution would expand out of the interaction region due
to its initial momentum distribution . This expansion could
be suppressed by using colder sources, such as BECs, which
would allow interaction times of about a minute. Other
ways to create larger area interferometers require diŒerent
techniques for manipulating the atoms, some examples of
which will be described in the next section.
6.
New techniques
Besides improvements to existing atom interferometer
schemes, considerable eŒort is being invested in the
development of completely new techniques. These can be
roughly divided into improved sources and novel ways to
manipulate the atoms.
As mentioned above, Bose ± Einstein condensate sources
could provide longer interaction times than those achievable with magneto-optic traps or atomic beams. They could
also provide higher particle ¯ ux as they are more dense
than conventional sources of cold atoms. This could lead to
an improvement in the intrinsic sensitivity of interferometers through a better signal-to-nois e ratio. An additiona l
advantag e of BECs is that some beam splitting mechanisms
can have a very uniform e ciency when operating on a
narrow momentum distribution . This leads to an increase
in the contrast of the interference fringes and hence to
better phase shift measurements. A group in Tokyo has
already constructed a Mach ± Zehnder interferometer with
a BEC and seen almost 100% contrast in the fringes [39].
Aside from very cold sources, more massive sources are
also creating interest. This is because the phase shift
experienced by a matter interferometer scales linearly with
the mass of the interfering particles. A molecular source
would therefore give rise to a much higher sensitivity than
single atoms. The analogu e of a Young’s double slit
interference experiment has already been demonstrated
91
with a carbon-60 source [40]. Similarly nanostructure s and
quantum dots are also being investigated. These are manmade structures with an even higher mass. They also
possess internal energy states which may allow them to be
manipulated with electromagnetic ® elds in a similar way to
atoms.
There are several promising new avenues for the further
development of atom manipulation . The ® rst possibilit y lies
in increasing the amount of momentum transferred. This
can produce larger spatial separations between the interferometer arms, larger enclosed areas, and hence more
sensitive interferometers. A recent method that has been
developed in Oxford, called the quantum accelerator
mode [41], involves the applicatio n of many pulses of a
standing wave of laser light. The key feature is that the
standing light wave is translated along its length by a
certain amount between each pulse. In this way, atoms with
the right initial conditions will receive a momentum
transfer of approximately two photon recoils with an
e ciency greater than 99% at every pulse. This can be
contrasted with the e ciency of a Raman process which at
best is 85% for every two photon recoils of momentum
transferred. Although this diŒerence does not seem overly
signi® cant, after twenty pulses the fraction of atoms
remaining in the Raman case has fallen to 4% , while that
in the accelerator mode case is still 82% . The accelerator
mode is therefore capable of transferring momenta up to,
say, 100 ±hk with high e ciency. Figure 16 shows experimental data where each line is a measurement of the
momentum distribution of an atomic ensemble after a given
number of light pulses. Each momentum distribution was
measured directly by allowing the atoms to fall through a
sheet of probe light, the absorption of which revealed the
time of ¯ ight of the atoms. In ® gure 16, a fraction of the
atomic ensemble which is gaining momentum linearly with
pulse number and moving out to high momenta is clearly
visible. The atomic source was a MOT which had a
momentum distribution such that only about 25% of the
atoms satis® ed the initial conditions to enter the accelerator
mode. However, once atoms are in the accelerator mode,
the data show their high probabilit y of remaining there. A
technique such as this may therefore be developed into a
beam splitter which is capable of transferring large
momenta to atoms thus creating a large spatial separation
between the interferometer arms. This in turn could create
a more sensitive atom interferometer.
