The Schrödinger-Cheshire Cat: When Properties Grin Without Their Particles

A. K. Pan

James D. Stein

Rashid Ahmad, Nawaz, Sumaira

Schrödinger's Cat was proposed by Erwin Schrödinger, the infamous thought experiment in which a cat in a box was both alive and dead simultaneously illustrating a quantum phenomenon known as superposition. In 2013, Yakir Aharonov and his co-authors conceived of an experiment suggesting that a particle can be separated from its property. They called the effect a "Quantum Cheshire Cat" that has been experimentally verified in the succeeding year. The name Quantum Cheshire Cat is inspired from a fanciful character of the Cheshire Cat in "\textit{Alice's Adventures in Wonderland"} a novel written by Lewis Carroll where the grin of cat is found without a cat. An important question arises here. Once the grin of the Cheshire Cat is separated, is there any correlation still left between the grin and the cat? To answer the question we propose a thought experiment in which Quantum Cheshire Cat is also a Schrödinger's Cat existing in superposition of happy(smiling) and sad(frowning) states. We name this cat as a "Quantum Mona Lisa Cat" for the reason that historically it is presumed that Mona Lisa's portrait contains both characteristics of happy(smiling) and sad(frowning) and either is observed depending upon the mood of the observer. We show that property separated from particle behave as "Quantum Mona Lisa Cat".

Peter John Bussey

A. Matzkin, A K Pan

We propose in this work a definite theoretical implementation of the three-box paradox - a scheme in which a single quantum particle appears to be present with certainty in two separate boxes - with spin-1 atoms. We further show how our setup can give rise to a "Cheshire cat grin" type of situation, in which an atom can apparently be found with certainty in one of the boxes while one of its properties (the angular momentum projection along a specifically chosen axis) appears to be in a different box. The significance of our findings are discussed relative to the status of the properties of a system obtained from weak measurements.