QUANTUM PHYSICS: ON ATOM-PHOTON ENTANGLEMENT

ScienceWeek http://scienceweek.com
The following points are made by B.B. Blinov (Nature 2004
428:153):

1) An outstanding goal in quantum information science is the
faithful mapping of quantum information between a stable quantum
memory and a reliable quantum communication channel(1). This
would allow, for example, quantum communication over remote
distances(2), quantum teleportation(3) of matter, and distributed
quantum computing over a "quantum internet".

2) Because quantum states cannot in general be copied, quantum
information can only be distributed in these and other
applications by entangling the quantum memory with the
communication channel.

3) Atom-photon entanglement has been implicit in many previous
experimental systems, from early measurements of Bell inequality
violations in atomic cascade systems to fluorescence studies in
trapped atomic ions. A prime example of current interest is
strongly coupled cavity quantum electrodynamics, where individual
atoms interact with photons in single-mode cavities(5). Another
example is the continuous-variable entanglement between ensembles
of atoms and light fields observed in systems containing
macroscopic numbers of atoms and photons. However, atom-photon
entanglement has not been directly observed in previous
experiments, as the individual atoms and photons have not been
under sufficient control.

4) The authors report quantum entanglement between an ideal
quantum memory -- represented by a single trapped 111-Cd+ ion --
and an ideal quantum communication channel provided by a single
photon emitted spontaneously from the ion. Appropriate
coincidence measurements between the quantum states of the photon
polarization and the trapped ion memory are used to verify their
entanglement directly. The direct observation of entanglement
between stationary and "flying" qubits(4) is accomplished without
using cavity quantum electrodynamic techniques(5) or prepared
non-classical light sources(3). The authors suggest this source
of entanglement may be used for a variety of quantum
communication protocols(2), and for seeding large-scale entangled
states of trapped ion qubits for scalable quantum computing.

References (abridged):

1. DiVincenzo, D. The physical implementation of quantum
computation. Fortschr. Phys. 48, 771-783 (2000)

2. Duan, L.-M., Lukin, M., Cirac, J. I. & Zoller, P. Long-
distance quantum communication with atomic ensembles and linear
optics. Nature 414, 413-418 (2001)

3. Bouwmeester, D., Ekert, A. & Zeilinger, A. (eds) Quantum
Cryptography, Quantum Teleportation, Quantum Computation
(Springer, Springer, 2000)

4. Gheri, K., Ellinger, K., Pellizzari, T. & Zoller, P. Photon-
wavepackets as flying quantum bits. Fortschr. Phys. 46, 401-415
(1998)

5. Haroche, S., Raimond, J. M. & Brune, M. in Experimental
Quantum Computation and Information (eds de Martini, F. & Brune,
M.) 3-36 (Proc. Int. School of Physics Enrico Fermi, course
CXLVIII, IOS Press, Amsterdam, 2002)

Nature http://www.nature.com/nature

--------------------------------

ON QUANTUM ENTANGLEMENT

The following points are made by B.M. Terhal et al (Physics Today
2003 April):

1) Erwin Schroedinger (1887-1961) coined the word entanglement in
1935 in a three-part paper (Naturwiss. 1935 48:807; 49:823,844;
Engl. trans.: Proc. Am. Philos. Soc. 1980 124:323) on the
"present situation in quantum mechanics." His article was
prompted by Albert Einstein, Boris Podolsky, and Nathan Rosen's
now celebrated "EPR paper" that had raised fundamental questions
about quantum mechanics earlier that year.

2) Einstein and his coauthors had recognized that quantum theory
allows very particular correlations to exist between two
physically distant parts of a quantum system; those correlations
make it possible to predict the result of a measurement on one
part of a system by looking at the distant part. On that basis,
the EPR paper argued that the distant predicted quantity should
have a definite value even before being measured if the theory
were to claim completeness and respect locality. However, because
quantum mechanics disallows such definite values prior to
measuring, the EPR authors concluded that, from a classical
perspective, quantum theory must be incomplete.

3) Schroedinger's 1935 perspective comes closer to the modern
view: The wavefunction or state vector gives us all the
information that we can have about a quantum system. About
entangled quantum states, he wrote, "The whole is in a definite
state, the parts taken individually are not," which we now
understand as the essence of pure-state entanglement. In that
same 1935 article, Schroedinger also introduced his famous cat as
an extreme illustration of entanglement: A cat physically
isolated in a box with a decaying atom and vial of cyanide
represents a quantum state having macroscopic degrees of freedom.
If the atom were to decay and trigger the release of cyanide, the
cat would die. The quantum-mechanical description of the system
is a coherent superposition of one state in which the atom is
still excited and the cat alive, and another state in which the
atom has decayed and the cat is dead. The isolated cat-trigger-
atom-cyanide system as a whole is in a definite entangled state,
even though the cat itself exists as a probabilistic mixture of
being alive or dead.

4) For the three decades following the 1935 articles, the debate
about entanglement and the "EPR dilemma" -- how to make sense of
the presumably nonlocal effect one particle's measurement has on
another -- was philosophical in nature, and for many physicists
it was nothing more than that. The 1964 publication (J.S. Bell:
Physics 1964 1:195) by John Bell changed that situation
dramatically. Bell derived correlation inequalities that can be
violated in quantum mechanics but have to be satisfied within
every model that is local and complete -- so-called local hidden-
variable models. Bell's work made it possible to test whether
local hidden-variable models can account for observed physical
phenomena. Early and ongoing recent experiments showing
violations of such Bell inequalities have invalidated local
hidden-variable models and lend support to the quantum-mechanical
view of nature. In particular, an observed violation of a Bell
inequality demonstrates the presence of entanglement in a quantum
system.

