Generalized intelligent states and SU(1,1) and SU(2) squeezing

Journal of Physics A: Mathematical and Theoretical, 2007

We show how su(2) intelligent states can be obtained by coupling su(2) coherent states. The construction is simple and efficient, and easily leads to a discussion of some general properties of su(2) intelligent states.

Journal of Physics A: Mathematical and General, 2001

Considering the equality sign in Robertson-Schrödinger uncertainty relation, the generalized intelligent spin states are derived. Applying different sets of parameters, several classes of generalized intelligent states are introduced. The generalized coherent spin states and the generalized squeezed spin states are introduced as their subgroups.

1997

We discuss a scheme for generation of single-mode photon states associated with the two-photon realization of the SU (1, 1) algebra. This scheme is based on the process of non-degenerate down-conversion with the signal prepared initially in the squeezed vacuum state and with a measurement of the photon number in one of the output modes. We focus on the generation and properties of single-mode SU (1, 1) intelligent states which minimize the uncertainty relations for Hermitian generators of the group. Properties of the intelligent states are studied by using a 'weak' extension of the analytic representation in the unit disc. Then we are able to obtain exact analytical expressions for expectation values describing quantum statistical properties of the SU (1, 1) intelligent states. Attention is mainly devoted to the study of photon statistics and linear and quadratic squeezing.

Journal of Russian Laser Research, 2007

A brief review of the history of ten workshops/conferences on “Squeezed States and Uncertainty Relations” and main achievements in the related fields of quantum physics for the period from 1991 to 2007 are presented.

International Journal of Modern Physics A

This review is intended for readers who want to have a quick understanding on the theoretical underpinnings of coherent states and squeezed states which are conventionally generated from the prototype harmonic oscillator but not always restricting to it. Noting that the treatments of building up such states have a long history, we collected the important ingredients and reproduced them from a fresh perspective but refrained from delving into detailed derivation of each topic. By no means we claim a comprehensive presentation of the subject but have only tried to recapture some of the essential results and pointed out their interconnectivity.

Journal of Physics A: Mathematical and Theoretical, 2012

We show how su(2) intelligent states can be obtained by coupling su(2) coherent states. The construction is simple and efficient, and easily leads to a discussion of some general properties of su(2) intelligent states.

Zeitschrift f�r Physik B Condensed Matter, 1988

The states OIA1A2) are considered, where the operators 0 are associated with a unitary representation of the group Sp(4, R), and the two-mode Glauber coherent states I A~ A2) are joint eigenstates of the destruction operators a I and a 2 for the two independent oscillator modes. We show that they are ordinary coherent states with respect to new operators bl and b2, which are themselves general linear (Bogoliubov) transformations of the original operators al, az and their hermitian conjugates a~, a* 2. We further show how they may be

Physical Review A, 1996

A class of squeezed states for the su(1,1) algebra is found and expressed by the exponential and Laguerre-polynomial operators acting on the vacuum states. As a special case it is proved that the Perelomov's coherent state is a ladder-operator squeezed state and therefore a minimum uncertainty state. The theory is applied to the two-particle Calogero-Sutherland model. We find some new squeezed states and compared them with the classical trajectories. The connection with some su(1,1) quantum optical systems (amplitude-squared realization, Holstein-Primakoff realization, the two mode realization and a four mode realization) is also discussed.

Quantum Information Processing, 2016

In this paper, after a brief review on the coherent states and squeezed states, we introduce two classes of entangled coherent-squeezed states. Next, in order to generate the introduced entangled states, we present a theoretical scheme based on the resonant atom-field interaction. In the proposed model, a Λ-type three-level atom interacts with a two-mode quantized field in the presence of two strong classical fields. Then, we study the amount of entanglement of the generated entangled states using the concurrence and linear entropy. Moreover, we evaluate a few of their nonclassical properties such as photon statistics, second-order correlation function, and quadrature squeezing and establish their nonclassicality features.

Considering the equality sign in Robertson-Schrödinger uncertainty relation, the generalized intelligent spin states are derived. Applying different sets of parameters, several classes of generalized intelligent states are introduced. The generalized coherent spin states and the generalized squeezed spin states are introduced as their subgroups.

Physica A-statistical Mechanics and Its Applications, 2003

We study squeezing in the most general case of superposition of two coherent states by considering 〈ψ|(ΔXθ)2|ψ〉 where is annihilation operator, θ is real, |ψ〉=Z1|α〉+Z2|β〉, |α〉 and |β〉 are coherent states and Z1,Z2,α,β are complex numbers. We find the absolute minimum value 0.11077 for infinite combinations with , with arbitrary values of α+β and θ. For this minimum value of 〈ψ|(ΔX0)2|ψ〉, the expectation value of photon number can vary from the minimum value 0.36084 (for α+β=0) to infinity. We note that the variation of 〈ψ|(ΔXθ)2|ψ〉 near the absolute minimum is less flat when the expectation value of photon number is larger. Thus squeezing can be observed at large intensities also, but settings of the parameters become more demanding.

Annals of Physics, 1995

By resorting to the Fock-Bargmann representation, we incorporate the quantum Weyl-Heisenberg algebra, q-WH, into the theory of entire analytic functions. The q-WH algebra operators are realized in terms of finite difference operators in the z plane. In order to exhibit the relevance of our study, several applications to different cases of physical interest are discussed: squeezed states and the relation between coherent states and theta functions on one side, lattice quantum mechanics and Bloch functions on the other, are shown to find a deeper mathematical understanding in terms of q-WH. The rôle played by the finite difference operators and the relevance of the lattice structure in the completeness of the coherent states system suggest that the quantization of the WH algebra is an essential tool in the physics of discretized (periodic) systems. PACS 02.20.+b; 02.90.+p; 03.65.Fd Annals of Physics (N.Y.), in press.

Springer Proceedings in Physics 205 (2018) 209-242, Proceedings of "Coherent States and their Applications: A Contemporary Panorama", CIRM Marseille, France, 2018

It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Ken-nard 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. Non-classical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superse-lection 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 sem-inal 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

We extend the definition of generalized coherent states to include the case of time-dependent dispersion. We introduce a suitable operator providing displacement and dynamical rescaling from an arbitrary ground state. As a consequence, squeezing is naturally embedded in this framework, and its dynamics is ruled by the evolution equation for the dispersion. Our construction provides a displacement-operator method to obtain the squeezed states of arbitrary systems. PACS numbers: 03.65.-w, 03.65.Ca, 42.50.-p 1 Electronic Mail: demartino@vaxsa.dia.unisa.it 2 Electronic Mail: desiena@vaxsa.dia.unisa.it 3 Electronic Mail: illuminati@mvxpd5.pd.infn.it Introduction. Coherent states are the quantum states that are closest to a classical, localized time-evolution; after the pioneering work by Schrodinger [1], they were discovered and their structure thoroughly clarified in the modern language of quantum field theory by Glauber, Klauder, and Sudarshan [2], [3]. Besides their conceptual rel...

Physics Letters A, 1980

A generalized Heisenberg-type uncertainty relation is obtained for two arbitrary operators both in the case of pure and of mixed states. As a rule equality is found to hold for pure quantum states only. New minimizing states called correlated coherent states, are constructed in explicit form, and their properties are studied.