PROJECT DESCRIPTION: ATOM INTERFEROMETER
A. Introduction
Atom interferometers, in which atom or molecule de Broglie waves are coherently
split and then recombined to produce interference fringes, hold tremendous promise to
become precision instruments. The ability to accurately measure interactions that
displace the de Broglie wave phase has led to qualitatively new measurements in three
broad areas: atomic and molecular physics, fundamental tests of quantum mechanics, and
new ways to measure acceleration and rotation. Our group has pioneered techniques in
each of these areas, including the first (and only) atom interferometry experiments that
employ physically separated paths to make precision measurements.
These
investigations are now ready to move beyond demonstrations - which have already
captivated widespread general interest - toward dedicated precision measurement
applications.
Figure 4. A schematic, not to scale, of our atom interferometer. The 0 th and 1st diffracted orders
from the first grating are redirected by the middle grating and form an interference pattern in the
plane of the third grating. The detector records the flux transmitted by the third grating. A
10µm thick silicon septum before the 2nd grating separates the two arms of the interferometer.
All critical components are mounted on a vibrationally isolated breadboard including the
gratings, an optical interferometer (thick lines) to measure the relative positions of the atom
gratings, and inertial sensors to monitor the overall board translation/rotation.
B. Recent Scientific Results and Publications:
Longitudinal interferometry -- Should we include this?
Most previous experiments in atom optics have involved manipulation of the
momentum of a matter wave transverse to its direction of propagation. However, one
may also alter a wave’s longitudinal momentum state, placing each atom in a
superposition involving different wavelengths corresponding to different longitudinal
momenta and energy.
Two doctoral dissertations in our group were devoted to
developing this theory and implementing experiments using resonance regions that can
create and recombine such longitudinal momentum coherences, essentially serving as
atomic beam splitters. By taking advantage of the freedom to apply different frequencies
to successive oscillatory field regions (a technique which we have originated, and term
“differentially detuned separated oscillatory fields” or DSOF), we have generalized
Ramsey's separated oscillatory field method and have demonstrated an interferometer
capable of manipulating longitudinal momentum coherences. We used this to determine
the complete description of the quantum state of a matter wave beam, by measuring its
density matrix or Wigner function. We used this technique on a perturbed atom beam,
and also on a beam originating directly from an oven - thereby resolving a long standing
controversy concerning this system’s correct quantum description.
Decoherence from Multiple Photon Scattering
Using our improved Mach Zehnder interferometer for atoms we completed a study of
quantum decoherence. The process of decoherence in quantum systems has been
described as the collapse of the wave function, and causes a transition from from
quantum mechanical to classical behavior. We have studied this emergence of classical
behavior by scattering a controlled number of photons from each atom within the
interferometer. We have demonstrated a calculatable and universal form of decoherence
which is relevant to quantum computation, quantum error correction,and quantum
communication. [KCR01]
Figure 5. Demonstration of the change in character of spatial decoherence with number of photon scattering
events. The interfering contrast is plotted as a function of the separation between the two interfering paths
at the point of scattering. Each curve corresponds to a different mean and standard deviation of the number
of scattering events (indicated). Contrast revivals in the small photon-number limit are clearly washed out
as more scattering events occur. In the large photon-number limit, the contrast loss relaxes towards a
gaussian.
Dispersion in the Matter Wave Index of Refraction
We recently measured the velocity dependence of the index of refraction seen by
sodium matter-waves passing through a gas target. In optical parlance, we measured the
dispersion, i.e. the variation of index with wavelength. Our experiment's unique
sensitivity to the phase shift of forward-scattered atoms provides data which have never
before been available for studing atom-atom interactions. In addition, our recent
experiment for the first time shows strong evidence for glory oscillations in the phase
shift - a novel interference effect which manifests as oscillations in the index of refraction
as a function of impact velocity [ADV95].
Much theoretical work has been stimulated by our earlier measurements of the
matter-wave index of refraction [SCE95], and there are conflicting predictions on how
the index should vary with velocity [ADV95, CAD97, FLK96, FLK97, VIG95 ]. The
variance in the predictions arises because the index is very sensitive to both long-range
(>5 Angstrom) and medium-range (0.5 to 5 Angstrom) inter-atomic potentials. We are
collaborating with theorist Robert Forrey in using these measurements to refine the
shapes of the long-range potentials between sodium and other gases (Ar, Kr, Xe, and N)
and test the new theoretical predictions inspired by our earlier work.
Figure 4. Preliminary data on the Re/Im ratio of the index of refraction for Na matter waves passing through Ar,
N2, Kr, and Xe. The data are plotted as a function of the velocity of the incident Na atoms. The solid lines are the
result of calculations using potentials found in the litterature [ADV95, BKZ91, CAD97, BZB92].
Electronic phase chopping
We have implemented a novel velocity-multiplexing scheme [HPC95, TIB01]
using two separated regions of inhomogeneous electric fields that can be pulsed on and
off in time. This overcomes the limitations of having a large spread in (and imprecise
knowledge of) atom velocities, and will allow us to make even more precise
measurements of atomic poliarzabilities.
