Coherent states of the asymmetric harmonic oscillator

TL;DR

This paper constructs and analyzes formal coherent states for an asymmetric harmonic oscillator, identifying specific parameter conditions under which these states maintain coherence over time.

Contribution

It introduces a method to construct coherent states for an asymmetric harmonic oscillator and identifies conditions for their temporal stability.

Findings

Coherent states generally become incoherent over time.

Special parameter ratios allow for stable, time-preserving coherent states.

The paper provides a detailed analysis of these states' properties.

Abstract

We constructed formal coherent states for an asymmetric harmonic oscillator, where the asymmetry parameter is the square root of the ratio of spring constants. Although these states are constructed based on both Glauber's and Perelomov's approaches, in general they do not satisfy all the properties required for coherent states. Over time, the coherent states introduced in this way generally become incoherent. However, there are some specific parameters for the square root ratios of the spring constants $\frac{4k+1}{4l+1}$ or $\frac{4k+3}{4l+3}$. For these parameters it is possible to construct coherent states on the subspace of the Hilbert space of eigenstates. These coherent states keep their coherence during the time evolution. This case is also analyzed.