Summary
In collaboration with Prof. Wolfgang Ketterle, the group has developed a novel atom
interferometer using Bose-Einstein condensates to measure h/m. This will contribute to a
precision measurement of the fine structure constant . Using a BEC as the atom source
and coherent multi-photon processes (standing wave light pulses) as beamsplitters and
combiners, multiple interfering paths can be manipulated in a controlled way within an
atom interferometer. The beamsplitters act only on the external momentum state. This
suppresses relative AC Stark shifts between the interfering paths (a common problem in
precision atom interferometry using laser cooled atoms). Combining a symmetric
interferometer geometry with a readout method sensitive to only the contrast of the
interference, allows for the direct suppression of phase noise from the beamsplitters. The
contrast signal contains the atomic phase evolution information, yielding a measure of the
photon recoil frequency. These features have been put together in the new interferometer
and the photon recoil frequency has been measured to one part in 10^5 [hope to have at
least this before long!] in the first generation sodium BEC apparatus. The interferometer
has the additional feature that it is scaleable to high precision using high order
beamsplitters. Demonstration of this is currently under way. Scaling to high orders and
extending the time separation between beamplitter pulses will take the statistical
uncertainties to better than 1ppb. This will be done in the next generation apparatus
involving extracted BECs. Systematic errors such as mirror vibrations and AC Stark
shifts are automatically suppressed in the scheme. Other systematic errors such as
inhomogeneous magnetic fields and optical wavefront distortions will be better
addressable in the new and improved machine, where magnetic shielding and high optical
quality viewports will be used.
I. Results from Prior NSF Support
This proposal is for continuation of work on "Atomic, Molecular, and Ionic Physics" under
grant PHY-92-22768 which runs through April 30, 2002. The total amount of this award is
$###,000 and the PI has received an equipment ($##,000) and two REU (totaling $##)
supplements. This grant provides the major source of funds for all experimental projects
supervised by the PI.
The PI is making a major change in apparatus to continue forefront research in the same
research directions: a precision measurement of the fine structure constant alpha, atom optics, and
atom interferometry. The high accuracy mass measurements of Rb or Na will be combined with
A new atom interferometer using a fountain geometry with BEC’s will be used to measure h/m in
Rb. This will be combined with recent mass measurements to determine the fine structure
constant at the ppb level. Other atom interferometry interests of the PI (using waveguides) and
studies of BEC;s in lower dimensions will be pursued in two collaborative projects with W.
Ketterle supported by joint funding., The PI is committed to moving his mass measurement
experiment to Fla State, and his room temperature atom interferometer will accompany postdoc
Alex Cronin to his new assistant professorship. We are requesting funding at a ##% higher level
than the current award for the first year and a half to get these apparati moved successfully to
their new homes. The reviewer should note that previous transfers of NSF-funded equipment by
the PI have paid off for the community. A vacuum system transferred (from a joint NSF grant
with D. Kleppner)I to W. Phillips was used for his pioneering Zeeman slowing experiments at
NIST, atom-molecule collision apparatus has enjoyed a decade of productivity at Weslyean under
the direction of Brian Stuart, and the atom trapping apparatus given to Ketterle became MIT’s
BEC#1. By year three, NSF funding will be devoted solely to the precision measurement of h/m.
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 [GROUPXX_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), Assistant Professor at Georgia Tech (Mike Chapman) and
Assistant Professor at Pittsburgh doing public policy (David Keith). Postdocs who worked with
the PI’s under NSF support include R. Freeman, W. Phillips, W. Ketterle, G. Lafyatis (Ohio
State), M. Xiao (Arkansas), Joerg Schmiedmayer (Heidelberg) and A-A Dhirani (Toronto).
Alumni who left since the last proposal was submitted are:
UPDATE
Assistant Prof., Georgia Inst. of Technology
1998 Edward Smith, Ph.D.
1998 Al-Amin Dhirani, (postdoc)
1998 Trey Porto, (postdoc)
PhD (from Harvard)
Assistant Prof., Univ. Toronto
NIST Fellow
Long term visitors/collaborators who worked on this project during the grant period included
Winthrop Smith (University of Connecticut), Herb Bernstein (Hampshire College) and Jana
Lehner (University of Ulm).