The velocity distribution of our atom beam limits the accuracy of several different
interferometer experiments. Most interactions we seek to study, such as the Stark shift,
gravity, or rotations, cause a phase shift that depends on interaction time, i.e. is
proportional to 1/velocity. A spread in velocity therefore causes a spread in phase-shift
of the interference pattern, which lowers the atom-interference contrast if the average
applied phase is too large. Velocity multiplexing [HPC95] has been proposed to
overcome this de-phasing without loosing the count rate as would happen with simple
velocity selection.
Atoms inside the interferometer which pass through one of these electric-field
gradients emerge with a relative phase shift between the beams. Toggeling the two
gradients on and off in time rapidly compared to an atom's transit time between the two
regions causes atoms of certain velocities to interfere destructively, and others
constructively – which will cause a revival in contrast only at large phase shifts, greatly
increasing our sensitivity to the interaction we are studying (since our phase error is
roughly the same).
Figure 4. The inhomogeneous electric field regions used to implement velocity multiplexing. The timevarying electric field gradients imprint a velocity-dependant phase on the atoms in the interferometer of
either 0 or  radians. This will enable us to study larger perturbations to the interferometer.
Figure 4. The revivals in contrast depend on the frequency at which the electric field regions are pulsed.
These data, taken in the absence of an applied potential, indicate the velocity multiplexing is working
properly.
250,000
C. Interferometry Techniques
and Groundwork
300
Counts/sec
250
200
150
200,000
150,000
4,000
Transverse interferometry -- Update
100
this section.
2,000
50
Our group has pioneered the
0
0
development of transverse atom
Detector Pos ition
interferometry with micro-fabricated
transmission diffraction gratings, Figure 5. (left) Interference fringes from the original
with 400 nm period gratings in 1991. The scan
employing a three grating Mach- interferometer
required 400 seconds of data, the contrast is 12.9%, and the
Zehnder geometry. Collaborating with Signal/Noise ratio is 2.2. (right) Recent interference fringes
H. Smith’s group at MIT to fabricate acquired with greatly improved 200nm gratings and a higher flux
The scans were acquired in 10 seconds. Contrast in the
improved gratings using Achromatic beam.
upper (lower) fringes is 17.6% (48.9%) and the resultant S/N is
Interferometric (optical) Lithography, 79.2 (21.4). Note the different vertical axes.
we
have
demonstrated
atom
interference fringes using 100-nm period gratings, which give twice the beam separation
of our standard 200-nm gratings. Using the impoved interferometer we recorded the
highest contrast interference fringes yet achieved with 100nm period gratings (14.9%).
Our interferometer was sensitive enough to uncover what appear to be variations in the
phase/period of the 100nm gradings as a function of position on the gating window – a
defect that ultimately limited the usefulness of theses gratings for use in atomic physics
experiments. We plan to use improved gratings fabricated by H. Smith’s group which
should substantially increase our contrast and hence signal to noise.
Apparatus Improvements:
We significantly upgraded our apparatus for transverse interferometry. The vacuum
envelope of our atomic beam machine has been replaced by a series of 6-way crosses,
achieving greater length, facilitating access to the equipment inside the chamber, and
permitting the rapid reconfiguration of modular flanges which hold additional atom
optical elements. The new apparatus is very stable, and allows the simultaneous pursuit
of several different experiments, involving both longitudinal and transverse matter-wave
interferometers. The separated beam atom optical elements (gratings) are placed on an
optical platform separate from the vacuum envelope, which substantially improves the
flexibility of the interferometer as well as its thermal and vibration isolation.
In our new apparatus we have installed a test facility which allows us to charactarize the
open fraction and fidelity of the nano-fabricated diffraction gratings. We can observe the
atom-beam diffracton patterns of ten different gratings per week, which compliments the
SEM and optical observations as part of our ongoing collaboration with H. Smith’s nanofabrication team at MIT.
New Vacuum Chamber and Vibrational Isolation
With the support of an NSF equipment supplement, we have recently constructed a new
vacuum chamber consisting of five identical six-way crosses, each ~50cm long. The new
chamber increases the overall length of our beam machine to ~3.5m, allows up to 200µm
separation between the arms of our transverse interferometer, and has a large number of access
ports for flexibility and modularity. Atom optical components are now mounted on a
vibrationally isolated optical breadboard (Fig. 4) to reduce phase drift (crucial for future precision
measurements), and to lower vibrational noise to less than 10nm rms (necessary to achieve high
contrast interference with 100nm period gratings.) Phase shifts due to residual inertial noise will
be measured and corrected for using high sensitivity inertial sensors. These improvements should
largely eliminate effects of both vibration and inertial noise, yielding about a factor of two
improvement in overall signal-to-noise.
