States for phase estimation in quantum interferometry

Abstract

Ramsey interferometry allows the estimation of the phase $\varphi$ of rotation of the pseudospin vector of an ensemble of two-state quantum systems. For $\varphi$ small, the noise-to-signal ratio scales as the spin-squeezing parameter $\xi$, with $\xi <1$ possible for an entangled ensemble. However states with minimum $\xi$ are not optimal for single-shot measurements of an arbitrary phase. We define a phase-squeezing parameter, $\zeta$, which is an appropriate figure-of-merit for this case. We show that (unlike the states that minimize $\xi$), the states that minimize $\zeta$ can be created by evolving an unentangled state (coherent spin state) by the well-known 2-axis counter-twisting Hamiltonian. We analyse these and other states (for example the maximally entangled state, analogous to the optical "NOON" state $|\psi >=(|N,0>+|0,N>)/\sqrt{2}$) using several different properties, including $\xi$, $\zeta$, the coefficients in the pseudo angular momentum basis (in the three primary directions) and the angular Wigner function $W(\theta ,\varphi )$. Finally we discuss the experimental options for creating phase squeezed states and doing single-shot phase estimation.

8 pages and 5 figures

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Cited by in corpus (12)

• Quantum states for Heisenberg-limited interferometry
• Optimal quantum states for frequency estimation
• Phase space geometry and optimal state preparation in quantum metrology with collective spins
• Digital Quantum Estimation
• Generation of a highly phase sensitive polarization squeezed N-photon state by collinear parametric downconversion and coherent photon subtraction
• Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough
• Speeding Up Squeezing with a Periodically Driven Dicke Model
• Phase Estimation with Non-Unitary Interferometers: Information as a Metric
• Quantum enhancement of N-photon phase sensitivity by interferometric addition of down-converted photon pairs to weak coherent light
• Optimal lossy quantum interferometry in phase space
• Dynamical generation of phase-squeezed states in a two-component Bose-Einstein condensates
• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group