A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length

Abstract

It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as "coherent states" today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Nonclassical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superselection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the seminal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here originate from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics community. CONTENTS* dey@iisermohali.ac.in; sanjibdey4@gmail.com † a.fring@city.ac.uk ‡ veronique.hussin@umontreal.ca A. Squeezed states 11 B. Schrödinger cat states 12 C. Photon-added coherent states 13 VI. Applications 13 VII. Concluding remarks 13 References 14 arXiv:1801.01139v1 [quant-ph] 3 Jan 2018 III. NON-HERMTIAN SYSTEMS IN MINIMAL LENGTH SCENARIOHaving introduced the general features of coherent states and nonclassicality, in this section, let us discuss a system on which our article is based on, i.e. some non-Hermitian models based on quantum mechanics in NC space and, then, we discuss how these models can be applied to physical systems like coherent states. A. Noncommutative quantum mechanicsThe original proposal of space-time noncommutativity is very old and was introduced in the pioneering days of quan-

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