We discuss a quantum-metrology protocol designed to estimate a physical
parameter in a Bose-Einstein condensate of N atoms, and we show that the
measurement uncertainty can decrease faster than 1/N. The 1/N scaling is
usually thought to be the best possible in any measurement scheme. From the
perspective of quantum information theory, we outline the main idea that leads
to a measurement uncertainty that scales better than 1/N. We examine in detail
some potential problems and challenges that arise in implementing such a
measurement protocol using a Bose-Einstein condensate. We discuss how some of
these issues can be dealt with by using lower-dimensional condensates trapped
in nonharmonic potentials.Comment: 32 pages, 1 figure, updated reference
