CASI: Cold
Atom Sagnac Interferometer
Pioneering
experiments at Yale [1,2]
and Stanford [3] displayed
recently the fascinating potential of matter-wave interferometers for
precision
measurements. Most prominent applications for such quantum sensors are
inertial
measurements, metrology and open questions in fundamental physics. For
example,
the measurement of rotations with atom interferometers is ten orders of
magnitude more sensitive compared to optical means, underlying the same
experimental
parameters. Our experiment investigates different strategies for the
realisation of a transportable matter-wave sensor, called CASI. CASI
stands for
Cold Atom Sagnac
Interferometer as it uses two counterpropagating
pulsed or continuous beams of cold 87Rb
atoms to measure rotations thanks to the Sagnac-effect
in a so-called Mach-Zehnder
type atom interferometer.
In this kind of interferometer the inertial
force is encoded in the
phase of the atomic wavefunction
via the interaction
with the atom optical elements, e.g. beamsplitters
and mirrors, which are realised with optical 2-photon transitions.
The use of cold atoms makes it possible to
realise compact devices with
sensitivities competitive with classical state-of-the-art sensors. The
heart of
our set-up will be a 15cm-long Mach-Zehnder
interferometer in spatial and/or temporal domain consisting of 3
atom-laser
interactions. The length of the complete sensor will be about 90 cm.
Each of
the 2 atom sources consists of 2 magneto-optical traps (MOT): A
2-dimensional
MOT, which forms a brilliant atomic beam,
that is
loaded into a 3D MOT to prepare a cold and intense atomic ensemble.
CASI has been designed as a transportable
device and can be compared
with other matter-wave sensors such as the cold caesium atom gyroscope
at the
BNM-SYRTE in
For
the realization of atom optical elements like beam splitters or
mirrors, one
has to think of suitable methods for manipulating the atoms. In
addition to
former widely used massive ruled gratings, today the interaction
between light
and matter is used for this purpose. This can be understood as a
coherent
exchange of photons and, thus, photon momenta.
This
is depicted on the right side. An atomic ensemble where the atoms have
two
energy levels |g> and |e> is split into two parts. The
interaction acts
on the internal as well as external degree of freedom. Therefore, a
mechanical
momentum can be transferred to the diffracted part. The fraction of the
number
of atoms that is diffracted depends on several parameters:
- laser power
- interaction time
- laser frequency
As a consequence, it seems favourable to
combine consecutive
interactions of this type to form different path topologies. In
addition, after
the final interaction the number of atoms in the different output ports
depends
on the laser phases at the times of interaction. When the number and
types of
interactions is chosen such that one or several of the possible paths
overlap,
an interference pattern of the atomic waves can be employed and an atom
interferometer arises. In this context, atom interferometers have many
similarities to the well known optical ones whereas here the parts of
light and
matter are interchanged. As an example this technique has been used for
atomic
clocks since many years whereas the 'optical' transition is realized by
a
microwave.
In contrary to atomic clocks, where the
interferometer is most sensitive
to frequency changes because of the chosen topology, one can employ
atom
interferometers that are suitable for measuring inertial forces thanks
to their
sensitivity to phase changes in the light field between the different
atom-light interactions. These phase changes arise from the fact, that
under
the influence of an external potential, e.g. the gravity field, the
atoms
experience different potentials for different interferometer paths.
This
results effectively in a temporal and/or spatial change of the times
and/or
points of the light-atom interaction, respectively. Naively spoken, the
phase
of the light field that the atoms 'see' changes.
Sagnac
effect
For a better understanding of our atom
interferometer let us first
consider the basic Sagnac
effect in an easy picture:
Two waves (red W1 and blue W2) travel around an
area with surface A
(grey colour). Without a rotation both waves starting from
point 1 arrive at the
same time at the end point 2.
But when the area A rotates with angular velocity W
the
waves arrive at different times at the end point 2. In that case,
despite a
time difference, both waves arrive at the end point with a different
phase.
This Sagnac phase f
must be calculated in relativistic terms and can be expressed like:
Eq.:1
where
A is the enclosed area, E the
relativistic energy of the considered wave and W
the angular velocity of the rotation. This formula is valid for all
natures of
waves and, hence, also for massive particles, which can be described as
de-Broglie waves. For
atoms, the Sagnac
phase is
Eq.:2
with
m the atomic mass.