Atom Gratings
The critical components of our interferometer are freestanding diffraction gratings for the
atoms or molecules. Our fabrication techniques for these gratings have undergone several
generations of improvement since our first interferometer in 1991 (Fig. 5). Future goals of using
a hexapole focusing magnet to increase beam flux by a factor of 20 and realizing a spatial
separation of several hundred microns between the two interfering paths, will require gratings that
are physically larger and of significantly smaller period than those available in the past. We have
therefore initiated a collaboration with the group of Prof. Hank Smith at the MIT Nanostructures
Laboratory who has developed a holographic process called Achromatic-Interferometric
Lithography. This technique provides excellent large-scale uniformity such that a 100nm period
grating will be phase coherent over an area as large as 1cm2. These gratings have already been
used to observe 15th order atomic diffraction peaks, and we hope to begin using them in our
interferometer early in the new grant period.
Thin Septum
Using precision fabrication tools available at the MIT Microsystems Technologies
Laboratory, we have developed new techniques for manufacturing narrow freestanding
membranes, or septa, which we use to physically isolate the atom waves traversing the two arms
of our interferometer. We now construct a septum by anodically bonding a thin (10µm), rigid
silicon wafer to a borosilicate glass substrate in which a cavity has been cut to permit passage of
the atom beam and to serve as a gas cell for the index of refraction experiments described below.
The silicon and glass possess matched coefficients of thermal expansion, allowing us to cool the
gas cell and septum to liquid nitrogen temperatures to increase the resolution of our index of
refraction experiment. Vacuum deposition of a metal film will create a conducting surface to be
used in both polarizability measurements and studies of relativistic effects.
D. Proposed Experiments
With our improved transverse interferometer, we plan now to emphasize new and more
precise measurements in atomic physics as well as fundamental experiments in quantum
mechanics. Exploiting the unique capability of our separated beam interferometer to apply welldefined interactions uniquely to one arm of the interferometer, we aim to significantly improve
our knowledge of atomic and molecular properties that are inaccessible by any other experimental
means. The extreme sensitivity of our device will also allow us to investigate novel relativistic
and topological phases that have engendered recent theoretical controversy.
Polarizability of Multiple Alkalis
An atom’s polarizability governs its interaction with electric fields and is an important
parameter in Van der Waals interactions, electric dipole transition rates, and long-range
interatomic potentials. Several theoretical groups have expressed their interest in polarizability
measurements including Prof. Walter Johnson who recently calculated the polarizability of
sodium to compare with our earlier measurement [GROUP95_SCE] as part of his program to
check the atomic structure theories of parity violation in cesium [NMW88, WBC97]. We
propose to measure the polarizabilities of the alkali metals through cesium to <0.1% accuracy—
more than an order of magnitude better than current values (except for sodium
[GROUP95_ESC]), and to measure their relative polarizability at the 0.01% level. The species
independence of our gratings (versus light gratings) allows us to switch alkalis easily, and
velocity multiplexing will increase our accuracy and precision to the 0.1% and 0.01% targets.
Our relative measurements will ultimately be normalized by a single, higher precision experiment
using a sodium BEC (see Sec. IV.C).
Mention 100 nm gratings, thin septum, and Chopper technologies.
Anisotropic Polarizability of Sodium Molecules
We propose to make the first measurement of both the parallel and the perpendicular
components of the polarizability of the dimer molecule Na2 using our techniques of
molecular [GROUP95_CEH] and contrast [GROUP94_SEC] interferometry. This will
permit tests of various approximations used in molecular structure calculations [BOK94,
MIB88]. The asymmetry of the polarizability causes the electric field induced phase shift
to depend on the molecule’s j, m state. The beating of interference patterns for
molecules with different j, m generates considerable structure as a function of field
strength and permits the accurate determination of both polarizability components.
Proposed experiments
Polarizability of Na using velocity multiplexing
Pol of Cs using 100 vel multiplexing
Pol of Na2
Ratio pols of all alkali
(Rotations using vel multiplexing)
Relativistic Effects
An atom’s extreme sensitivity to electric and magnetic fields means that the
relativistically small fields generated by its motion can produce observable phase shifts.
These relativistic fields add velocity dependent terms to the atomic Hamiltonian,
resulting in a difference between the canonical and kinematic momenta, and questions
remain about how to incorporate such relativistic terms into the standard non-relativistic
formulation of quantum mechanics [WAR97]. These phase shifts are also intriguing by
virtue of their linear velocity dependence, which cancels the usual 1 v dispersion of phase
shifts in an interferometer, resulting in a velocity independent and sometimes purely
topological phase.
Induced Dipole in a Magnetic Field
It has recently been predicted [WEH95, WIL94] that a neutral, polarizable particle
which moves in crossed electric and magnetic fields acquires a non-trivial quantum phase
resulting from the interaction between the induced electric dipole moment and the
motion-induced electric field. Another author contends that the predicted effect is
unobservable [HAG96].
