www.sciencemag.org SCIENCE VOL 344 11 APRIL 2014 161
where |0; denotes a particle in the ground
state and |1; denotes the excited particle. This
state, called the W state in quantum information processing and the Dicke state in quantum optics, is rather robust against decoher-ence relative to other entangled states, such
as Schrödinger’s-cat states or Greenberger-Horne-Zeilinger (GHZ) states, the many-particle generalization of Einstein-Podolsky-Rosen pairs.
Preparation of indistinguishable particles
in a Bose-Einstein condensate is routinely
performed in laboratories worldwide, and
excitations of the atoms’ hyperfine states can
be achieved with microwave fields. The key
question, then, is “When has a single excitation entered the system?” Haas et al. tackled this problem using a high-finesse optical
cavity formed by two opposing mirrors at
the ends of optical fibers. Photons typically
bounce between these mirrors more than
10,000 times. Precisely tuning the resonator
length to the wavelength of a weak impinging laser beam leads to light transmission
with a small line width. Such a resonator
is extremely amenable to even the slightest
change of refractive index of its contents.
In fact, a single atom in an excited state
changes the effective optical path length for
the light field sufficiently to render the resonator opaque, while atoms in other internal states are transparent for the light field.
Thus, even for many atoms in one internal
state, the laser beam is fully transmitted, but
if an external microwave field injects just a
single excitation, the transmission vanishes,
heralding the presence of the entangled W
state (see the figure).
Full information about a quantum state—
even about a single quantum system—is in
general not available from a
single measurement. Rather,
a whole series of measure-
ments must be performed to
extract the so-called density
matrix that contains all state
populations as well as coher-
ence and correlation prop-
erties of the quantum state.
For an increasing number
of atoms, this task becomes
harder because the number
of values to be determined
scales as 2N × 2N, which becomes a large num-
ber even for small numbers of particles (8).
Instead, Haas et al. considered only a relevant
subpart of the full density matrix spanned
by symmetric Dicke-type states with vary-
ing numbers of excitations shared. By first
manipulating the prepared quantum state via
microwave fields and subsequently checking
for the presence of excitations, they deter-
mined the overlap of the state prepared with
one of the Dicke states.
Research into larger and other entangled states not only drives the development
of emerging quantum applications; it elucidates the fundamental question, “Why
does quantum physics explain perfectly
everything we know about the microscopic
world but is never observed in our everyday
macroscopic life?” Only with experiments
creating and analyzing larger and larger
entangled states will we be able to track,
and perhaps steer, the quantum-to-classical
1. A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 47, 777
2. F. Haas et al., Science 343, 180 (2014); 10.1126/
3. R. Blatt, D. Wineland, Nature 453, 1008 (2008).
4. T. Monz et al., Phys. Rev. Lett. 106, 130506 (2011).
5. O. Mandel et al., Nature 425, 937 (2003).
6. J. Estève, C. Gross, A. Weller, S. Giovanazzi, M. K.
Oberthaler, Nature 455, 1216 (2008).
7. M. F. Riedel et al., Nature 464, 1170 (2010).
8. H. Häffner et al., Nature 438, 643 (2005).
High rate count
Low rate count
N atoms between mirrors
in state |0; ( ) or |1; ( ) Weak microwave excitation
Fiber ends form
Fiber ends form
How darkness sheds light on entanglement. (A) An ensemble of N atoms in their internal ground state (blue) is transparent to a light field resonant with the cavity formed by
the ends of two fibers (green). As a result, the photon count rate detected through one of
the fibers is “high.” (B) Upon irradiation with a weak microwave field, exciting atoms to
another hyperfine state (red), a single excitation in the ensemble renders the resonator
opaque. The corresponding photon count rate is “low” and indicates an entangled atomic
state in the resonator.
Materials both Tough and Soft
Jian Ping Gong
Tough elastomers are created by adapting an approach previously used for hydrogels.
Hydrogels and elastomers are soft materials that have similar network structures but very different affini-
ties to water. Consisting mostly of water,
hydrogels resemble biological soft tissues
and have great potential for use in biomedical
applications; they tend to be very brittle, like
fragile jellies. Elastomers are formed of non-
hydrated polymer networks and are widely
used as load-dispersing and shock-absorbing
materials. They are stretchable but break eas-
ily along a notch. On page 186 of this issue,
Ducrot et al. (1) show that the toughness of
elastomers can be improved substantially by
combining two different network materials,
an approach previously applied to hydrogels.
Double-network hydrogels contain 80 to
90 weight percent (wt %) of water, yet are
both hard and strong, with mechanical properties comparable to that of rubbers and cartilages (2, 3). The gels consist of two interpenetrating polymer networks with contrasting mechanical properties. The first network
is highly stretched and densely cross-linked,
making it stiff and brittle. The second network is flexible and sparsely cross-linked,
making it soft and stretchable.
The toughness of a material is its ability to absorb mechanical energy and deform
without fracturing. One definition of material toughness is the fracture energy, which
is the energy per unit area required to make
Faculty of Advanced Life Science, Hokkaido University, Sapporo, 060-0810, Japan. E-mail: firstname.lastname@example.org.