Compared to an optical wave in the visible spectrum, the intrinsic Sagnac phase for an atom (our
case: Rubidium) is 10 orders
of magnitude bigger assuming equal area A. This great advantage is the
main
motivation for employing matter wave interferometers as inertial
sensors.
Mach-Zehnder-Interferometer
As described previousely,
for the measurement
of rotations one has to implement an interferometer with enclosed area A perpendicular to the axis of
rotation. A good choice for
this purpose is the analogon
to the optical Mach-Zehnder
type interferometer. In this type, a 50:50 beam
splitter first devides
the incoming wave into two
equal parts, then a mirror redirects the diverging waves and finally
both parts
are recombined with another 50:50 beam splitter.
As can be imagined, this scheme can be realised
for atomic waves with
well controlled laser light fields using the type of interaction
described
previously.
In terms of atom optics, the beam splitters,
respectively the mirrors,
are named p/2
and p
pulses for historical reasons. As denoted in the picture, the number of
atoms
in the two output ports now depends on the laser phases
f during each interaction. This specific laser
phase,
demonstrated here with the laser wavefronts,
can now
be altered due to external potentials. For example, for an
acceleration in the direction of the beam before the last p/2
pulse, the atom can therefore now be in an antinode
of the light field, as it would have been in an node without the
acceleration.
The result would be a different interference pattern between the 2
atomic paths
and hence different output intensities.
The targeted goal of realising an extremely
sensitive sensor for
rotations gives several stringent requirements to the experimental
setup:
- A
stable and well controlled atomic source
- A
low phase noise interferometer laser
- A
sophisticated detection of the interference pattern, that means, the
two output ports
Another goal is the transportability of the
entire experiment.This
has two reasons: First for a possible comparison of two atomic rotation
sensors
(see
GOM_homepage),
and also as a ground based test facility
for future satellite missions (see
HYPER_homepage).
Atomic
source
As previously mentioned, CASI is working with
laser-cooled atoms. One
atomic source consists of a double MOT-system, which is a 2-dimensional
MOT, that is loading a
3D-MOT with high atomic flux. From
the 3D-MOT the atoms are launched onto a ballistic parabolic trajectorie using the moving
molasses technique. In
principle, the 3D-MOT can also function as a post-cooling stage only,
to be
operated in a continuus
mode, which would result in a
collimated cold atomic beam.
The reason for the use of cold atoms is the
following: As can be seen
from Eq.:1, the Sagnac
phase is proportional to the
enclosed area A. This area depends both on the interferometer length L
and the
ratio of the transverse to longitudinal velocity:
As the interferometer length is limited by the reqiurement
of a transportable setup and the transverse velocity is mainly
determined by
the used photon's momentum, the option for CASI is to improve the
velocity
ratio to get a biggest area as possible. Although multiple photon kicks
could
in principle be used, our approach is to reduce the atomic launch
velocity.
Therefore laser cooling seems well suited, as the velocity spread of
the atoms
can also be reduced in that way.
As already described in [1], CASI will also use
two sources,
that are emitting atoms in opposing directions. As the
interferometer
lasers are applied perpendicular to the atomic launch direction, in
this way a
differential measurement can be achieved: Most of the external
perturbations
will cause an interferometer phase shift, that is independent of the
atom's
velocity direction, whereas the sign of the Sagnac
phase changes, with changing the atomic velocity direction. So, by
using two
atom interferometers, that use the same laser beams, and substracting
these signals, the desired rotational signal can be read out only.
Interferometer
laser
As it is important to have a well controlled
frequency and phase for the
beam splitting lasers, CASI will use a Phase locked Raman Laser System
for this
purpose. This has several advantages: The use of 2-photon Raman
transitions
between different atomic Hyperfine
ground levels
allows to treat the atom as an effective 2-level system, because
spontaneous
emission can be neglected and the spectral resolution of the
transitions is
high. As the two Raman beams are applied in counterpropagating
directions, the atom will absorb a photon from one beam, which is
reemitted
into the other beam. That way, the atom gets the double transverse
velocity.
The phase-lock is implemented at 6,8
GHz, the
Rubidium-87 Hyperfine splitting between ground levels F=1 and F=2. For
this
frequency, well established microwave equipment can be used.