This effect represents the next logical extension of
investigations into various topological phases sparked by the remarkable discovery of the
Berry phase and its simplest examples, the Aharanov-Bohm and Aharanov-Casher
effects.
One proposal calls for a separated beam of neutral atoms to pass on either side of a
charged foil immersed in a magnetic field so that the cross product E  B has opposite
sign on the two sides—an arrangement easily achieved using our thin septum technology.
We propose to look for the predicted induced dipole phase shift of ~0.01rad, easily within
the milliradian resolution of our interferometer.
Anandan Force
A second controversy concerns Anandan’s [ANA89a, ANA89b] prediction of a
classical force acting on neutral dipoles in crossed electric and magnetic fields,
F  (  B ) 
1
 E 2
 

E  (  B) ,
c
t
c
Casella and Werner [CAS94, CAW92, WER94] claim that for a spin 1/2 particle, the last
term in the above expression is unobservable in principle, but Anandan and others
disagree [ANH94, WAR97]. We propose to resolve this controversy by applying a
differential electric field to atoms whose magnetic moments are precessing in a magnetic
field such that the E  (  B) force keeps the same sign throughout the measurement, but
is opposite on the two sides of the interaction region. The force will be sensitively
detected using longitudinal interferometry.
OLD MATERIAL:
We continue to pioneer new measurement techniques using coherent atom optics (such as
beam-splitters, mirrors and lenses) to manipulate matter waves. We operate an atom
interferometer, similar to a Mach-Zhender optical interferometer, which splits deBroglie
waves of matter into two physically separate paths. After an interaction region where
each atom can pass simultaneously on both sides of a metal foil the matter waves
recombine, forming interference fringes. We monitor the phase and contrast of these
fringes, which are extremely sensitive to any forces on the atoms.
This year we completed three experiments on decoherence, we are midway through a
measurement of the matter wave index of refraction, and we are developing a novel atom
optic for velocity multiplexing. Each project described in this report refines atom
interferometry as a tool for making measurements of atomic properties and probing
fundamental issues in quantum physics.
We apply atom interferometry toward fundamental and applied scientific
problems such as studying quantum mechanics and making better gyroscopes. Matterwave interference enables novel and more sensitive studies of interactions between atoms
and their environment (e.g., static E-M fields, radiation, and other atoms).
We are devoted to using atom interferometry on a range of fundamental and applied
scientific problems. Our atom interferometer realizes a Mach-Zehnder geometry using
three nanofabricated transmission gratings, and generates an atom-beam interference
pattern. Its most unique feature is a spatial separation of the two interfering beam paths,
which permits the application of an interaction to only one of the two paths. Presently we
are measuring the index of refraction seen by sodium matter waves passing through a
target-gas which we have confined to one arm of the interferometer. We recently
mounted the gratings on an optical breadboard suspended vibration-free inside the
vacuum system, which makes better contrast and phase stability. We have also doubled
the separation between the two arms of the interferometer by incorporating a new set of
nano-fabricated diffraction gratings which each have a 100-nm period. These
improvements are geared towards making more precise measurements of basic atomic
properties.
Long-term research objective:
Matter wave interferometers, in which de Broglie waves are coherently split and then
recombined to produce interference fringes, have opened exciting new possibilities for
precision and fundamental measurements with complex particles. The aim of our research
program is to extend the ideas and techniques of atom optics and atom
interferometry which underlie atom interferometers, to use these devices to make
qualitatively new and/or more precise measurements in atomic physics, and to perform
fundamental experiments in quantum mechanics based on our ability to measure
interactions that displace the de Broglie wave phase or change the quantum coherence of
the beams (reducing the amplitude of the interference pattern).
Science and Technology objective:
To develop the techniques of atom optics and atom interferometers, and to find new
applications in many scientific and technical arenas. We have pioneered applications in
three major areas: precision measurements in atomic physics, atom interferometric
inertial sensors, and investigations of fundamental quantum mechanical principles.
Approach:
Our transverse Mach-Zehnder interferometer for atoms and molecules uses three
nanofabricated transmission gratings, and generates a "white-fringe" (i.e. insensitive to
momentum spread in the beam) interference pattern. Its most unique feature is a spatial
separation and isolation of the two interfering beam paths, permitting the application of
an interaction to only one of the two paths. Also, we have recently constructed a novel
interferometer in which the two interfering paths are separated in longitudinal momentum
space. It is ideally suited to the study of interactions that change the kinetic or potential
energy of an atom, leading to time-dependent superpositions of states with different total
energies. We have also started atom interferometry experiments using a Bose-Einstein
condensate in collaboration with Ketterle. Using BEC and lasers we have developed a
means of amplifying a matter wave which can enhance the contrast of atom interference
fringes.
Progress:
Using our improved Mach Zehnder interferometer for atoms we completed a study of
quantum decoherence. The process of decoherence in quantum systems has been
described as the collapse of the wave function, and causes a transition from from
quantum mechanical to classical behavior. We have studied this emergence of classical
behavior in three different experiments. By scattering a controlled number of photons
from each atom within the interferometer we have demonstrated a calculatable and
universal form of decoherence which is relevant to quantum computation, quantum error
correction,and quantum communication.
