Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout

Abstract

We show that the lowest quantum Cramér-Rao bound achievable in interferometry with a one-axis twisted spin coherent state is saturated by the asymptotic method of moments error of a protocol that uses one call to the one-axis twisting, one call to time-reversed one-axis twisting, and a final total spin measurement (i.e., a twist-untwist protocol). The result is derived by first showing that the metrological phase diagram for one-axis twisting is asymptotically characterized by a single quantum Fisher information value $N(N+1)/2$ for all times, then constructing a twist-untwist protocol having a method of moments error that saturates this value. The case of finite-range one-axis twisting is similarly analyzed, and a simple functional form for the metrological phase diagram is found in both the short-range and long-range interaction regimes. Numerical evidence suggests that the finite-range analogues of twist-untwist protocols can exhibit a method of moments error that asymptotically saturates the lowest quantum Cramér-Rao bound achievable in interferometry with finite-range one-axis twisted spin coherent states for all interaction times.

Globally optimal interferometry with lossy twin Fock probes

“…at oversqueezed interaction times t = O(N −α ), with 0 < α < 1/2, has asymptotic QFI equal to N(N+1) 2 for MZ interferometry, which is asymptotically equal to that of the TF probe state of the same particle number [44]. However, a twist-untwist protocol [45,46] (which is obtained from Eq.…”

“…Frontiers in Physics frontiersin.org random unitary optical rotations to a continuous-variable probe state [50, 51], bosonic phase diffusion is a unitary error which reduces the phase coherence in the arms of the interferometer. In a modern context, the fact that one-axis twisting can reduce the performance of atom interferometry may seem surprising given that the one-axis-twisted split Bose-Einstein condensate e −iχJ 2 z e −i π 2 Jy |N, 0〉 exhibits Heisenberg scaling as a probe for the MZ interferometric phase (i.e., J y rotation) for O(N −1/2 ) ≲ χ ≲ o(1), transitioning to Heisenberg limit scaling at χ ~O(1) [44]. To demonstrate the effect of bosonic phase diffusion on interferometric sensitivity, we use a well-known Bayesian parameter estimation method [1,52,53] and the phase-diffused probe state…”