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 ready to move beyond demonstrations - which have
already captivated widespread general interest - toward dedicated precision measurement
applications.
Figure 1. A schematic 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 through 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:
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 calculable and
universal form of decoherence which is relevant to quantum computation, quantum error
correction, and quantum communication. [KCR01]
Figure 2. 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 photonnumber 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 studying atomatom interactions. In addition, our recent experiment 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 3. 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.
A.
B.
Figure 4A. 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 4B.
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.
C. Interferometry Techniques and Groundwork
Atom Gratings
Our group has pioneered the development of transverse atom interferometry with microfabricated transmission diffraction gratings, employing a three grating Mach-Zehnder geometry.
Collaborating with H. Smith’s group at MIT to fabricate improved gratings using Achromatic
Interferometric (optical) Lithography, we have demonstrated atom interference fringes using 100nm period gratings, which give twice the beam separation of our standard 200-nm gratings. This
larger separation will make separated beam interferometry feasible with cesium atoms, and has
expanded the velocity range we can use. The excellent large-scale uniformity of these gratings
will make it possible to use a hexapole magnet to focus our atom beam to increase the beam flux
by a factor of 20.
New Vacuum Chamber and Vibration Isolation
With previous NSF support we upgraded our interferometer for longer paths, better phase
stability, and more flexability to adapt experiments. The new vacuum chamber is ~3.5m long,
which allows up to 200µm separation between the arms of our transverse interferometer, and has
a large number of access ports for flexibility and modularity. The atom optical components are
now mounted on a vibrationally isolated breadboard 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.)
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 to emphasize new and more precise
measurements in atomic physics as well as fundamental experiments in quantum mechanics. Our
first priority is to measure the polarizability of cesium. 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 [TIB01] will increase our accuracy and precision to the 0.1% and 0.01%
targets.
We have already demonstrated most of the technologies needed to make a dedicated effort to
measure polarizabilities with increased precision. The successes we will build upon include: lowphase drift in our apparatus (due to the isolated breadboard), the 100 nm atom gratings which are
required for separating beams with short de Broglie wavelengths, and the electronic phase
choppers.
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.
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,
1
 E 2
F  (  B )   

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.