This year we have also made new measuremnts of the matter-wave index of refraction.
Our experiment's unique sensitivity to the phase shift of forward-scattered atoms provides
data which have never before been available. These measurements offer a new test for
theories of inter-atomic potentials, which in many cases only predict potential minima
with 5% to 10% accuracy. In addition, with the present experiment we see evidence for
glory undulations in the phase shift as a function of matter-wave deBroigle wavelenth. In
collaboration with Robert Forrey [FLK97] and Jim Baab, theorists who have expertise in
the complex scattering calculations necessary to fit our data, we will determine the NaAr, Na-Xe, Na-Kr, and Na-N2 inter-atomic potentials more accurately than ever before.
Technology Transfer
Our demonstration of the inertial sensing capabilities of atom interferometers continues
to garner widespread interest both within the scientific community where it is hoped such
devices will eventually lead to tests of general relativity, and in the military where atom
interferometers may one day replace laser gyroscopes in some inertial navigation
systems. Our grating fabrication efforts in collaboration with Prof. Henry Smith at MITs
Microsystems Technology Laboratory are helping to test the large scale reproducibility
and feature-size limits of UV lithography.Our most recent demonstration of a calculatable
and universal form of decoherence is relevant to qunatum omputation, quantum error
correction and quantum communication. Because quantum interference is essential for
these quantum information processing applications, the process of decoherence needs to
be understood. The kind of decoherence we studied, which results from an environment
where multiple scattering events each cause a small amount of decoherence, is one of the
major problems faces by current efforts on quantum computation. It is too early to predict
the ultimate destiny of atom amplification, but is seems likely that it will result in
improved signal-to-noise in future matter wave devices.
Better knowledge of inter-atomic potentials will be one important result from our matterwave index of refraction experiment. Theoretical understanding of inter-atomic potentials
has applications in other areas including the lighting industry and atmospheric chemistry.
III. PROJECT DESCRIPTION: ATOM INTERFEROMETER
A. Introduction
Matter wave interferometers, in which de Broglie waves are coherently split and recombined
to produce interference fringes, have opened new possibilities for precise and fundamental
measurements with complex particles. Following the near simultaneous demonstration of four
atom interferometers in 1991 [CAM91, KAC91, KET91, RWK92] intense activity has been
devoted to interferometers using different atomic species, geometries, and components.
Interferometers have now been
made for hydrogen [CWM93],
helium
[PFK97],
neon
[GML95], sodium [KAC92],
magnesium [HPR97, HPR98,
SSM92],
argon
[ROB95],
potassium [CLL94], calcium
[MOO95, YOM98], rubidium
[CKS97], molecular iodine
[BCD94], and cesium [FSW98, Figure 4. A schematic, not to scale, of our atom interferometer. The 0th and 1st
diffracted orders from the first grating are redirected by the middle grating and
form an interference pattern in the plane of the third grating. The detector records
the flux transmitted by the third grating. A 10µm thick silicon septum before the
2nd grating separates the two arms of the interferometer. All critical components
are mounted on a vibrationally isolated breadboard including the gratings, an
optical interferometer (thick lines) to measure the relative positions of the atom
gratings, and inertial sensors to monitor the overall board translation/rotation.
GBK97, SGA96, WHH97, ZYC94], and for various trapped species [CKS97, CKS97, HMW98,
SHI96, SSH93, WMM98].
Our goal is to advance atom interferometric techniques and to apply them to obtain new
scientific results. So far, our results have fallen into four classes: measurements of atomic and
molecular properties, investigations of fundamental physics, measurement of inertial effects, and
application of new techniques. During the last three years we have published pioneering work in
each of these areas, including measurements of the index of refraction of atomic gasses for Na
and Na2 de Broglie waves [GROUP95_SCE, GROUP97_HCL] fundamental studies of quantum
decoherence [GROUP95_CHL], rotation sensing [GROUP97_LHS], and demonstration of a
novel longitudinal coherence rephasing effect [GROUP98_SDK], and we have completed a
search for longitudinal momentum coherences in an atomic beam (paper in progress). Some
examples of our advances in atom interferometry technique include improvements in
nanofabrication techniques for atom gratings [GROUP95_RTCa, GROUP95_RTCb] and the
invention [GROUP98_PRD] and demonstration of amplitude modulation optics and longitudinal
interferometry.
B. Scientific Results and Publications from Prior NSF Support
Our atom/molecule interferometer utilizes a Mach-Zehnder geometry with three
nanofabricated transmission gratings to generate a “white-fringe” (i.e. insensitive to momentum
spread in the beam) interference pattern. Its most unique feature is complete spatial separation of
the interfering beam paths, which permits the application of an interaction to only one of the two
paths (Fig. 4).
