Measurement operator for quantum nondemolition measurements

TL;DR

This paper derives a general measurement operator for quantum nondemolition measurements of atomic ensembles, analyzing its effects and showing how it can generate spin squeezing and Schrödinger cat states.

Contribution

It provides a comprehensive POVM formulation for QND measurements applicable to arbitrary parameters, including new approximate expressions and practical examples.

Findings

QND measurement applies Gaussian modulation for short interaction times.

Derived POVM expressions in various limits, including projective measurement.

Demonstrated generation of spin squeezing and Schrödinger cat states.

Abstract

We derive a measurement operator corresponding to a quantum nondemolition (QND) measurement of an atomic ensemble. The quantum measurement operator takes the form of a positive operator valued measure (POVM) and is valid for arbitrary interaction times, initial coherent state amplitudes, and final photon measurement outcomes. We analyze the dependence on various parameters and show that the effect of the QND measurement for short interaction times is to apply a Gaussian modulation of the initial state wavefunction. We derive approximate expressions for the POVM in various limits, such as the short interaction time regime and projective measurement limit. Several examples are shown which shows how spin squeezing and Schrodinger cat states can be generated using the measurement.