On the quantum information entropies and squeezing associated with the eigenstates of isotonic oscillator

TL;DR

This paper investigates the quantum information entropies and squeezing phenomena in the eigenstates of the isotonic oscillator, confirming entropy bounds and analyzing squeezing effects in position and momentum spaces.

Contribution

It provides a detailed analysis of entropy and amplitude squeezing in isotonic oscillator eigenstates, including numerical visualizations and verification of fundamental inequalities.

Findings

Lower bound of entropy sum is satisfied by all states.

Existence of position entropy squeezing in eigenstates.

Amplitude squeezing observed in position quadrature.

Abstract

In this paper we calculate the position and momentum space information entropies for the quantum states associated with a particular physical system, i.e. the isotonic oscillator Hamiltonian. We present our results for its ground states, as well as for its excited states. We observe that the lower bound of the sum of the position and momentum entropies expressed by the Beckner, Bialynicki-Birula and Mycielski (BBM) inequality is satisfied. Moreover, there exist eigenstates that exhibit squeezing in the position information entropy. In fact, entropy squeezing, which occurs in position, will be compensated for by an increase in momentum entropy, such that the BBM inequality is guaranteed. To complete our study we investigate the amplitude squeezing in $x$ and $p$-quadratures corresponding to the eigenstates of the isotonic oscillator and show that amplitude squeezing, again in $x$, will be revealed as expected, while the Heisenberg uncertainty relationship is also satisfied. Finally, our numerical calculations of the entropy densities will be presented graphically.