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.

Review article, contribution to the proceedings of "Coherent States and their Applications: A Contemporary Panorama", CIRM Marseille, France

References in corpus (22)

• Making Sense of Non-Hermitian Hamiltonians
• Coherent Perfect Absorbers: Time-reversed Lasers
• Universality of Quantum Gravity Corrections
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Physics on Smallest Scales - An Introduction to Minimal Length Phenomenology
• Position-dependent noncommutativity in quantum mechanics
• Fermionic coherent states for pseudo-Hermitian two-level systems
• q-deformed noncommutative cat states and their nonclassical properties
• Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
• Time-dependent q-deformed coherent states for generalized uncertainty relations
• Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations
• Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations
• Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model
• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• Noncommutative quantum mechanics in a time-dependent background
• Probing noncommutative theories with quantum optical experiments
• Isospectral Hamiltonians from Moyal products
• Modification of Schrödinger-Newton equation due to braneworld models with minimal length
• Coherent States in Gravitational Quantum Mechanics
• Intertwining operators for non self-adjoint Hamiltonians and bicoherent states
• $q$-deformed quadrature operator and optical tomogram

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• Bi-coherent states as generalized eigenstates of the position and the momentum operators
• Uncertainty relations for a non-canonical phase-space noncommutative algebra
• Enhanced quantum phase estimation with $q$-deformed nonideal nonclassical light
• Refractive index profiles for a $\mathcal{P}\mathcal{T}$-symmetric optical structure