During the current grant period, the PI was elected to the National Academy of Science and
served as a Centennial Speaker of the American Physical Society. Students who worked on these
projects since the last proposal were awarded two NSF fellowships, two MIT fellowships, a
Department of Defense fellowship, and two NSERC fellowships. Postdoctoral personnel won an
Otto-Hahn Medal for Young Scientists (from Max-Planck Society), a NIST postdoctoral
fellowship, and a NSERC postdoctoral fellowship.
Project Description: Towards the Best Measurement of alpha.
A. Why and How to Measure alpha
Why Measure alpha?
Once it is accepted that the speed of light c is just the ratio between two different units for
2
the same physical quantity, the fine structure constant   e c emerges as a relationship
between the fundamental quanta of the physical world: h the quantum of action and e the
quantum of charge. There are two important reasons to measure alpha accurately: it relates two
of the most fundamental constants, and accurate measurements of alpha in different regimes of
physics (e.g. atomic, QED, condensed matter) offer one of the few “outside the specialty” checks
for global errors in each specialty.
The g-2 measurement of the electron and positron at 4ppb by Dehmelt’s group (VanDyck
et al, PRD, 34, 722 (1986)) has stood as the best measurement of alpha for 15 years.
Unfortunately, the second most accurate value of alpha is worse by a factor of over five, which
limits the scientific value of cross-field comparisons. Fortunately a new and more robust route to
measuring alpha has emerged in the last decade which offers a real chance to provide the most
accurate alpha at the ppb level. It rests on such simple and solid physical foundations that a
comparison of it with g-2 will be regarded by many as a check of QED at an unprecedented level
of precision.. The basic approach is (Bradley et al. PRL 83, 4510 (1999)):
2 
2 R 10 3 mp
N h
c M p me A
where R is the Rydberg constant and M p is the mass of the proton in atomic units. All
quantities in this expression have errors below 0.2ppb except the electron/proton mass ratio,
mp me at 2ppb. However, Gabrielse plans an improved measurement of the positron/proton
masss ratio (priv comm Sept 2001). This expression therefore opens the real possibility of a
measurement of alpha below the ppb level (note to the square root) if N A h can be determined
accurately.
The quantity N A h (called the molar Planck constant – (B.N. Taylor Metrologia, 31, 181
(1994)) can be determined by measuring the speed v and deBroglie wavelength dB of a particle
whose atomic mass M is known
dB v 
h 10 3

N h
m M A
For example Krueger’s measurements for a neutron together with our latest value for M n
(Kruger et al, Metrologia 36, 147 (1999)) give a value of alpha at the 37ppb level. Atom
interferometry offers far greater precision in the velocity measurement than the mechanical
method of Krueger.
The use of atom interferometry adds robustness to the overall route to alpha in another way
besides the simplicity of its physics – the physical quantities necessary to determine the molar
Planck constant ( N A h ) can be measured using any atom. To measure N A h using an atom, e.g.
Cs, requires a triplet of measurements: the D-line frequency (straightforward with the new comb
generators), the atomic mass, and the recoil frequency shift. Motivated by S. Chu and the
Stanford measurement of h mCs we measured the atomic mass of Cs (and Na and Rb, see Sec.
##) and Hänsch’s group (Udem et al, PRL 82, 3568 (1999)) the wavelength of the D-line in Cs,
both with errors well below 1ppb. Unfortunately the promise of a ppb measurement of N A h has
not yet been realized because the Stanford recoil frequency experiment has been beset by
fluctuations beyond those expected from statistical considerations alone (B.C. Young, Ph.D.
thesis, Stanford, 1998). Recently they have reported convergence at 8ppb (REF??).
In the rest of this section we propose a new variant of atom interferometry which, when
combined with the advantages of to measure using a BEC as the atom source, offers numerous
advantages over the heroic Stanford experiment. Indeed, our mass measurements of Rb and Na
were motivated by this possibility.
C. Recoil Phase from Contrast Interferometry
Basic Idea :
We have devised an interferometer configuration with several significant advantages over the
one used to measure the recoil velocity and thereby h/m in Cs. This new interferometer offers
relative freedom from vibration as well as a phase which grows quadratically with the number of
momenta transferred to the atoms rather than linearly. It offers the possibility of a much higher
precision in less time with a simpler, smaller apparatus.
