Globally optimal interferometry with lossy twin Fock probes

Abstract

Parity or quadratic spin (e.g., $J_z^2$) readouts of a Mach-Zehnder (MZ) interferometer probed with a twin Fock input state allow to saturate the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles, but only when the interferometer phase $\theta$ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at $\theta =0$, whereas better-than-standard quantum limit performance of the $J_z^2$ readout is restricted to an $o(\sqrt{N})$ 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 $\theta$. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on twin Fock states, showing that method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of $\theta$ 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 $|\frac{N}{4},\frac{N}{4},\frac{N}{4},\frac{N}{4}⟩$ and its lossy counterparts, showing that an advantage for estimation of any linear function of the local MZ phases ${\theta }_1$, ${\theta }_2$ (compared to independent probing of the MZ phases by two copies of $|\frac{N}{4},\frac{N}{4}⟩$) appears when more than one particle is lost.

13 pages, 2 figures

References in corpus (14)

• Optimal Quantum Phase Estimation
• Twin matter waves for interferometry beyond the classical limit
• Long Phase Coherence Time and Number Squeezing of two Bose-Einstein Condensates on an Atom Chip
• An Atomic Gravitational Wave Interferometric Sensor (AGIS)
• Detecting multiparticle entanglement of Dicke states
• Experimental generation of multi-photon Fock states
• Optimal Quantum-Enhanced Interferometry
• Atom interferometry with trapped Bose-Einstein condensates: Impact of atom-atom interactions
• Quantum states for Heisenberg-limited interferometry
• Short-Depth Circuits for Dicke State Preparation
• Dynamical quantum phase transitions in a spinor Bose-Einstein condensate and criticality enhanced quantum sensing
• Quantum Fisher Information as the Convex Roof of Variance
• Robustness of Heisenberg-limited interferometry with balanced Fock states
• Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout

Cited by in corpus (1)

• Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage