Physics 4, 41 (2011)

Viewpoint
Bragging rights
Joseph H. Thywissen
Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada

Published May 23, 2011
When it comes to probing ultracold atoms in optical lattices, has direct imaging put Bragg diffraction
out of business?

Subject Areas: Atomic and Molecular Physics, Optics
A Viewpoint on:
Coherent Light Scattering from a Two-Dimensional Mott Insulator
Christof Weitenberg, Peter Schauß, Takeshi Fukuhara, Marc Cheneau, Manuel Endres, Immanuel Bloch, and Stefan
Kuhr
Phys. Rev. Lett. 106, 215301 (2011) – Published May 23, 2011

X-ray scattering is a powerful tool to investigate thestructure of materials. In particular, because x rays havea wavelength comparable to the spacing between ions ina solid, coherent scattering from a crystalline material
leads to constructive interference in so-called “Bragg” directions, similar to the diffraction peaks of visible lightreflected off a periodic grating. Crystallographers measure these Bragg angles to infer the structure of a solid,
while biologists and chemists apply x-ray scattering tocrystals of large molecules—most famously, to discover
the double helix structure of DNA. Similarly, measurements of the scattering outside the Bragg peaks can reveal deviations from perfect order, or excitations.
In many ways, neutral atoms moving in an optical lattice mimic the behavior of electrons moving in a conventional crystalline solid—only the period of the optical crystal is 1000 times longer than the ionic crystal,and of course atoms are more massive than electrons.
For this reason, the energy and temperature scales relevant to neutral atomic systems are a billion times lower
than their electronic counterparts, hence the need for“ultracold” conditions. In an article appearing in Physical Review Letters [1], Christof Weitenberg from theMax Planck Institute for Quantum Optics in Garching,
Germany, and colleagues compare angle-resolved scattering and direct microscopy of ultracold atoms (Fig. 1).
Their work is one of the most precisely controlled lightscattering experiments to date, and the first to apply
crystallographic methods to neutral atoms prepared in
an insulating phase. While recent work has demonstrated
site-resolved images of such cold-atom lattices [2, 3], inthis new work, Weitenberg et al. shift the focus of theirmicroscope away from the lattice and into the far field
to measure the angular distribution of light scattered offsuch atoms. In this way, they are able to distinguishcoherent from incoherent scattering, and demonstrate a
detection method for magnetic ordering of atomic spins.
DOI: 10.1103/Physics.4.41
URL: http://link.aps.org/doi/10.1103/Physics.4.41

One might guess that microscopy would be the best
way to learn about structure. Why then is angle-resolved
scattering such a widespread technique? Exploring threedimensional structure with microscopy is slow, because
it requires examining atoms plane-by-plane or worse:
scanning techniques acquire information point-by-point.
Even if one had the patience for such a task, electron
microscopy (such as transmission electron microscopy)
cannot penetrate further than a few hundred nanometers
into a material, because electrons scatter too strongly. X
rays and neutrons scatter weakly, allowing them to penetrate into the bulk; but no good lenses are available
for these probes. So structural determination of solids isnearly always done with far-field analysis of scattered xrays or neutrons.
In contrast, visible light scattering from neutral atoms
can produce both angle-resolved data [4] and spatial images. In the last few years, a new generation of optical lattice experiments have implemented high-resolution
microscopy [2, 3, 5, 6]. In addition to requiring sophisticated optics, site-resolved imaging requires light to playthe dual role of imaging probe and the coolant, keeping
the atoms trapped while each scatters thousands of photons. The sample size is kept manageably small, to lessthan a thousand atoms. Although three-dimensional reconstruction is the goal of at least one group [5], others[2, 3] work in a geometry where the atoms are restricted
to move in a single plane.
The two-dimensional geometry of an isolated plane isalso easier for crystallography. For a single-frequency
laser beam, Bragg scattering from a three-dimensional
crystal will only occur at specific incident angles. However, for a two-dimensional crystal, coherent diffraction
occurs for any incident beam angle. Weitenberg et al.
are able to use their laser-cooling light, which impinges
on the atoms from several in-plane directions, for crysc 2011 American Physical SocietyPhysics 4, 41 (2011)

