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We have previously shown that quantum-enhanced atom interferometry can beachieved by mapping the quantum state of squeezed optical vacuum to one of theatomic inputs via a beamsplitter-like process [Phys.~Rev.~A \textbf{90}, 063630(2014)]. Here we ask the question: is a better phase sensitivity possible ifthe quantum state transfer (QST) is described by a three-mode-mixing model,rather than a beamsplitter? The answer is yes, but only if the portion of theoptical state not transferred to the atoms is incorporated via informationrecycling. Surprisingly, our scheme gives a better sensitivity for lower QSTefficiencies and with a sufficiently large degree of squeezing can attainnear-Heisenberg-limited sensitivities for arbitrarily small QST efficiencies.Furthermore, we use the quantum Fisher information to demonstrate the nearoptimality of our scheme.

Heisenberg-limited metrology with a squeezed vacuum state, three-mode mixing, and information recycling