Techniques and Groundwork
New Vacuum Chamber and Vibrational Isolation
With the support of an NSF equipment supplement, we have recently constructed a new
vacuum chamber consisting of five identical six-way crosses, each ~50cm long. The new
chamber increases the overall length of our beam machine to ~3.5m, allows up to 200µm
separation between the arms of our transverse interferometer, and has a large number of access
ports for flexibility and modularity. Atom optical components are now mounted on a
vibrationally isolated optical breadboard (Fig. 4) to reduce phase drift (crucial for future precision
measurements), and to lower vibrational noise to less than 10nm rms (necessary to achieve high
contrast interference with 100nm period gratings.) Phase shifts due to residual inertial noise will
be measured and corrected for using high sensitivity inertial sensors. These improvements should
largely eliminate effects of both vibration and inertial noise, yielding about a factor of two
improvement in overall signal-to-noise.
Atom Gratings
The critical components of our interferometer are freestanding diffraction gratings for the
atoms or molecules. Our fabrication techniques for these gratings have undergone several
generations of improvement since our first interferometer in 1991 (Fig. 5). Future goals of using
a hexapole focusing magnet to increase beam flux by a factor of 20 and realizing a spatial
separation of several hundred microns between the two interfering paths, will require gratings that
are physically larger and of significantly smaller period than those available in the past. We have
therefore initiated a collaboration with the group of Prof. Hank Smith at the MIT Nanostructures
Laboratory who has developed a holographic process called Achromatic-Interferometric
Lithography. This technique provides excellent large-scale uniformity such that a 100nm period
grating will be phase coherent over an area as large as 1cm2. These gratings have already been
used to observe 15th order atomic diffraction peaks, and we hope to begin using them in our
interferometer early in the new grant period.
Thin Septum
Using precision fabrication tools available at the MIT Microsystems Technologies
Laboratory, we have developed new techniques for manufacturing narrow freestanding
membranes, or septa, which we use to physically isolate the atom waves traversing the two arms
of our interferometer. We now construct a septum by anodically bonding a thin (10µm), rigid
silicon wafer to a borosilicate glass substrate in which a cavity has been cut to permit passage of
the atom beam and to serve as a gas cell for the index of refraction experiments described below.
The silicon and glass possess matched coefficients of thermal expansion, allowing us to cool the
gas cell and septum to liquid nitrogen temperatures to increase the resolution of our index of
refraction experiment. Vacuum deposition of a metal film will create a conducting surface to be
used in both polarizability measurements and studies of relativistic effects.
Velocity Multiplexing
Velocity multiplexing [GROUP95_HPC] involves cutting a broad velocity distribution into a
number of closely spaced peaks, each of which accumulates an even multiple of  phase shift in
a subsequent interaction region so that the interference patterns all add up in phase. It can
increase the relative accuracy of our phase shift measurements to 10-4 and remove uncertainties in
the beam velocity distribution as a systematic error in our experiments. An improved version
using the separated oscillatory fields developed for longitudinal interferometry rather than the
choppers as proposed in [GROUP95_HPC], will create a picket fence of alternating ground and
excited hyperfine levels as a function of velocity such that each ground state velocity group
receives an even multiple of  phase shift under the applied interaction and each excited state
velocity group receives an odd multiple of  phase shift. A subsequent additional  phase shift
between the two states will allow both groups of atoms to interfere constructively, producing a
high contrast interference signal. This method will reduce our effective velocity width from the
current 5% to less than 0.5%.
D. Proposed Experiments
Having made major improvements in our interferometer during the last grant period and
developed techniques for longitudinal interferometry, we plan now to emphasize new and more
precise measurements in atomic physics as well as fundamental experiments in quantum
mechanics. Exploiting the unique capability of our separated beam interferometer to apply well
defined interactions to only one arm of the interferometer, we aim to significantly improve our
knowledge of atomic and molecular properties that are inaccessible by any other experimental
means. These measurements are of obvious significance as we attempt to deepen our
understanding of atoms and quantum mechanics, and hone the predictive power of theoretical
models describing them. Atom interferometers by their nature are also ideal tools with which to
investigate the important problem of quantum coherence and decoherence. Because atoms
possess a rich internal structure in addition to their external motion, our interferometer provides a
unique opportunity to study differential decoherence between internal and external degrees of
freedom and to probe the fundamental limits on the coherence of ever larger and more
complicated systems. Finally, the extreme sensitivity of our device will allow us to investigate
novel relativistic and topological phases that have engendered recent theoretical controversy.