FIG. 1: Measuring the angular distribution of light scatteredfrom cold atoms in an optical lattice. Bosonic rubidium atoms
are held in a square lattice with a periodicity of 532 nm.
Optical molasses beams (four red beams in the xy plane) at
780 nm are also incident on the atoms, and scatter light out ofthe plane (some of the coherently diffracted light is shown).
To measure the angular distribution of scattered light, thefocal plane of a microscope is placed roughly 20 microns below
the lattice plane. Alternatively, to image the occupancy ofthe lattice sites, this focal plane would be coincident with thesquare lattice. (Credit: C. Weitenberg et al.[1])tallographic analysis (see Fig. 1). Since this is the samelight they use to image the atoms, no dedicated crystallography beam is required.
In fact, in a two-dimensional geometry, imaging andcrystallography are not very different. Both involve thedetection of scattered light. To take a crystallographic
measurement, the angles of scattered beams are measured after they propagate away from the sample. Spatial
imaging uses a lens (or several lenses) to reunite scattered beams at an image plane and interferometricallyreconstruct the distribution of scattering sources. These
two modes of data acquisition cannot be simultaneous,
because ideal imaging erases all information about thedirection in which light was scattered in the first place:
all rays are brought into focus. Conversely, in the far
field, the image is blurred out of recognition. This complementarity is simply the uncertainty principle applied
to the position and wave vector of light.
In their new work, Weitenberg et al. take advantageof this complementarity and compare the results of theirdiffraction experiment to a real-space image of the atomicdensity. They find excellent agreement between the measured diffraction angles and what you would expect for
the imaged positions of the atoms. They also observethat the peaks become more defined as the sample size
grows, as it must for perfect crystalline order.
DOI: 10.1103/Physics.4.41
URL: http://link.aps.org/doi/10.1103/Physics.4.41

In their experiments, not all of the light scatters coherently into a diffraction peak, however. Instead, someof the light scatters incoherently, forming a diffuse background outside of the Bragg angles. Although one may
be tempted to discard this background as a technical detail, doing so would “throw the baby out with the bathwater.” Light that is scattered in ways other than perfectdiffraction is informative: the scrambled phase can reveal
the fingerprints of excitations or of limited long-range order. In Weitenberg et al.’s experiment, it turns out that
85% of the incident light is scattered incoherently. The
reason is that the process of cooling the atoms changes
the internal states of the atoms, which in turn scrambles the scattering phase randomly and independently ateach site, destroying coherence. (Recall that cooling andscattering involve the same light.) When looking at microscopy images alone, these dynamics were not apparent
because an image can be formed from either coherent orincoherent light.
As a further step, Weitenberg et al. implement a
scheme to detect magnetic-spin ordering. Their imaging technique is not sensitive to the initial spin state of
the atoms, for the same reason that incoherent light isbeing generated: the laser cooling beams scramble the internal states. However, they can convert the initial spin
patterns into density patterns by removing one of two
spin states with a resonant light “blast.” Although spontaneous generation of magnetic-spin ordering does notoccur in their experiment, they imprint a stripe patternusing localized spin-flips [7] to demonstrate that diffraction could, in principle, detect such an ordering. Theteam observes a second Bragg peak in the scattered light,
corresponding to the period of the stripe ordering.
Researchers without the advanced imaging system of
the Max Planck team should be encouraged that Braggdiffracted light passed the test of comparison to images.
Analysis in situ reveals ordering and structure lost in
the time-of-flight analysis used by most cold-atom experiments. But Weitenberg et al. did not learn anything
about lattice occupancy from diffracted light that they
didn’t already know from microscopy images. So has microscopy put cold-atom crystallography out of business?
Not quite. Observing scattered light in the far field can
trump imaging in a number of circumstances. First, as
discussed above, for large or three-dimensional samples,
crystallography can obtain information about the bulk,
where imaging may be impractical. Second, one can acquire information with less than one photon per atom,
thus probing the system nondestructively and quickly.
The Max Planck team acquires light for several tenthsof a second, whereas earlier work using Bragg scatteringobserved average motional dynamics with microsecond
resolution [8]. Depending on the physics under investigation, one may not need to know exactly which sites areoccupied, so complete imaging is not necessary. Photonefficient probing may also be the best option when scattering thousands of photons per atom is not possible,
for instance, in more shallow lattices, or when probingc 2011 American Physical SocietyPhysics 4, 41 (2011)
molecules with open transitions. Of course, the challengeof “photon efficiency” is that it produces a small signal
for samples of only a few hundred atoms, without furthertricks [9].
A third advantage of angle-resolved intensity measurements is that scattering can probe excitations. The response of a system to excitations reveals physics (suchas pairing) that leaves no direct trace in images of lattice occupancy. So far, experiments have detected opticalexcitations excitations by looking at the recoiling atoms
instead of the scattered photons [10]. Such an approachcreates the excitation nondestructively, but then destroys
the sample during detection. Weitenberg et al.’s results
encourage us to dream of yet another generation of experiments, in which quantum many-body physics, such as
magnetic ordering, is probed nondestructively with justa few scattered photons.

Acknowledgments
The author thanks David McKay, Ken Burch, andArun Paramekanti for discussions.

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About the Author
Joseph H. Thywissen

Joseph Thywissen is a Canada Research Chair in the Department of Physics at the University of Toronto. His experimental AMO research group studies gases at several billionthsof a degree above absolute zero. Professor Thywissen received his doctorate from Harvard
University, was a postdoctoral fellow at the Institut d’Optique, and is currently a Scholar
at the Canadian Institute for Advanced Research, in the Quantum Materials program.

DOI: 10.1103/Physics.4.41
URL: http://link.aps.org/doi/10.1103/Physics.4.41

c 2011 American Physical Society