  Algorithmic cooling (AC) is a method to purify quantum systems, such as
ensembles of nuclear spins, or cold atoms in an optical lattice. When applied
to spins, AC produces ensembles of highly polarized spins, which enhance the
signal strength in nuclear magnetic resonance (NMR). According to this cooling
approach, spin-half nuclei in a constant magnetic field are considered as bits,
or more precisely, quantum bits, in a known probability distribution.
Algorithmic steps on these bits are then translated into specially designed NMR
pulse sequences using common NMR quantum computation tools. The $algorithmic$
cooling of spins is achieved by alternately combining reversible,
entropy-preserving manipulations (borrowed from data compression algorithms)
with $selective$ $reset$, the transfer of entropy from selected spins to the
environment. In theory, applying algorithmic cooling to sufficiently large spin
systems may produce polarizations far beyond the limits due to conservation of
Shannon entropy.
  Here, only selective reset steps are performed, hence we prefer to call this
process "heat-bath" cooling, rather than algorithmic cooling. We experimentally
implement here two consecutive steps of selective reset that transfer entropy
from two selected spins to the environment. We performed such cooling
experiments with commercially-available labeled molecules, on standard
liquid-state NMR spectrometers. Our experiments yielded polarizations that
$bypass$ $Shannon's$ $entropy$-$conservation$ $bound$, so that the entire
spin-system was cooled. This paper was initially submitted in 2005, first to
Science and then to PNAS, and includes additional results from subsequent years
(e.g. for resubmission in 2007). The Postscriptum includes more details.