A diŒerent approach to the manipulation of atoms lies in
the ® eld of guided atomic waves and more particularly
using miniaturized integrated atom optics. Such systems
allow the construction of atom interferometers which are
more akin to the optical ® bre and ring laser interferometers
that have proved so successful as robust methods of
measuring rotations. These devices are optical interferometers whose enclosed area is greatly enhanced, compared to
R. M. Godun et al.
92
constant. Atoms which align themselves so as to have a
component of magnetic moment parallel to the magnetic
® eld (l b
e U > 0) are strong ® eld seeking and will execute
circular orbits around the wire as shown in ® gure 17 (a).
This behaviour is acceptable for wires in free space;
however, if the wire is on a surface then it will not be
possible to guide the atoms with this con® guration since
they will come into contact with the surface. A way around
this problem is to use weak ® eld seeking atomic states
(l b
e U < 0) and apply an additiona l magnetic ® eld Bb ia s
which is perpendicular to the wire. This creates a magnetic
® eld minimum, a distance
rs ˆ
Figure 16. Experimental data showing the transfer of momentum to atoms using a quantum accelerator mode. The plot shows
the variation of the atomic momentum distribution with
increasing number of pulses. The fraction of the initial
distribution that satis® es the conditions to enter the mode is
approximately 25% . Once in the mode, the probability to remain
there is over 99% per pulse.
their outward physical dimensions, by guiding light many
times around a looped ® bre, or a laser cavity [37]. These
compact systems are routinely used for inertial navigatio n
in aircraft, missiles and even the tips of drills used for oil
prospecting. We will now review several of the potential
methods for guiding atom waves which would allow the
construction of analogous atom optical devices.
Experiments at Innsbruck [16] and Harvard [42] have
taken the ® rst steps in this direction by using microfabricated wires on the surface of a chip. Both of these
experiments are based on guiding atoms using the magnetic
® eld gradient produced by current carrying wires.
The potential experienced by a neutral particle with
magnetic moment, l , in a magnetic ® eld, B, is V ˆ ¡l B. If
the gradient of the magnetic ® eld is non-zero then the
particle will experience a force. In the case of a current
carrying wire the magnetic ® eld is given by
Bˆ
l0I 1
2p
r
b
eU ,
where I is the current in the wire, r is the radial distance
from the wire and b
e U is a unit vector in the azimuthal
direction around the wire. Assuming that the magnetic ® eld
direction experienced by the atom changes slowly compared to the Larmor precession of the magnetic moment
(the adiabatic approximation) , we can treat l b
e U as a
l0
2p
I
Bbias
away from the centre of the wire. Thus the weak ® eld
seeking atoms are trapped in a long tube parallel to the
wire, see ® gure 17 (b), which can now be mounted onto a
surface. Many other types of wire con® guration are
possible. For example, at Harvard four wires have been
mounted on a chip to create a magnetic potential with a
minimum above the surface, with no need for an external
bias ® eld. This shows that `integrated’ atom optics is truly
becoming a reality.
The group at Innsbruck have also demonstrated atomic
beam splitters using these methods, both in free space and
on a surface. The essential idea is simply to divide the
current carrying wire into two at a `Y-junction’. The ratio
of the currents in the arms of the Y determines the
beamsplitting ratio. Although the coherence preserving
properties of such atom optical elements have yet to be
con® rmed, there is no reason to suspect that they should
not be usable in an atom interferometer with a suitable
atomic source. The main criterion for such a source is that
only a single mode of the atomic waves should propagate in
the waveguide. For the currents and wire sizes which seem
to be feasible this will mean using a Bose ± Einstein
condensate. It is possible to build atomic sources, such as
a magneto-optic trap, right onto the chip containing the
atom optics. Eventually it should be feasible to create a
BEC on the chip and couple it directly into the single mode
guide created by the wire. This type of technology might
enable atom optics and interferometry to move into the
realm of mass production with a consequent increase in the
applications for such devices.
