PROJECT DESCRIPTION
I. Results from Prior NSF Support
This proposal is for continuation of work on "Atomic, Molecular, and Ionic Physics" under
grant PHY-92-22768 for the period May 1, 1996 to April 30, 1999. The total amount of this
award is $678,000 and the PI has received an equipment ($80,000) and two REU (totaling
$18,400) supplements. This grant provides the major source of funds for all experimental
projects supervised by the PI. We are requesting funding at a 18% higher level than the 1995
award to open a new frontier (interferometry with Bose-Einstein condensates) and to help offset
the effects of the nationwide cancellation of the Joint Services Electronics Program which
contributed approximately $90,000/yr to the PI's program through its block grant to MIT.
A. Human Resources Development and Theses
New scientific results together with relevant publications will be discussed in later sections
devoted to the specific scientific projects. All group publications from the last three years are
indicated in the bibliography as [GROUP9X_XXX]. Here we discuss an arguably equal payoff
of our program—the human resources payoff. Ph.D. students recently supported by this project
are currently Permanent Staff at JILA (Eric Cornell), Director of Time Standards at Naval
Research Labs (Chris Ekstrom), and Staff Member at Harvard doing experiments pertinent to
global climate modeling (David Keith). Alumni who left during this grant period (after earning
the degree indicated) are:
1998 Roland Nguyen, B.S.
1998 Edward Smith, Ph.D.
1998 Al-Amin Dhirani, (postdoc)
1998 Trey Porto, (postdoc)
1999 Richard Rubenstein Ph.D.
1999 Celeste Yang, B.S. from Caltech
2000 Michael Bradley, Ph.D.
2001 David Kokorowski Ph.D.
2001 Martin Tiberg B.S.
Consultant, Mars and Company
PhD received from Harvard, February 1998
Faculty at University of Tronto
NIST Fellow
Boston Consulting Group
PhD candidate at Berkeley
Eaton Semiconductor
Postdoctoral Fellow, MIT
M.S. candidate, Royal Inst.Tech., Stockholm
Baruch P. Feldman B.S. candididate still
Sidney Burks B.S. student still
Joshua Jackson B.S. student still
Miranda Priebe, B.S. student still
Long term visitors/collaborators who worked on this project during the grant period were
Jörg Schmiedmayer (Universität Innsbruk), Bernd Rohwedder (University of Santiago, Chile),
Winthrop Smith (University of Connecticut), Herb Bernstein (Hampshire College) and Jana
Lehner (University of Ulm).
During the current grant period, the PI was elected Fellow of the Optical Society of America,
to the Board of Directors of the Optical Society of America, was selected as a Centennial Speaker
of the American Physical Society, and was awarded a Fannie and John Hertz Mentor’s
Honorarium. Students who worked on these projects in the grant period were awarded three NSF
fellowships, an AT&T Bell Labs Doctoral Fellowship, a K.T. Compton fellowship (from MIT), a
Department of Defense fellowship, and an NSERC fellowship. Postdoctoral personnel won an
Otto-Hahn Medal for Young Scientists (from Max-Planck Society), an Erwin Schrödinger
Award, a NIST postdoctoral fellowship, and a NSERC postdoctoral fellowship.
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B. Impact
Counting only national and international scientific meetings, the PI has been invited to
present about 30 invited talks on our NSF-supported work during the last three years, resulting in
many conference proceedings [GROUP96_PCHb, GROUP96_SCH, GROUP97_KHS,
GROUP98_KDH, GROUP98_PCH, GROUP98_RBP]. Some of these talks were given by other
group members and some were declined, so the PI does spend considerable time at MIT
supervising the project. In addition to a lengthy review of our interferometer experiments
[GROUP97_SCE], we have reviewed certain aspects of our work and atomic physics in general
for wider audiences [GROUP95_GOP, GROUP96_CHP, GROUP96_PCHa, GROUP96_PHL,
GROUP97_PAP, GROUP97_PCE, GROUP98_WWP]. The broad appreciation of atomic
physics generated in part by our research is further evidenced by the many third-party write-ups
in both popular and general professional magazines, including Science [SEI97], Nature [SUD96],
Discover [POO97], the American Physical Society’s Physics News in 1997 [SCS97], Scientific
American [YAM97], and others [HEC96, WAT96].
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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, have now 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 [REF],
fundamental tests of quantum mechanics [REF], and new ways to measure acceleration [REF]
and rotation[REF]. Our group has pioneered techniques in each of these areas, including the first
(and only) atom interferometry experiments that employ physically separated paths. In the last
three years we have been applying these techniques to make new types of 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 in the photon bath regeim. 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.
3
Dispersion in the Matter Wave Index of Refraction
We are now measuring the velocity dependence of the index of refraction seen by sodium
matter-waves passing through a gas target. In optical parlance, we measure 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 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 our
recent measurements to refine the shapes of the long-range potentials between sodium and other
gases (Ar, N2, Kr, and Xe) and to 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
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 large. Velocity multiplexing
[HPC95] has been proposed to overcome this de-phasing without loosing the count rate as would
happen with simple velocity selection.
We have implemented our novel velocity-multiplexing scheme [HPC95, TIB01]. Rather than
using choppers we employ two separated regions of inhomogeneous electric fields that can be
pulsed on and off in time. Velocity multiplexing overcomes the limitations of having
uncertainties and variation in the atoms’ velocity distribution, and will allow us to make much
more precise measurements of atomic poliarzabilities.
4
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
[REF]. Collaborating with T. Savas in H. Smith’s group at MIT to fabricate improved gratings
using Achromatic Interferometric (optical) Lithography, we have demonstrated atom interference
fringes using 100-nm period gratings. These give twice the beam separation of our standard 200nm gratings. These gratings will make separated beam interferometry feasible with cesium
atoms, and have expanded the velocity range we can use. The excellent large-scale uniformity of
these gratings will also make it possible to use a hexapole magnet to focus our atom beam to
increase the 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. The
atom optical components are now mounted on a vibrationally isolated breadboard to reduce phase
drift (crucial for future precision measurements), and to suppress vibrational noise to less than
10nm rms (necessary to achieve high contrast interference with 100nm period gratings.)
Furthermore, the apparatus now has a large number of access ports for flexibility in designing
experiments.
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 above.
Vacuum deposition of a metal film will create a conducting surface to be used in proposed
polarizability measurements and studies of relativistic effects.
5
D. Proposed Experiments
With our improved 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 calculated the polarizability of sodium to
compare with our earlier measurement [GROUP95_SCE] as part of his program to check the
atomic structure theories needed to interpret measurement of atomic parity violation in cesium
[NMW88, WBC97]. We propose to measure the polarizabilities of the alkali metals from Na to
Cs 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 (unlike 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.
We have already demonstrated most of the technologies required for measuring
polarizabilities with increased precision. The successes we shall build upon include: low-phase
drift in our apparatus because of the isolated breadboard, an ultra-thin 10m septum, the 100-nm
atom gratings which are required for separating beams with short de Broglie wavelengths, and the
electronic method of velocity multiplexing.
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 phase shift to depend on the molecule’s orientation so
that the contrast decreases more rapidly with electric filed if the asymmetry is higher.
Relativistic Effects
An atom’s extreme sensitivity to electric and magnetic fields is sufficient 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. 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
6
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 ExB 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.
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8
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9
[GROUP95_HPC] T.D. Hammond, D.E. Pritchard, M.S. Chapman, A.Lenef and
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Wehinger and D.E. Pritchard, "Index of Refraction of Various Gases for
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