On oscillatorlike developments and further improvements in squeezing

TL;DR

The paper develops oscillatorlike deformations by introducing a parameterized creation operator $a_{\lambda}^{\dagger}$ that preserves the real spectrum $E_n = n + \frac{1}{2}$ while producing $\lambda$-dependent eigenfunctions corresponding to squeezed states. It then constructs a generalized pair of operators $b$ and $b^{\dagger}$ from $a$ and $a^{\dagger}$, yielding Schrödinger-like Hamiltonians with closed-form eigenvalues and eigenfunctions that can be made selfadjoint or non-Hermitian, enabling systematic control of coherence and squeezing. Through analysis of the ground state and a suite of $\lambda$-deformations, the work demonstrates multiple scenarios where squeezing in the position coordinate $x$ occurs without altering the energy spectrum, supported by explicit examples and moment calculations. Finally, it identifies a selfadjoint $H_{\lambda}$ family with orthogonal eigenfunctions that interpolate to the standard harmonic oscillator at $\lambda=1$, discusses experimental relevance and connections to subnormal operator theory, and suggests extensions to fermionic sectors and supersymmetric frameworks.

Abstract

A recent proposal of new sets of squeezed states is seen as a particular case of a general context admitting realistic physical Hamiltonians. Such improvements reveal themselves helpful in the study of associated squeezing effects. Coherence is also considered.