Another route towards building better atom interferometers is the use of hollow ® bres for atom guiding. By using
either magnetic or optical forces atoms can be channelled
through the hollow core of the ® bre and be kept away from
the walls. The magnetic technique has been demonstrated
at the University of Sussex [43] and is accomplished by
using special ® bres which are manufactured to have four
wires embedded in their walls as pictured in ® gure 18. The
Prospects for atom interferometry
93
Figure 18. The con® guration of wires used in the Sussex
experiments to create quadrupolar magnetic ® elds to guide
atoms down the central hole of the ® bre.
Figure 17. The magnetic ® elds and the resulting atom
trajectories in the cases of (a) circular ® eld lines from a current
carrying wire and (b) the same current carrying wire with an
oŒset bias magnetic ® eld. In each case the atoms are guided
along the path de® ned by the wire. [We thank D. Cassettari for
allowing us to reproduce this ® gure from the Innsbruck group.]
current carrying wires produce a magnetic potential which
traps the weak ® eld seekers in the ® bre core. In the Sussex
experiments the core had a radius of 261 l m and it was
found that atoms which were coupled into the guide
remained within a 100 l m radius of the centre of the ® bre.
Even though the atoms were allowed to propagate for tens
of centimetres the only signi® cant loss appeared to be
caused by collisions with the background gas.
Optical forces can also be used to guide atoms through a
hollow ® bre. When an atom is placed in an optical ® eld
which is detuned by a frequency D from an atomic
transition and has an intensity I, the energy of the atom
shifts by an amount which is proportiona l to I/D . This is
the ac Stark shift and can give rise to what are known as
dipole forces if a gradient in the intensity exists [20]. For
example, if the light is tuned below the atomic resonance
(negative D ) the atom will experience a force towards
regions of higher intensities (high ® eld seeking), while it will
be attracted towards lower intensities (low ® eld seeking)
when the light is blue-detuned (positive D ). A typical
application of the dipole force is the re¯ ection of atoms
from a glass surface in which blue-detuned light has been
totally internally re¯ ected. In such a situation an evanescent wave will be formed on the outside of the glass. This
wave will have an intensity pro® le which falls oŒ
exponentially as the distance from the surface is increased.
Since the atoms in this situation are weak ® eld seeking they
will be repelled from the glass, eŒectively realizing an
evanescent wave mirror. This process can also be used for
atom wave guiding in a hollow core ® bre. If blue-detuned
light is coupled into the walls of such a ® bre, an
exponentially decaying evanescent light ® eld will leak out
of the walls and into the ® bre core. Although a group at
JILA in Boulder, Colorado were able to guide atoms
through a 6 cm long piece of hollow ® bre [44] using this
idea as the basis of their technique, there still remain a
number of signi® cant problems to overcome. For example,
the attenuation of the light in the ® bre walls and the
existence of laser speckle which can lead to regions in the
® bre where the intensity of the light is greatly reduced will
both need to be addressed. However, it should eventually
be possible to develop atom beamsplitters and then atom
interferometers which are based on these methods.
7.
New experiments
With the improvements in atom interferometry that may
soon be availabl e there are many new fundamental and
94
R. M. Godun et al.
technologica l applications ahead. For example, atom
interferometers oŒer the very real possibility of becoming
the most sensitive way of measuring rotations. Perhaps the
most important use of rotation sensors at the moment is for
navigation . By monitoring changes in orientation and
acceleration, the gyroscopes in an inertial navigatio n
system can determine current location if the position of
the starting point is known. The di culty with such systems
is that if small errors from the gyroscope are allowed to
accumulate the knowledge of position will be poor.
Although it is possible to oŒset some of these problems
through supplementary data from satellite-based systems,
the need for more precise gyroscopes is clear.