Physics Today http://www.physicstoday.org

--------------------------------

Notes by ScienceWeek:

A "hidden variables theory" is one of a class of physical
theories which deny that the quantum state of a physical system
is a complete specification. The hidden variables are those
components of the hypothetical complete state that are not
contained in the quantum state.

"Bell's inequality", formulated by John Bell (1928-1990) in 1964,
is one of a family of inequalities concerning the probabilities
of joint occurrence of certain events in two well-separated parts
of a composite system, the inequality implied by any hidden
variables theory that satisfies an appropriate locality
condition. In this context, in general, a locality condition is a
condition such that no interaction between two entities can occur
in less time than the time required for light to travel from one
entity to the other. For example, any apparent instantaneous
effect of one entity upon the other entity implies locality is
not obeyed.

"Bell's theorem" is the theorem that no hidden variables theory
satisfying an appropriate locality condition can make statistical
predictions in complete agreement with those of quantum
mechanics. In other words, there are situations in which quantum
mechanics predicts a violation of Bell's inequality. Another
formulation is that any hidden variables theory that forbids
instantaneous interactions cannot make predictions in complete
agreement with those of quantum mechanics.

--------------------------------

QUANTUM COMPUTING: IONS, PHOTONS, AND COMMUNICATION LINKS

The following points are made by Eugene Polzik (Nature 2004
428:129):

1) The initial proposal(1) for a quantum computer by Ignacio
Cirac and Peter Zoller in 1995 has since been followed up by a
train of theoretical and experimental breakthroughs, which last
year arrived at the demonstration of elementary quantum logic
gates using trapped ions(2,3). Recently, Blinov et al(4) reported
the first observation of entanglement between a trapped ion and
light -- a significant step towards building a quantum network.

2) Entanglement is a quantum correlation between various parts of
a system and is required for processing quantum information. The
quantum logic gates(2,3) involving trapped ions were built with
short-range entanglement, over only a few micrometers, created by
electrical interaction between the ions. Such short-range
interaction is not suitable for linking distant nodes of a
quantum computer, let alone a large-scale network of such
computers. Quantum networks should be linked with light, which is
the best long-distance carrier of information, be it classical or
quantum.

3) In a classical computer, bits of information are physically
implemented as charges on tiny capacitors, and can take two
distinct values, usually denoted 0 and 1. Quantum mechanics,
however, allows for a superposition of states. This
superposition, called a quantum bit or "qubit", dramatically
enhances computing and communication capabilities. More
specifically, in the work of Blinov et al(4), a qubit formed by a
trapped ion can exist in a superposition of two different
orientations of its magnetic momentum, say "up" and "down", or +1
and -1. The trick by which Blinov et al(4) entangled an ion and a
photon was to bring the ion into this superposition of states
through the emission of the photon.

4) According to the conservation of angular momentum, if the ion
is created in a spin-down state, the emitted photon is circularly
polarized (a property of its electric-field vector) in the right-
hand direction. Similarly, if the ion is created in a spin-up
state, the emitted photon has left-hand circular polarization.
Most importantly, if the ion ends up in an unknown superposition
of spin-up and spin-down states, the emitted photon has a
complementary superposition state. This is the essence of
entanglement of two qubits.

5) Such an entangled state has been generated before, most often
between two photons, but also for two ions(2,3), two atoms(5) or
an atom and a microwave photon in a cavity(5). In fact,
entanglement between atoms and light has been hinted at in a
variety of experiments: for example, in the quantum correlations
in light emitted by atomic ensembles; in work on spin squeezing
and the entanglement of atomic ensembles; and in early
experiments on Bell inequalities, in which two photons were
emitted by a single atom.

6) The real breakthrough achieved by Blinov et al.4 is that, for
the first time, entanglement has been observed between a
stationary computational qubit (a trapped ion) and a "flying"
communication qubit (an optical photon). The emitted photon can
carry a unique piece of information about the state of the ion
over a long distance. Another advantage of the system is that
trapped ions have exceptionally long lifetimes in entangled
states. Although in this experiment the lifetime of demonstrated
entanglement did not exceed a microsecond, it can potentially be
increased by many orders of magnitude.

References (abridged):

1. Cirac, J. I. & Zoller, P. Phys. Rev. Lett. 74, 4091-4094
(1995)

2. Liebfried, D. et al. Nature 422, 412-415 (2003)

3. Schmidt-Kaler, F. et al. Nature 422, 408-411 (2003)

4. Blinov, B. B., Moehring, D. L., Duan, L. -M. & Monroe, C.
Nature 428, 153-157 (2004)

5. Rauschenbeutel, A. et al. Science 288, 2024-2028 (2000)

Nature http://www.nature.com/nature

ScienceWeek http://scienceweek.com

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Frederick Martin McNeill
Poway, California, United States of America
mmcneill@fuzzysys.com
http://www.fuzzysys.com
http://members.cox.net/fmmcneill/
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