The Laser itself are
Diode Lasers in MOPA
configuration. The same scheme is used for the cooling light for the
two
sources. By using diodes, the benefits are low cost and easy to use
Laser
sources.
Detection
For a good signal-to-noise ratio, the detection
of both output ports is
planned. A well controlled atomic number at the interferometer input is
in
principle not needed that way, but still favourable. The detection
scheme, as
well as the state preparation entering the interferometer, relies on
optical
pumping and fluorescence detection. It is very similar to the
techniques used
in atomic fountain clocks and therefore well established.
At the moment, the experiment is still under
construction, but several
experimental steps have already been achieved. The atomic sources have
been
realised and the crucial experimental parameters were characterized.
Examples
are given in the picture below.
A first version of the Raman-Laser-System has
been set up and
characterized. The graphics below show a picture of the two lasers and
a
measurement of the laser beatnote
at 6,834 GHz
recorded on a fast photodiode. Our MOPA Lasers deliver each more than
500 mW optical power
and the residual phase error between them
is about 0,039 rad. For
highest resolution rotation
measurements this will be further improved (expected phase error ~
1mrad) with
the use of a ultrastable
microwave reference oscillator. This oscillator system has already been
build in cooperation with
BNM-SYRTE and will replace the
actual oscillator soon.
As the two key components of the experiment,
sources and Raman Laser,
had been set up, we performed a first serious of atom interferometric
measurements. These were just for testing purposes, and without a sensitivity to inertial forces.
Shown below are Rabi
oscillations between the 2 atomic ground states |F=1,mf=0>
and |F=2,mf=0> while changing the
interaction time of the Raman
Laser with the atoms. The measurements were performed in the horizontal
fountain geometry, this means with freely falling atoms.
For testing the sensitivity to any frequency
effects (e.g. Zeeman-,
AC-Stark) we can perform a Ramsey-type
measurement, which is a serious of two
p/2-pulses encolsing
a free evolution time. Scanning the frequency
difference of the lasers results in a Ramsey pattern like it is also
shown above.
Finally we performed measurements in a Mach-Zehnder-type
topology, here in time domain. While scanning the difference in
Raman-Laser
phases between the last 2 pulses we produce the well known
interferometer
fringes.
At
the moment we are working on systematic studies for improving several
experimental steps, that
are not inertial sensitive,
for example atomic state preparation or different detection schemes.
After that
we plan to do first interferometric
measurements in
time domain that are actually sensitive to rotations. For this purpose,
an
anti-vibration platform, which will support the whole experimental
platform,
has already been tested.
Publications:
Differential
atom interferometry
beyond the
standard quantum limit,
K. Eckert, P. Hyllus,
D. Bruß, U. Poulsen, M. Lewenstein, C. Jentsch, T. Müller, E.M. Rasel and W. Ertmer
PRA 73,
013814 (2006)
Atom
Optics, Guided Atoms, and Atom Interferometry
.
J.J. Arlt,
G. Birkl, E.M. Rasel and W.
Ertmer, Adv. At.
Mol. Opt.Phys.
50, 55-89 (2005)
HYPER:
A Satellite
HYPER: Hyper-Precision
Cold Atom Interferometry
in Space,
E.M. Rasel et al. ESA Assesment
Study Report, ESA-SCI (2000) 10
Dr. Ernst Rasel,
group leader
Tobias
Müller, PhD student
Thijs Wendrich,
PhD student
Michael Gilowski,
Diploma student
Former
members:
Dr. Christian Jentsch
References:
[1] Gustavson,
T.L., Landragin,
A., and Kasevich, M.A.,
Class. Quant. Grav. 17,
2385 (2000)
[2] Snadden,
M.J., McGuirk,
J.M., Bouyer, P.,
Haritos, K.G., and Kasevich,
M.A., Phys. Rev. Lett. 81,
971 (1998)
[3] Peters, A., Chung, K.Y., and
[4] Yver-Leduc,
F., Cheinet,
P., Fils, J., Clairon, A., Dimarcq, N., Holleville, D., Bouyer, P., and Landragin, A., J.
Opt. B 5,
36 (2003)
For
further information regarding the experiment or for job opportunities,
please
contact: rasel@iqo.uni-hannover.de