The Superposition of Two Identical States: The Empty State

TL;DR

This paper introduces the concept of empty states, a new class of superposition states formed by self-superposition, and explores their mathematical, statistical, and nonclassical properties across various quantum states.

Contribution

It defines and analyzes a novel class of states called empty states, providing multiple representations and applying them to Fock and coherent states.

Findings

Derived three representations of empty states

Identified properties of the empty state of coherent states

Explored the nonclassical features of the new states

Abstract

In this paper we define and study a new class of states (the empty states). These states are the superposition of two identical states (self-superposition state). We defined three different representations of theses states, namely, the source, the operator, and the self-superposition representations. Then, we apply the empty state to an elementary example state and find its three different representations. We apply the empty state to Fock states and find an undetermined state. Then, we apply the empty state to the coherent state to produce the empty state of the coherent state (the EC state), and determine some of its mathematical, statistical and nonclassical properties.