Relational superposition measurements with a material quantum ruler

Abstract

In physics, it is crucial to identify operational measurement procedures to give physical meaning to abstract quantities. There has been significant effort to define time operationally using quantum systems, but the same has not been achieved for space. Developing an operational procedure to obtain information about the location of a quantum system is particularly important for a theory combining general relativity and quantum theory, which cannot rest on the classical notion of spacetime. Here, we take a first step towards this goal, and introduce a model to describe an extended material quantum system working as a position measurement device. Such a "quantum ruler" is composed of $N$ harmonically interacting dipoles and serves as a (quantum) reference system for the position of another quantum system. We show that we can define a quantum measurement procedure corresponding to the "superposition of positions", and that by performing this measurement we can distinguish when the quantum system is in a coherent or incoherent superposition in the position basis. The model is fully relational, because the only meaningful variables are the relative positions between the ruler and the system, and the measurement is expressed in terms of an interaction between the measurement device and the measured system.

arXiv comment30 pages, 6 figures

References in corpus (25)

• Quantifying Coherence
• Relational Quantum Mechanics
• Reference frames, superselection rules, and quantum information
• Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber
• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Quantum entropy and special relativity
• Quantum mechanics and the covariance of physical laws in quantum reference frames
• Quantum interferometric visibility as a witness of general relativistic proper time
• Classical world arising out of quantum physics under the restriction of coarse-grained measurements
• The Trinity of Relational Quantum Dynamics
• Weak measurements are universal
• Relational Observables in Gravity: a Review
• Gravitational redshift in quantum-clock interferometry
• Scalable and Programmable Phononic Network with Trapped Ions
• Coherent Superposition States as Quantum Rulers
• What is the relativistic spin operator?
• On Relativistic Material Reference Systems
• General relativistic effects in quantum interference of "clocks"
• Relational observables in Asymptotically safe gravity
• Classical Mechanics without Absolute Space
• Time evolution of coupled multimode and multiresonator optomechanical systems
• Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
• Mesoscopic Mechanical Resonators as Quantum Non-Inertial Reference Frames
• Relational evolution with oscillating clocks