Sub-Planck phase-space structures and Heisenberg-limited measurements

2005/08/31 by F. Toscano, Fabricio Toscano, Diego A. R. Dalvit +4
Computer Science · Physics and Astronomy · #Quantum Electrodynamics and Casimir Effect #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.73.023803

published as Phys. Rev. A 73, 023803 (2006) · 7 pages, 2 figures

arxiv created 2005/12/13 · openalex publication_date 2006/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how sub-Planck phase-space structures in the Wigner function [W. H. Zurek, Nature (London) 412, 712 (2001)] can be used to achieve Heisenberg-limited sensitivity in weak-force measurements. Nonclassical states of harmonic oscillators, consisting of superpositions of coherent states, are shown to be useful for the measurement of weak forces that cause translations or rotations in phase space, which is done by entangling the quantum oscillator with a two-level system. Implementations of this strategy in cavity QED and ion traps are described.

Citations

• Distribution functions in physics: Fundamentals
• Quantum-enhanced measurements: beating the standard quantum limit
• Quantum Entanglement of a Large Number of Photons
• Decay of the Loschmidt Echo for Quantum States with Sub-Planck-Scale Structures
• Density Operators for Coherent Fields
• Manipulating quantum entanglement with atoms and photons in a cavity
• Multiphoton path entanglement by non-local bunching