The key to this is a three-path geometry (see figure 1). The fundamental interferometric
measurement is not fringe position but rather fringe contrast, an idea originally demonstrated by
our group [ref] The fringe contrast, here detected by Bragg backscattering, oscillates in time at
twice the recoil frequency, allowing accurate measurement of the recoil phase in a single shot.
(In contrast, only a single point on the fringe is obtained in the Stanford geometry.)


Figure 1: Schematic of the three path contrast interferometer. Paths 1, 2 and 3 interfere at the
echo point where a weak laser beam records the time variation of the matter wave interference
pattern by reflection. is time measured from the echo point.
In our interferometer (Fig 1), an expanded sodium BEC is split into three momentum states.
by a short 1s Kapitza-Dirac diffraction light pulse (Refs). The zero momentum state (path 2) is
a copy of the original condensate. The other two coherent components move in opposite
directions at the 2-photon recoil speed (along paths 1 and 3). At time T a second order Bragg
pulse of ~10s duration is applied; this reverses the directions of the extreme paths while leaving
the middle path unaffected. This causes the paths of the three BEC’s to come back together
around time 2T – 2T – it is a -pulse in momentum space that cuases an “echo”.
In a normal two-leg interferometer paths 1 and 2 would interfere to produce a standing wave
of atoms which would move down at the recoil speed. The overlap of this atomic standing wave
with a standing wave of light would cause an oscillation in the scattered intensity of the light
which would be interpreted to yield a phase.
In our three-leg contrast interferometer, the atom interference pattern around time 2T can be
thought of as being the sum of two standing waves of atoms, one (from paths 1 and 2) moving up
and the other (from paths 2 and 3) moving down. If at 2T the two sets of fringes are in phase, then
their hills and valleys add to produce maximum contrast. Since the fringes of the two
interferometers move in opposite directions, a quarter recoil period later (i.e. at time 2T + ) the
hills of one coincide with the valleys of the other, and the two standing waves add to produce no
net contrast. Our mathematical treatment shows that the interferometer signal can then be written
as:
S(T,) = C(T,)sin2[2k(2T+)]
where C(T,) is the envelope function (determined from condensate parameters) and 2k is the 2photon recoil frequency. Defining (T) as the phase of the signal at =0, we can extract 2k from
an accurate determination of (T). For sodium, its oscillation period vs  is 5s. Note that the
readout pulse will only reflect off a matter-wave grating with 2k wavenumber (due to
phasematching); therefore the grating produced be paths 1 and 3 (at 4k) produces no detected
signal.
Contrast oscillations in mutltipath interferometers have been applied to h/m
measurements by Sleator [ref], and can produce sharper than sinusoidal fringes, [our paper and
also Hansch]. Our scheme has several additional advantages that are particularly advantageous
for a precision h/m measurement:
 The phase scales as N^2, allowing a precise measurement in a small region, advantageous
because it reduces the effects of magnetic and laser beam inhomogeneities
 The phase can be measured accurately in a single shot
 The backscattering readout should enable us to obtain a 1/sqrt(N) eerror
 The signal is free from noise due to vibrations in the position of the Bragg pulse relative to
the Kapitza-Dirac pulse – such vibrations displace both of the standing waves at time 2T,
which does not affect the contrast. (Vibrations are a huge problem in the Stanford
experiment [young thesis Fig??])
 The use of a BEC allows us to cleanly separate and address the various arms of the
interferometer in momentum space, so that ac Stark shifts are the same for all arms.
Demonstration of Principle
We have very recently demonstrated this scheme in our old BEC machine, using horizontal
light beams because the BEC is not accessible for vertical beams. With horizontal geometry the
interaction time is only ##ms before the atoms fall out of view, and most of this time was used to
expand the condensate prior to the application of any interferometer pulses. Nevertheless, the
signal obtained (Fig. 2) is robust and allows a fit to the phase to 50mr (10^-4 overall) in a single
shot.
MORE DESCRIPTION HERE?
Figure 2: Contrast signal obtained from the three-path interferometer. For this data, T=0.3ms. The
expected 5s oscillation shows up with an envelope function with gaussian-fitted width of 25s.
The fit yielded a phase error of ~ 50mrad giving a precision of 10-4 in this single iteration of the
experiment.

