Nonlinear Coherent States: Main Tools

O. Pavón-Torres, José Manuel Dávila, Máximo Augusto Agüero Granados

We summarize some crucial results from mathematical models that help us understand the relevance of gener-alized coherent states (GCS), a fundamental method used for the description of non-linear problems in physics. We mainly concentrate our review in the following models: ferromagnetism, nonlinear Schr¨odinger equation with external potential, nonlinear quantum oscillators, Bose - Einstein condensation (BEC) and the DNA quasi-spin model. Such models and some applications of the wide variety these involve are outlined. As variational trial states, the coherent states (CS) allow the estimation of the ground state energies and properties, yielding results which become exact in a number of nonlinear differential equations for dynamical variable of each model. Mainly we concentrate our review on two types of coherent states, The first one are based on the Heisenberg - Weyl group where it is applied the bosonization effect. The second one is based on the SU(2)/U(1) Lie group. For this case when the Hamiltonian and all physical operators are constructed by the elements of a Lie algebra, the generalized coherent states approach is directly applied without bozonization.

J. Récamier, M. Gorayeb, Wolf Luis Mochán +1 more

Nicholas Rivera

Nonlinear dynamics provide an indispensable resource for creating quantum states of light, as well as other bosonic systems. Seminal work using second- and third-order nonlinear optical crystals, cavity quantum electrodynamics, and superconducting circuits, have enabled generating squeezed states, as well as various non-Gaussian quantum states (e.g., single photons, cat states) at both infrared and microwave frequencies. Nevertheless, it remains challenging to generate quantum states of light in broad portions of the electromagnetic spectrum: for example, at terahertz frequencies and at ultraviolet and X-ray frequencies. In this Perspective, I discuss a variety of emerging material platforms, as well as emerging theoretical and experimental tools, which enable overcoming these challenges. The main argument of this Perspective is that advances in driving nonlinear dynamics of material excitations, will enable generating quantum states of these material excitations as well as quantum states of light at new frequency ranges. I will further argue that in order to realize much of the promise of this nascent field, there is a need for innovation in the laser systems used to drive these nonlinear dynamics: specifically, innovations in realizing high-power laser sources that have very low noise, having quantum statistics similar to coherent states of light which describe lower intensity laser systems. I will highlight some experimental and theoretical work, in understanding quantum noise dynamics in complex laser systems, that can address these challenges.

Jean-Pierre Antoine, Bagarello, Fabio, Jean‐Pierre Gazeau

Ali Mahdifar, R. Roknizadeh, M. H. Naderi +4 more

Mostafa Hashem, M M Elkhateeb, A.‐B. A. Mohamed +2 more

Abstract This paper presents a comprehensive investigation into the complex dynamics of optical tomography and quantum coherence within a nonlinear interaction system. The system under study is composed of an Ξ-type qutrit and a deformed cavity-field, analyzed for two distinct initial states: coherent states and even coherent states. Our analysis thoroughly considers the influence of intrinsic decoherence, a critical factor in understanding quantum system evolution. This study explores the remarkable sensitivity of optical tomography distributions (OTDs) to key parameters, including the initial state, evolution time, and the effects of a Kerr-like nonlinearity. We demonstrate that while coherent states initially appear classical, they display early-stage quantum interference due to their intrinsic parity symmetry, evolving into intricate patterns over time. This evolution is particularly susceptible to intrinsic decoherence, which significantly dampens these quantum features. Our findings show that the OTD is a powerful tool for tracking coherence loss and for accurately capturing the combined effects of nonlinearity and state symmetry on a system’s quantum state.