Scienti® c application s of a high precision atom-interferometer gyroscope include measurements of variations in
the Earth’s rotation rate, rotational movements of tectonic
plates and eŒects predicted by the theory of General
Relativity. In the latter case, one would measure the
precession of a reference frame de® ned by a gyroscope
relative to the distant stars. Two eŒects are predicted, the
geodetic eŒect which results from rotation around a
massive non-rotating body and the Lense ± Thirring (or
`frame dragging’, as it is sometimes known) eŒect produced
by rotation of a massive body. It is this last prediction that
has proved the hardest to test. Although there has been an
experiment which used changes in the orbital parameters of
two satellites to determine the Lense ± Thirring precession
to within about 20% of its predicted value [45], there clearly
remains scope for improvement. Problems of long-term
stability mean that atom interferometers still have some
way to go before they can be competitive in this ® eld. For
instance, the atom interferometer gyroscope at Yale
currently has the best reported short term rotation rate
sensitivity of 6 10 ¡ 1 0 rad s¡ 1 during one second of
integration time [35]. This is still far from the predicted
6 10¡ 1 5 rad s¡ 1 of the Lense ± Thirring eŒect near the
Earth’s surface (including low Earth orbit). However
improvements in the long-term stability, which at the
moment limits the useful integration time of this instrument, may push the sensitivity within reach. Even so, it is
still likely that a new interferometer with a larger enclosed
area will need to be built. At Yale there are plans to build a
20 m long device which would increase the area and hence
the sensitivity by a factor of 100 over the current 2 m
instrument.
As mentioned previously, atom interferometers have also
proved their worth in the measurement of the Earth’ s
gravitational acceleration. Other interesting possibilitie s for
atom interferometers in the context of gravity include a
better determination of the gravitational constant, G, and
the investigatio n of alternative theories of gravitation .
Regarding this last point, it is surprising how many aspects
of gravitationa l force are still poorly understood. For
example, it is only very recently that it has been possible to
test the inverse square law with good precision below the
centimetre length scale [46]. Several theories [47,48] have
speculated that there could be a marked deviation of
gravity from the inverse square law on a scale that ranges
from a centimetre down to the Planck length of
1.6 10¡3 5 m. Clearly, further investigatio n is needed and
it is possible that atom interferometry could have a role to
play. Atoms oŒer the advantag e of being microscopic
particles which can get very close to a test mass. One
scenario might be an atom interferometer with one arm
running alongside the test mass. The gravitational ® eld
would induce a phase shift which would enable the form of
the potential (its dependence on distance from the test
mass, for example) to be deduced.
8.
Conclusion
We have discussed the physical basis of atom interferometry and have demonstrated that although it is a relatively
new ® eld, it has already created a tremendous wealth of
interest and research. This is due to the enormous range of
potential application s of instruments based on atom
interferometry, including clocks, gyroscopes and accelerometers. Furthermore, the opportunitie s that technological
advances will bring for investigatio n of fundamental
physics such as general relativity and quantum mechanics
are extremely exciting.
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Rachel Godun is a Junior Research Fellow at
Christ Church, Oxford University. As a member
of the Atom Interferometry Group in Oxford, she
performed experimental studies of beam splitting
mechanisms for her DPhil thesis under the
supervision of Professor Keith Burnett.
Michael d’ Arcy is a Jowett Senior Exhibitioner at
Balliol College, Oxford University. Following
studies in particle physics, he joined the Atom
Interferometry Group to undertake experimental
investigations of quantum chaos in atom optics.
He is currently working towards an understanding of quantum-classical correspondence in a
chaotic Bose ± Einstein system.
Gil Summy is a lecturer in Physics at the
University of Oxford. He has been interested in
the ® eld of quantum and atom optics since the
early 1990s when he was a student studying with
Professors David Pegg, Bill MacGillivray and
Max Standage at Gri th University in Australia.
He has been associated with the atom interferometry group at Oxford since its inception in 1994.
His current areas of research include quantum
chaos and atom interferometry with BECs.
Keith Burnett is Head of Atomic and Laser
Physics and a Fellow of St John’s College at
Oxford University. His background lies in
theoretical and experimental studies of atom ±
light interactions. His current research is mainly
into the theory of coherent matter waves and
atoms in intense laser ® elds, but he is also
involved in experimental atom optics.