Antibunching observed in cold,
dense gases of fermionic atoms
&
A two-body correlation could help elucidate many-body phenomena,
including the emergence of high-Tc superconductivity.
In the late 1990s, physicists figured
out how to adjust the interaction between atoms in cold, dense gases. Provided the atoms’ energy levels are favorable, a magnetic field suffices to
tune the interaction from weak to
strong or from repulsive to attractive.
With that tuning ability came the
prospect of exploring few- and manybody phenomena over ranges of conditions far wider than available in a given
crystal, liquid, or nucleus. Antiferromagnetism and high-Tc superconductivity await their realization in cold
atomic gases, but Cooper pairing, Efimov trimers, Mott insulators, and the
Berezinskii-Kosterlitz-Thouless transition have already been observed.
Now, two independent groups have
added another coherent phenomenon
S1
to the cold-atom repertoire: antibunching. Antibunching is the fermionic
equivalent of bosonic bunching. Half a
century ago, Robert Hanbury Brown
and Richard Twiss sought and found
bunching in photons from a mercury
discharge lamp.
The two cold-atom groups used different techniques. Immanuel Bloch of
Johannes Gutenberg University in
Mainz, Germany, and his collaborators
released potassium-40 atoms from an
optical lattice; they observed antibunching in the shadow cast by the
atoms on a CCD camera.1 Wim Vassen
of Amsterdam’s Free University,
Christoph Westbrook of the Optics Institute in Orsay, France, and their collaborators released helium-3 atoms
from a single-well trap; they observed
Figure 1. Bunching and
antibunching occur when
the paths taken by indistinguishable particles
interfere on their way
from source points S1
and S2 to detection points
D1 and D2. As a result,
the arrival of atoms at
two locations (yellow
patches) is correlated. In
the Amsterdam–Orsay
experiment, the freely
expanding atoms land on
a microchannel plate
(dark disk), which
records their positions
and arrival times.
(Adapted from ref. 2.)
S2
D1
D2
Δy
Δx
18
March 2007
Physics Today
antibunching in the pattern of atoms
falling onto a microchannel plate.2
Although fermionic antibunching
has been observed before—in electrons, neutrons, and high-energy particles—the Mainz and Amsterdam–
Orsay groups are the first to measure
the length scale over which the effect’s
coherence extends. In both experiments, the length is consistent with
textbook theory.
Of more significance, the two experiments foreshadow the use of antibunching and bunching as diagnostic
tools. Typically, one releases trapped
atoms and images the shadow of the expanding cloud. The technique reveals
density differences but not Cooper pairing and other phenomena that don’t affect density.
But buried in the noise of those same
images lies an antibunching or bunching signal. Three years ago, Harvard
University’s Ehud Altman, Eugene
Demler, and Mikhail Lukin showed
how to analyze correlations within the
noise and extract the signature of coherent phenomena such as Cooper pairing and magnetic order.3 If physicists
succeed in creating a cold-atom analogue of a high-Tc superconductor, now
they have a way of probing it.
Seeing stars
The original Hanbury Brown and Twiss
effect—bunching—appears when a
light source is viewed by two nearby
detectors. As shown in the inset in figure 1, photons from two source points
S1 and S2 reach two detectors D1 and D2
in two ways: via the shorter blue paths
and via the longer red paths. Because
photons are indistinguishable, the
paths interfere.
The interference is constructive for
photons and other bosons. If you could
hear photons arrive like light rain on a
tin roof, the pitter-patter would sound
oddly bunched up. For 40K atoms, 3He
atoms, and other fermions, the interference is destructive. The fermions’
analogous pitter-patter would sound
just as odd as the bosons’, but in the op-
© 2007 American Institute of Physics, S-0031-9228-0703-320-0
Cooling helium-3
Of the two new antibunching experiments, the Amsterdam–Orsay one
comes closest to Hanbury Brown and
Twiss’s original. Rather than take a
shadow image of the cloud, the Amsterdam–Orsay group recorded the location and arrival time of the atoms as
they fell under gravity and landed on a
microchannel plate. Figure 1 shows the
setup schematically.
Using an MCP has the advantage of
providing a three-dimensional view of
the cloud. Horizontal positions come
from the MCP itself; vertical position is
derived from arrival times. Correlations
appear and can be analyzed in any of
the three dimensions. But there’s a disadvantage: Slowly moving atoms lack
the kinetic energy to trigger an electron
avalanche in an MCP. Consequently, the
atoms have to be in excited states. Of
the atoms cooled to degeneracy so far,
only helium has a convenient and longlived metastable state.