Polarizability of Multiple Alkalis
An atom’s polarizability governs its interaction with electric fields and is an important
parameter in Van der Waals interactions, electric dipole transition rates, and long-range
interatomic potentials. Several theoretical groups have expressed their interest in polarizability
measurements including Prof. Walter Johnson who recently calculated the polarizability of
sodium to compare with our earlier measurement [GROUP95_SCE] as part of his program to
check the atomic structure theories of parity violation in cesium [NMW88, WBC97]. We
propose to measure the polarizabilities of the alkali metals through cesium to <0.1% accuracy—
more than an order of magnitude better than current values (except for sodium
[GROUP95_ESC]), and to measure their relative polarizability at the 0.01% level. The species
independence of our gratings (versus light gratings) allows us to switch alkalis easily, and
velocity multiplexing will increase our accuracy and precision to the 0.1% and 0.01% targets.
Our relative measurements will ultimately be normalized by a single, higher precision experiment
using a sodium BEC (see Sec. IV.C).
Anisotropic Polarizability of Sodium Molecules
We propose to make the first measurement of both the parallel and the perpendicular
components of the polarizability of the dimer molecule Na2 using our techniques of molecular
[GROUP95_CEH] and contrast [GROUP94_SEC] interferometry. This will permit tests of
various approximations used in molecular structure calculations [BOK94, MIB88]. The
asymmetry of the polarizability causes the electric field induced phase shift to depend on the
molecule’s j, m state. The beating of interference patterns for molecules with different j, m
generates considerable structure as a function of field strength and permits the accurate
determination of both polarizability components.
Velocity Dependent Index of Refraction
We were the first to investigate the index of refraction of gasses for sodium matter waves, by
measuring the phase shift when the sodium (and molecular sodium) de Broglie waves in one arm
of our interferometer passed through a gas cell. This measurement discriminated among various
sodium-buffer gas interaction potentials appearing in the literature [GROUP95_SCE], and
stimulated theoretical calculations of the index [CAD97, FLK96, FLK97, VIG95]. We now
propose to extend our study by varying the velocity of our sodium beam to adjust the average
center of mass energy of the inter-atomic collisions, and to reduce the uncertainty in center-ofmass energy by cooling the buffer gas to liquid nitrogen temperatures. In optical parlance, we
will measure the dispersion, i.e. the variation of index with wavelength. We are collaborating
with theorist Robert Forrey to conceive measurements that will best refine the shapes of the longrange potentials between sodium and other gases and test the new theoretical predictions inspired
by our earlier work. We hope to observe glory oscillations; a novel interference effect which
manifests as oscillations in the index of refraction as a function of impact velocity [ADV95].
Decoherence
In a recent experimental realization [GROUP95_CHL] of Feynman’s gedankenexperiment,
we explicitly demonstrated that the loss of interference due to scattering a single photon from an
atom in our interferometer is directly related to the degree of “which-path” information contained
in the final state of the scattered photon. While this supports the general picture of decoherence
as “monitoring by the environment,” theorists warn [APZ97] that the intuition derived from
simple experiments does not necessarily extend to cover more realistic systems such as might be
encountered in quantum computers. We propose to extend our previous experiment to approach
the limit of a single quantum object interacting with a thermal environment (i.e. blackbody
radiation), the mechanism most often invoked to explain the fragility of superposition states in
quantum computation.
The appropriate regime for blackbody decoherence involves scattering many photons, each
causing a small amount of dephasing. We expect that for N isotropic scattering events the
interfering contrast (a measure of the coherence) will be reduced by exp[N(kphotond) 2 / 6] , where d
is the spatial separation of the atomic superposition state [GROUP97_SCE]. An unexpected
implication is that even a large particle with dense internal levels coupled to a thermal radiation
field need not be completely isolated from the environment to exhibit spatial interference. Note,
however, that a single spontaneously scattered photon can destroy any coherence between
internal atomic/molecular states. For this reason, quantum computation based on spatial
[CLD96, SUM97] (as opposed to internal) superposition states is potentially much more robust
against this type of decoherence.
Popular Press:
Articles on recent work performed by our interferometer group have appeared in
AIP Physics Bulletin on Physics News, P.F. Schewe, B. Stein, Jan. 4, 1996; T. Sudbery,
Nature 379 (1996) 403; J. Hecht, Laser Focus World 32 (1996) 20 ; D. H. Freedman,
Discover 17 (1996) 58; Physics Today 50 (1997) 9; C. Seife, Science 275 (1997) 931; P.
Yam, Scientific American, June 1997, 124. R. Pool, Discover, December 1997, 103.
And by M. Browne, NY Times (Science Section) August 15, 1995. It’s a Molecule. No,
it’s more like a wave.
Publications:
Measurement of the density matrix of a longitudinally modulated atomic beam,
Rubenstein RA, Kokorowski DA, Dhirani A-A, Roberts TD, Gupta S, Lehner J, Smith
WW, Smith
ET, Bernstein HJ, Pritchard DE, Physical Review Letters vol 83, no.12, (20 Sept. 1999),
pp.2285-8.
