Detecting Macroscopic Indefiniteness of Cat States in Bosonic Interferometers

TL;DR

This paper presents a practical method to detect the macroscopic indefiniteness of Schrödinger cat states in bosonic interferometers by analyzing statistical distributions and Fisher information, avoiding full quantum state tomography.

Contribution

It introduces a novel approach combining statistical and interferometric measurements to assess the indefiniteness of macroscopic quantum superpositions without full state reconstruction.

Findings

The method can distinguish between quantum indefiniteness and classical mixtures.

Simulations show the loss of indefiniteness with increasing temperature.

The approach is feasible with current cold atom technology.

Abstract

The paradigm of Schr\"{o}dinger's cat illustrates how quantum states preclude the assignment of definite properties to a macroscopic object (realism). In this work we develop a method to investigate the indefiniteness of cat states using currently available cold atom technology. The method we propose uses the observation of a statistical distribution to demonstrate the macroscopic distinction between dead and alive states, and uses the determination of the interferometric sensitivity (Fisher information) to detect the indefiniteness of the cat's vital status. We show how combining the two observations can provide information about the structure of the quantum state without the need for full quantum state tomography, and propose a measure of the indefiniteness based on this structure. We test this method using a cat state proposed by Gordon and Savage [Phys. Rev. A 59, 4623 (1999)] which is dynamically produced from a coherent state. As a control, we consider a set of states produced using the same dynamical procedure acting on an initial thermal distribution. Numerically simulating our proposed method, we show that as the temperature of this initial state is increased, the produced state undergoes a quantum to classical crossover where the indefiniteness of the cat's vital status is lost, while the macroscopic distinction between dead and alive states of the cat is maintained.