Two years ago Westbrook and his collaborators used an MCP to observe
bunching in a cold gas of 4He atoms,
which are bosons.4 Observing antibunching in fermions is more challenging because Pauli’s exclusion principle
prevents cold fermions from exchanging
energy when they collide. As a result, the
standard technique for reaching the lowest temperatures—evaporative cooling—won’t work by itself.
To create a near-degenerate Fermi
gas, cold-atom researchers apply evaporative cooling to a mixture of bosons
and fermions. Drawing off the highestenergy atoms leaves the remainder to reequilibrate through collisions and reach
the same ultralow temperature. At that
point, a burst of resonant RF radiation
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can be applied to spring the bosons, but
not the fermions, from the trap.
Sympathetic cooling works for
lithium-6 and lithium-7 and other
fermion–boson mixtures, but it has
proved hard to apply to 3He and 4He for
a variety of technical reasons. Last year
Vassen’s group succeeded in creating
the first 3He degenerate Fermi gas.5
When Vassen heard of Westbrook’s
4
He bunching experiment, he proposed
a collaboration. The Orsay team took its
detector to Amsterdam. Within a few
months, the Orsay and Amsterdam researchers had combined their respective instruments and seen their first
antibunching signal. For a direct comparison with bunching, the experiment
was repeated with 4He under the same
trapping conditions. Figure 2 shows the
results of the two runs.
In principle, bunching or antibunching is total. If you monitored the contents
of two nearby volume elements of phase
space, you’d count twice as many bosons
as you’d expect from random noise and
no fermions. But as figure 2 shows, the
degree of bunching or antibunching detected is 10% at most. The shortfall arises
from the detector, which gathers the signal from several volume elements simultaneously, blurring and therefore reducing the observable correlation.
Optical lattices
The Mainz group worked with 40K
atoms, which can be sympathetically
and readily cooled in the presence of rubidium-87. Once the 40K atoms had
reached 2 μK, they were loaded into a
3D optical lattice whose individual
wells were deepened to confine the
atoms, one per well.
It’s possible to think of the Mainz experiment in terms of interfering paths,
just as in the Amsterdam–Orsay and
Hanbury Brown and Twiss experiments. But an equivalent, condensedmatter view reveals how antibunching
carries information about the band
structure of an optical lattice.
Like the most loosely bound electrons in a crystal, the trapped 40K atoms
behave like plane waves whose amplitudes are modulated by the lattice period. An atom’s momentum state is a
superposition of its crystal momentum
q and the momentum 2nk it acquires
in an nth-order diffraction from a lattice
of wavenumber k.
After release, the atoms travel for
time t for a distance xn = (q +
2nk)t/m, where m is the atoms’ mass.
Atoms with identical crystal momentum q would end up in positions
equally spaced by a distance L =
1.05
CORRELATION
posite sense: The drops would avoid
arriving together.
Particles emitted by lamps and atom
clouds originate from more than two
points. Bunching or antibunching occurs when, for all the source pairs, the
phase difference between the crossed
and uncrossed paths remains small.
Widening the separation between the
detectors smears the phase differences
and dissolves the interference.
Hanbury Brown and Twiss’s experiment inspired the foundation of quantum optics, but the pair’s intent was to
determine the angular sizes of mainsequence stars. They converted two
World War II searchlights into light
buckets, pointed them at Sirius, and correlated the two signals. By separating
the detectors until the correlation vanished, they deduced the star’s diameter.
1
1
0.95
0.90
0
1
2
3
VERTICAL SEPARATION (mm)
Figure 2. Helium-3 atoms (red
points) are antibunched on a time
scale that corresponds to a vertical
separation of about 1 mm. Helium-4
atoms (blue points) are bunched
on the same scale. For each plot,
1000 clouds were trapped and
released to attain a sufficient
signal-to-noise ratio. (Adapted
from ref. 2.)
2kt/m. But fermions can’t occupy the
same crystal momentum state. If an
atom arrives at x, others won’t be found
at x + L, x + 2L, and so on.
To detect this antibunching, the
Mainz group used the standard technique of illuminating the released
atoms with a resonant laser and recording the shadow on an optical CCD. Calculating the point-to-point correlation
from the image yields the expected
minima at integer multiples of L.
Doing so proved challenging. The
image integrates the atoms’ positions
along the laser’s line of sight. Regardless of how well the optics resolve the
cloud, several phase-space volume elements are combined, damping the observed correlation.
By carefully removing sources of extraneous noise, the Mainz group saw
antibunching at a low but significant
factor of 10−3. Like the Amsterdam–
Orsay group, the Mainz group had previously used their setup to observe
bunching with bosonic atoms (87Rb).6
Figure 3 shows results from both runs.
