Globally optimal interferometry with lossy twin Fock probes

Journal Article · 19 March 2024 · Frontiers in Physics

DOI: https://doi.org/10.3389/fphy.2024.1369786 · OSTI ID:2326107

Volkoff, T. J.; Ryu, Changhyun

Parity or quadratic spin (e.g., $J_z^2$ ) readouts of a Mach–Zehnder (MZ) interferometer probed with a twin Fock (TF) input state allow saturating the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles but only when the interferometer phase θ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at θ = 0, whereas better-than-standard quantum limit performance of the $J_z^2$ readout is restricted to an $o\left(\sqrt{N}\right)$ occupation imbalance. We show that a method of moments readout of two quadratic spin observables $J_z^2$ and $J_{+}^2+J_{-}^2$ is globally optimal for Dicke state probes; i.e., the error saturates the QFI for all θ . In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on TF states, showing that the method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of θ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four-mode state $|\frac{N}{4},\frac{N}{4},\frac{N}{4},\frac{N}{4}\rangle$ and its lossy counterparts, showing that an advantage for the estimation of any linear function of the local MZ phases θ ₁ and θ ₂ (compared to independent probing of the MZ phases by two copies of $|\frac{N}{4},\frac{N}{4}\rangle$ ) appears when more than one particle is lost.

• Sponsoring Organization: USDOE
• OSTI ID: 2326107
• Alternate ID(s): OSTI ID: 2350640
• Journal Information: Frontiers in Physics, Journal Name: Frontiers in Physics Vol. 12; ISSN 2296-424X
• Publisher: Frontiers Media SACopyright Statement
• Country of Publication: Switzerland
• Language: English