The relative error in the measurement is k/k=0/0 ~ (0.5*Nph)-1/2/0 where Nph is the
number of atoms (or the number of photons detected if less). This should be the statistical
precision per iteration of the experiment. We are currently a factor of ~10 from this limit, mostly
because we have had only one successful run, but also because aberrations in the horizontal
optical setup introduce time-dependent errors as the atoms fall into different parts of the beam.
This motivates a shift to a vertical geometry for the proposed experiment - a switch also made at
Stanford between (REF Weiss) and (REFS).
Scaling up the interferometer:
Figure 3 shows how our contrast interferometer can be extended to improve the measurement
precision by increasing 0. Increasing the time between interferometer pulses increases the
sensitivity linearly. Employing extra Bragg pulses within the interferometer to accelerate paths 1
and 3 to higher momentum states, increases the sensitivity quadratically with the diffraction order
chosen. If N pairs of photons are used, we obtain :
S(T,) = C(T,)sin2[N22k2T+’+q]
where ’ is an offset phase representing the atomic phase evolved during the time taken to
accelerate and decelerate the paths to and from momentum 2Nhk (curved portion of paths in
figure 3).
Thus the sensitivity scales faster (by the factor N) than the area (enclosed between paths
1 and 3) of the interferometer. Using large N will be useful in reducing errors that scale with the
size (both in space and time) of the interferometer (like inhomogeneous or fluctuating magnetic
fields and beam collimation errors).
Figure 3 : Scaling up using extra Bragg pulses inside the interferometer. The interferometer
of figure 1 is shown inside the (N=3) scaled up version .
The contrast technique allows for even more dramatic reduction of systematic effects. A
“zigzag”path in momemtum space can be implemented (figure 4) employing consecutive second
order Bragg processes to turn around paths 1 and 3 multiple times to increase T without
increasing the physical extent of the interferometer. This would reduce errors due to wavefront
distortions and inhomogeneous magnetic fields.. For an even number of -pulses, we expect
cancellation of systematics due to local field inhomogeneities.
Figure 5 shows a modest realization of this geometry. For a fountain launch velocity of
0.5m/s, N=10 and T=50ms, the expected statistical precision from a single iteration of the
experiment is ~1ppb. The vertical extent of the interferometer is only ~6cm, small compared to
today’s precision fountain experiments [refs].
Figure 5 : Three path interferometer in fountain geometry. A launch velocity of 0.5m/s,
T=50ms and N=10 have been used in the figure. The expected statistical precision is 1ppb from a
single iteration of the experiment.
New Apparatus with Fountain Geometry:
The proposed precision h/m experiment will be performed on extracted BECs in a new atom
interferometer with vertical orientation to allow for a fountain geometry. This apparatus will
require high quality large optics and magnetic shielding. This will be constructed by the PI and
the personnel supported under this grant, and then “plugged into” one of the new BEC apparati
that are being constructed jointly by the PI and Wolfgang Ketterle with other funding. This will
allow for very long interferometer times (~ 0.1 seconds), because the atoms will not fall out of the
beams. The vertical geometry also reduces systematic errors due to optical wavefront curvature as
the atoms receive their momentum kicks from the same part of the laser field. Moreover, the
detection will use a camera so that different transverse parts of the sample can be measured
separately, and the expansion/compression of the transverse sample size measured and controlled.
The extension to longer times imposes strict collimation requirements that can be easily met with
an expanded BEC, and the vertical geometry requires frequency chirps on the Bragg beams. We
will also use high optical quality viewports (/20) removed from the interaction region as far as
possible to minimize beam wavefront distortions.
B. BEC Atom Optics and Interferometry – Current Work
The combination of Bose Einstein Condensed atoms and atom interferometry offers exciting
possibilities for scientific payoffs in both fields. To exploit the lush possisbilities, the PI has
devoted a small part of his current grant to a collaborative research program with Prof. Ketterle
using the original MIT BEC apparatus (which was initially constructed with money from
Pritchard's NSF grant before being transferred to Ketterle's sole supervision in 1993). In the
future the PI will collaborate with Ketterle on BEC waveguide physics supported by a MURI and
in developing new techniques for the formation of large BEC’s supported by the Ultracold atom
center. This NSF renewal will be devoted to a precision measurement of the recoil shift in order
to produce a measurement of the fine structure constant at the ppb level.