In 2005 Deborah Jin of NIST in Boulder, Colorado, and her collaborators
trapped 40K atoms and tuned a magnetic field to coax the fermions into
weakly bound molecular pairs. After
releasing the molecules from the trap,
they detuned the field to break up the
March 2007
Physics Today
19
c
b
d
0.2
4
2
0.1
0
–2
–4
0.2
0.1
0
–400 –200 0 200 400
x (μm)
–400 –200 0 200 400
x (μm)
0
–400 –200
0
200
x (μm)
400
–200
0
x (μm)
CORRELATION
DENSITY
a
200
Figure 3. When released from an optical lattice, rubidium-87 atoms bunch, whereas potassium-40 atoms antibunch. Panels
(a) and (c) show the density profiles of the 87Rb and 40K clouds, respectively. Cross-correlating the 87Rb density profile yields
the bunching signal in (b). Cross-correlating the 40K density profile yields the antibunching signal in (d). (87Rb images
adapted from ref. 6; 40K images adapted from ref. 1.)
molecules and imaged the expanding
cloud. The newly unbound atoms separated from each other in opposite, correlated directions. Following Altman,
Demler, and Lukin’s recipe, the NIST
group found and measured those pairwise correlations in the shot noise of
the image.7
It’s hoped that an optical lattice filled
with fermionic atoms could mimic a
high-Tc superconductor. Conceivably, a
NIST-like experiment in an optical lattice
could reproduce and reveal the mysterious correlations that lead to the emer-
gence of cuprate superconductivity.
In his autobiography, Hanbury
Brown recalled with bemusement the
theoretical controversies his and
Twiss’s effect stirred up. One suspects
he’d be pleased to see it find another experimental application.
Charles Day
3.
4.
5.
References
1. T. Rom, T. Best, D. van Oosten, U. Schneider, S. Fölling, B. Paredes, I. Bloch, Nature
444, 733 (2006).
2. T. Jeltes, J. M. McNamara, W. Hogervorst,
W. Vassen, V. Krachmalnicoff, M.
6.
7.
Schellekens, A. Perrin, H. Chang, D.
Boiron, A. Aspect, C. I. Westbrook, Nature
445, 402 (2007).
E. Altman, E. Demler, M. D. Lukin, Phys.
Rev. A 70, 013603 (2004).
M. Schellekens, R. Hoppeler, A. Perrin, J.
Viana Gomes, D. Boiron, A. Aspect, C. I.
Westbrook, Science 310, 648 (2005).
J. M. McNamara, T. Jeltes, A. S. Tychkov,
W. Hogervorst, W. Vassen, Phys. Rev. Lett.
97, 080404 (2006).
S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, I. Bloch, Nature 434, 481
(2005).
M. Greiner, C. A. Regal, J. T. Stewart, D. S.
Jin, Phys. Rev. Lett. 94, 110401 (2005).
Three-dimensional mapping of dark matter
reveals the expected filamentary scaffold
Model simulations of the large-scale distribution of galaxies have long suggested that galaxies
form on a filamentary network of dark matter. Now gravitational lensing has yielded a look at
that network.
In 2004 and 2005, the Cosmic Evolution Survey was granted almost 1000
hours of observing time on the Hubble
Space Telescope. COSMOS, an international collaboration of some 90 astronomers headed by Nick Scoville of
Caltech, used this extraordinary allotment of scarce HST time to peer at very
distant galaxies in a patch of sky about
nine times as big as the full Moon.
Not far from the North Pole of our
own galaxy, this patch was chosen for its
relative freedom from obscuring foreground stars, dust, and local galaxies.
The COSMOS exposure has yielded well
measured positions and shapes for half
a million galaxies out to a redshift z of 3.
That’s a glimpse all the way back to how
20
March 2007
Physics Today
galaxies looked 11 billion years ago.
Having completed a gravitationallensing analysis of that prodigious accumulation of observational data, the
collaboration has now reported the
most extensive and detailed study to
date of how the distribution of dark
matter on a cosmological scale has been
evolving over the past 8 billion years.1
The showpiece of the study is the threedimensional dark-matter map displayed in figure 1. Charting the distribution of the dark matter lets the
COSMOS team examine how that distribution has governed the clustering of
ordinary matter into accumulations of
gas and stars.
Nonbaryonic dark matter made up
of still-unidentified weakly interacting
elementary particles is presumed in
standard cosmology to account for
about 85% of all matter. Because it neither emits nor reflects photons at any
wavelength, astronomers can map it on
large scales only through its gravitational-lensing distortion of background
galaxies (see PHYSICS TODAY, November 2006, page 21).
Exploiting the Hubble
Pioneering gravitational-lensing studies
of dark matter on large scales have been
carried out in recent years with groundbased telescopes.2 But atmospheric blurring makes it difficult for ground-based
telescopes to measure the typically
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