Showing papers on "Coherent states in mathematical physics published in 2023"

Thermal States on Mittag-Leffler Fock Space of the Slitted Plane

Abstract: Number states and thermal states form an important class of physical states in quantum theory. A mathematical framework for studying these states is that of a Fock space over an appropriate Hilbert space. Several generalizations of the usual Bosonic Fock space have appeared recently due to their importance in many areas of mathematics and other scientific domains. One of the most prominent generalization of Fock spaces is the Mittag-Leffler (ML) Fock space of the slitted plane. Natural generalizations of the basic operators of quantum theory can be obtained on ML Fock spaces. Following the construction of the creation and annihilation operators in the Mittag-Leffler Fock space of the slitted plane by Rosenfeld, Russo, and Dixon, (J. Math. Anal. Appl. 463, 2, 2018). We construct and study the number states and thermal states on the ML Fock space of the slitted plane. Thermal states on usual Fock space form an important subclass of the so called quantum gaussian states, an analogous theory of more general quantum states (like squeezed states and Bell states) on ML Fock spaces is an area open for further exploration.

Stretched Coherent States

Abstract: The fundamental properties of recently introduced stretched coherent states are investigated. It has been shown that stretched coherent states retain the fundamental properties of standard coherent states and generalize the resolution of unity, or completeness condition, and the probability distribution that $n$ photons are in a stretched coherent state. The stretched displacement and stretched squeezing operators are introduced and the multiplication law for stretched displacement operator is established. The results of the action of the stretched displacement and stretched squeezing operators on the vacuum and the Fock states are presented. Stretched squeezed stretched coherent states and stretched squeezed stretched displaced number states are introduced and their properties are studied. The inner product of two quantum mechanical vectors was defined in terms of their stretched coherent state representations, and functional Hilbert space was introduced.

Estimating Fock-state linear optics evolution using coherent states

Abstract: This paper presents two methods for simulating the interference of bosonic Fock states through linear interferometers using coherent states. The first method repeats the interferometer, injects coherent states in particular modes, and uses symmetric combinations of the outputs to reconstruct the state amplitudes of the Fock-state interference. The second method constructs a new interferometer that can be probed with coherent states on individual inputs to extract the required state amplitudes. The two approaches here show explicitly where the classical computational difficultly arises. In the first approach, the computational hardness is in the measurement post-processing, and in the second approach, it is within the construction of the required state evolution.

Generalized hypergeometric coherent states for special functions: mathematical and physical properties

Abstract: In continuation of our previous works J. Phys. A: Math. Gen. 35, 9355-9365 (2002), J. Phys. A: Math. Gen. 38, 7851 (2005) and Eur. Phys. J. D 72, 172 (2018), we investigate a class of generalized coherent states for associated Jacobi polynomials and hypergeometric functions, satisfying the resolution of the identity with respect to a weight function expressed in terms of Meijer's G-function. We extend the state Hilbert space of the constructed states and discuss the property of the reproducing kernel and its analytical expansion. Further, we provide the expectation values of observables relevant to this quantum model. We also perform the quantization of the complex plane, compute and analyze the probability density and the temporal stability in these states. Using the completeness relation provided by the coherent states, we achieve the thermodynamic analysis in the diagonal $P$-representation of the density operator.

Considerations of the duality in generalized coherent states formalism

Abstract: In the paper, a pair of dual operators is introduced with which a dual pair of generalized displacement operators is constructed. With these entities it is shown that the Barut - Girardello and Klauder - Perelomov generalized coherent states are dual states. The characteristics of these coherent states are constructed, separately and comparatively.