Quantum Information Processing, Vol. 2, No. 6, December 2003 (© 2004)
Experimental Simulation of Spin Squeezing
by Nuclear Magnetic Resonance
Suddhasattwa Sinha, Joseph Emerson, Nicolas Boulant,
Evan M. Fortunato, Timothy F. Havel,
and David G. Cory
Received May 3, 2004; accepted July 14, 2004
We report on the experimental simulation of spin squeezing using a liquid-state
nuclear magnetic resonance (NMR) quantum information processor. This was
done by identifying the energy levels within the symmetric subspace of a system
of n spin-1/2 nuclei with the energy levels of the simulated spin-(n/2) system. The
results obtained for our simulations of spin-1 and spin-3/2 systems are consistent
with earlier theoretical studies of spin squeezing, and illustrate interesting rela-
tions between the degree of squeezing and the strength of the correlations among
the underlying spin-1/2 particles.
KEY WORDS: Coherent and squeezed spin states; nuclear magnetic resonance;
quantum information processing.
PACS: 03.65.Bz; 03.67.–a; 03.67.Lx.
The minimum uncertainty associated with complementary observables is
given by the uncertainty relations. For example, the position and momen-
tum ﬂuctuations in a coherent state of the quantum harmonic oscillator
are both equal to the quantum limit
h/2. States for which the ﬂuctua-
tions in one of these observables is less than the standard quantum limit
h/2, while the ﬂuctuations in the complementary observable increase so
as to satisfy the uncertainty relation, are called “squeezed states”.
a squeezed state can be visualized as an ellipse of constant uncertainty in
Squeezed spin states have been deﬁned using analogous criteria,
and several experimental demonstrations of spin squeezing have been pub-
lished. They include interaction of collection of atoms with squeezed
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1570-0755/03/1200-0433/0 © 2004 Springer Science+Business Media, Inc.