Optimized Binomial Quantum States of Complex Oscillators with Real Spectrum

TL;DR

This paper introduces optimized binomial quantum states for complex oscillators with real spectra, demonstrating their behavior as photon-added coherent states under certain conditions, expanding the understanding of nonclassical states in quantum systems.

Contribution

It presents a novel class of bi-orthonormal superpositions of energy eigenstates for complex oscillators, linking them to known quantum states like photon-added coherent states.

Findings

States behave as photon-added coherent states when the imaginary potential is canceled.

States are bi-orthonormal superpositions with binomial coefficients.

Applicable to complex oscillators with real spectra.

Abstract

Classical and nonclassical states of quantum complex oscillators with real spectrum are presented. Such states are bi-orthonormal superpositions of $n+1$ energy eigenvectors of the system with binomial-like coefficients. For large values of $n$ these optimized binomial states behave as photon added coherent states when the imaginary part of the potential is cancelled.