A clock of atoms is spin-squeezed to a Wineland parameter .

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Quantum Information and Technology, Ch Quantum metrology and sensing

Problem

A clock of

N=10^5

atoms is spin-squeezed to a Wineland parameter

\xi^2=0.05

. ((a)) Find the one-shot phase uncertainty

\Delta\varphi=\xi/\sqrt N

. ((b)) Find the factor by which this beats the standard quantum limit,

1/\sqrt N

. ((c)) Find the factor by which it still falls short of the Heisenberg limit,

1/N

. ((d)) State whether the atoms are certified entangled by this value of

\xi^2

, and why. ((e)) Find the

\xi^2

(and the equivalent figure in decibels,

-10\log_{10}\xi^2

) that would be needed for a tenfold gain over the standard quantum limit.

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