Every atom in the condensate has the same phase. This gives an
incredible robustness of BEC interference fringes. BEC interferometers
thus have large spatial (or temporal) extent of fringes [ATM97]. This
will lead to improved accuracy of measurements. An adiabatically
expanded BEC has velocity spread around 10-2 cm/sec (cf. 3 cm/sec recoil
velocity from absorption of a photon) allowing a BEC interferometer to
use Bragg diffraction beamsplitters [ref] that keep all interfering
subcondensates in the same internal state, separating them solely in
momentum space. Having all subcondensates in the same internal state
eliminates systematic relative phase shifts due to the AC Stark effect
and variations in the bias fields used to maintain the quantization
axis. Phase-coherent amplification of the amplitude of a BEC
subcondensate [IPG99] can enhance the size of the interference signal.
The long coherence time and the addressability of individual
interferometer arms while keeping atoms in the same internal state are
advantages of BEC interferometry beyond cold atoms. We will exploit
these in our h/m interferometer. BEC’s are also easily manipulated with
low power off-resonant light (using the AC Stark shift). This allows
for extraction of BEC’s from their production area to a dedicated
chamber configured for a precision experiment [GCL01].
Current Work
We performed Bragg diffraction of a BEC to measure its momentum
distribution[ref]. We created an atom amplifier and demonstrated its coherence using an
atom interferometer [ref]. We also studied vortex excitation in a BEC using an
interferometric technique [ref]. We are currently demonstrating a BEC interferometer
capable of measuring the photon recoil momentum[ref?], the last key element towards a
ppb measurement of . The next generation BEC machine (already built) features a
method of extracting condensates into a separate science chamber which can be
configured independently and offline for different experiments [ref]. We will design and
implement a dedicated science chamber for a precision measurement of h/m at the sub
ppb level [ref Chu].
Experimental Techniques
Current Techniques:
The demonstration experiment is being performed in the first generation BEC
experiment (which was initially constructed with money from Pritchard’s NSF grant
before being transferred to Ketterle’s sole supervision).
The group has been one of the pioneers of optical standing wave diffraction of
atoms [refs]. The straightforward extension to BECs has followed naturally [ref] and has
found tremendous applications [refs-mainly Phillips] in the field.
The efficient application of the optical phase gratings requires large detuning of
the light from the intermediate state and shaping and fast switching capabilities of the
pulses. The large detuning (1.8GHz) is obtained via an AOM from the same dye laser
which is used for the laser pre-cooling. We reuse the light that is used for the |F=2>|F’=3> cooling transition (which is red-detuned by the sodium hyperfine frequency from
the |F=1> condensate atoms). We use AOM’s (IntraAction, 30MHz) driven by phase
locked synthesizers (SRS, DS345) and standard RF switches (MiniCircuits) before the
amplifiers (MiniCircuits) to switch the pulses on and off. All the pulses are applied
horizontally. The second order Bragg pulse is shaped to a Gaussian envelope to minimize
off resonant population of unwanted momentum states.
The reflection of the third pulse is detected with a photomultiplier tube
(Hamamatsu) which is placed at an image plane of the condensate. A small iris (300m
diameter) is placed in an intermediate image plane to spatially filter out stray light.
To reduce the effects of the condensate mean field, we decompress the magnetic
trap before releasing the BEC. We also wait ~15ms after release to apply the
interferometer pulse sequence. These two techniques lower the density and
correspondingly, the mean field energy by two orders of magnitude, which is necessary
to get a good signal.
Bragg and Kapitza-Dirac processes do not change the atomic internal state. This
makes our interferometer free from systematics due to relative AC Stark shifts, which has
been the main source of uncertainty in precision Raman interferometers [refs].
The dedicated science chamber will have -metal shielding in the vertical
extension to create a constant, small (100 milligauss) bias field for the reduction of
systematics from inhomogeneous bias fields. We will also use atoms in the m=0 state
(which we can create simply by an RF Landau-Zener sweep) to make the atoms first
order magnetic field insensitive.
A separate laser (with arbitrary intermediate-state detuning and high power) will
be used to generate high-order diffraction gratings. The statistical precision will be
improved by adding in high order Bragg pulses within the interferometer (as described
above).