Detecting Macroscopic Indefiniteness of Cat States in Bosonic Interferometers

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.