Londitudinal atom optics: Measuring the density matrix of a matter wave beam, Richard
Rubenstein, Ph.D. Thesis, MIT, (Febrrary 1999)
Measurement of the density matrix of a longitudinally modulated atomic beam,
Rubenstein RA, Kokorowski DA, Dhirani A-A, Roberts TD, Gupta S, Lehner J, Smith
WW, Smith ET, Bernstein HJ, Pritchard DE, Physical Review Letters, vol.83, no.12, 20
(Sept. 1999), pp.2285-8.
Longitudinal atom optics using localized oscillating fields: A fully quantum-mechanical
treatment, Pritchard DE, Rubenstein RA, Dhirani A, Kokorowski DA, Smith ET,
Hammond TD, Rohwedder B., Physical Review A, vol.59, no.6, (June 1999), pp.464152.
Search for off-diagonal density matrix elements for atoms in a supersonic beam.
Rubenstein RA, Dhirani A-A, Kokorowski DA, Roberts TD, Smith ET, Smith WW,
Bernstein HJ, Lehner J, Gupta S, Pritchard DE, Physical Review Letters, vol.82, no.10, (8
March 1999), pp.2018-21.
Atom interferometers and atomic coherence, Pritchard DE, Chapman MS, Hammond TD,
Kokorowski DA, Lenef A, Rubenstein RA, Smith ET, Schmiedmayer J, Akademie
Verlag. Fortschritte der Physik-Progress of Physics, vol.46, no.6-8, (1998), pp.801-8.
Germany.
Fully quantized treatment of molecular beam resonance, Kokorowski DA, Dhirani A,
Hammond TD, Rohwedder B, Rubenstein RA, Smith ET, Pritchard DE, Akademie
Verlag. Fortschritte der Physik-Progress of Physics, vol.46, no.6-8, (1998), pp.849-53.
Germany
Velocity rephased longitudinal momentum coherences with differentially detuned
separated oscillatory fields, Smith ET, Dhirani A-A, Kokorowski DA, Rubenstein RA,
Roberts TD, Huan Yao, Pritchard DE, Physical Review Letters vol 81, no.10, pp.1996-9
(7Sept. 1998)
Velocity rephased coherences in a longitudinal atom interferometer, E.T. Smith, Ph.D.
Thesis, Harvard University, (June 1998)
Optics and interferometry with atoms and molecules, J. Schmiedmayer, M.S. Chapman,
C.R. Ekstrom, T.D. Hammond, D.A. Kokorowski, A. Lenef, R.A. Rubenstein, and D.E.
Pritchard, in Atom Interferometry, P. Berman, ed., Academic Press, San Diego (1997)
Determining the density matrix of a molecular beam using a longitudinal matter wave
interferometer, A. Dhirani, D.A. Kokorowski, R.A. Rubenstein, T.D. Hammond, B.
Rohwedder, E.T. Smith, and D.E. Pritchard, J. Mod. Optics vol 44, 2583 (1997)
Longitudinal quantum beam tomography, D.A. Kokorowski and D.E. Pritchard, J. Mod.
Optics vol 44, 2575 (1997).
Atom interferomery: Dispersive Index of Refraction and Rotation induced phase shifts for
matter-waves, Troy Hammond, Ph.D. Thesis, MIT, (February 1997)
Using an atom interferometer to take the gedanken out of Feynman's
gedankenexperiment,
Pritchard DE, Hammond TD, Lenef A, Schmiedmayer J, Rubenstein RA, Smith ET,
Chapman MS, American Institute of Physics Conference Proceedings, no.388, (1997),
pp.223-8. USA.
Atomic beam propagation effects: Index of refraction and longitudinal tomography,
Kokorowski DA, Hammond TD, Smith ET, Rubenstein RA, Dhirani A, Schmiedmayer J,
Pritchard DE, SPIE-Int. Soc. Opt. Eng. Proceedings of Spie, vol.2995, (1997), pp.289300. USA.
Interferometry with atoms and molecules: a tutorial, Pritchard DE, Chapman MS,
Ekstrom CR, Hammond TD, Kokorowski D, Lenef A, Rubenstein RA, Schmiedmayer J,
Smith ET, SPIE-Int. Soc. Opt. Eng. Proceedings of Spie, vol.2995, (1997), pp.22-32.
USA
Matter-wave index of refraction, inertial sensing, and quantum decoherence in an atom
interferometer , Hammond TD, Chapman MS, Lenef A, Schmiedmayer J, Smith ET,
Rubenstein RA, Kokorowski DA, Pritchard DE, Revista Brasileira de Fisica, vol.27,
no.2, (June 1997), pp.193-213.
Rotation sensing with an atom interferometer, Lenef A, Hammond TD, Smith ET,
Chapman MS, Rubenstein RA, Pritchard DE, Physical Review Letters, vol.78, no.5, (3
Feb. 1997), pp.760-3.
Photon scattering and atomic interference, Schmiedmayer J, Chapman MS, Hammond
TD, Lenef A, Rubenstein RA, Smith E, Pritchard DE, MAIK Nauka/Interperiodica
Publishing. Laser Physics, vol.6, no.2, (March-April 1996), pp.284-9. Russia