Barut-Girardello coherent states for and and their macroscopic superpositions

The European Physical Journal Plus, 2021

A new class of states of light is introduced that is complementary to the wellknown squeezed states. The construction is based on the general solution of the three-term recurrence relation that arises from the saturation of the Schrödinger inequality for the quadratures of a single-mode quantized electromagnetic field. The new squeezed states are found to be linear superpositions of the photon-number states whose coefficients are determined by the associated Hermite polynomials. These results do not seem to have been noticed before in the literature. As an example, the new class of squeezed states includes superpositions characterized by odd-photon number states only, so they represent the counterpart of the prototypical squeezed-vacuum state which consists entirely of even-photon number states.

Annals of Physics, 2015

A one-parameter generalized Wigner-Heisenberg algebra(WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule [x,p λ ] = i(1+ 2λR) and also highlights the dynamical symmetries of the pseudo-harmonic oscillator(PHO). The present article is devoted to the study of new cat-states built from λdeformed Schrödinger coherent states, which according to the Barut-Girardello scheme are defined as the eigenstates of the generalized annihilation operator. Particular attention is devoted to the limiting case where the Schrödinger cat states are obtained. Nonclassical features and quantum statistical properties of these states are studied by evaluation of Mandel's parameter and quadrature squeezing with respect to the λ−deformed canonical pairs (x,p λ). It is shown that these states minimize the uncertainty relations of each pair of the su(1, 1) components.

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.

Pramana, 1997

A definition of coherent states is proposed as the minimum uncertainty states with equal variance in two hermitian non-commuting generators of the Lie algebra of the hamiltonian. That approach classifies the coherent states into distinct classes. The coherent states of a harmonic oscillator, according to the proposed approach, are shown to fall in two classes. One is the familiar class of Glauber states whereas the other is a new class. The coherent states of spin constitute only one class. The squeezed states are similarly defined on the physical basis as the states that give better precision than the coherent states in a process of measurement of a force coupled to the given system. The condition of squeezing based on that criterion is derived for a system of spins.

2005

States which minimize the Schr\"odinger--Robertson uncertainty relation are constructed as eigenstates of an operator which is a element of the $h(1) \oplus \su(2)$ algebra. The relations with supercoherent and supersqueezed states of the supersymmetric harmonic oscillator are given. Moreover, we are able to compute gneneral Hamiltonians which behave like the harmonic oscillator Hamiltonian or are related to the Jaynes--Cummings Hamiltonian.

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

Journal of Physics A: Mathematical and Theoretical

Current definitions of both squeezing operator and squeezed vacuum state are critically examined on the grounds of consistency with the underlying su(1,1) algebraic structure. Accordingly, the generalized coherent states for su(1,1) in its Schwinger two-photon realization are proposed as squeezed states. The physical implication of this assumption is that two additional degrees of freedom become available for the control of quantum optical systems. The resulting physical predictions are evaluated in terms of quadrature squeezing and photon statistics, while the application to a Mach-Zehnder interferometer is discussed to show the emergence of nonclassical regions, characterized by negative values of Mandel's parameter, which cannot be anticipated by the current formulation, and then outline future possible use in quantum technologies.

Canadian Journal of Physics, 2004

By introducing a generalization of the (p, q)-deformed boson oscillator algebra, we establish a two-parameter deformed oscillator algebra in an infinite-dimensional subspace of the Hilbert space of a harmonic oscillator without first finite Fock states. We construct the associated coherent states, which can be interpreted as photon-added deformed states. In addition to the mathematical characteristics, the quantum statistical properties of these states are discussed in detail analytically and numerically in the context of conventional as well as deformed quantum optics. Particularly, we find that for conventional (nondeformed) photons the states may be quadrature squeezed in both cases Q = pq 1 and their photon number statistics exhibits a transition from sub-Poissonian to super-Poissonian for Q 1 they are always sub-Poissonian. On the other hand, for deformed photons, the states are sub-Poissonian for Q > 1 and no quadrature squeezing occurs while for Q

Journal of Physics A: Mathematical and Theoretical, 2012

A set of generalized squeezed-coherent states for the finite u(2) oscillator is obtained. These states are given as linear combinations of the mode eigenstates with amplitudes determined by matrix elements of exponentials in the su(2) generators. These matrix elements are given in the (N + 1)-dimensional basis of the finite oscillator eigenstates and are seen to involve 3 × 3 matrix multi-orthogonal polynomials Q n (k) in a discrete variable k which have the Krawtchouk and vector-orthogonal polynomials as their building blocks. The algebraic setting allows for the characterization of these polynomials and the computation of mean values in the squeezedcoherent states. In the limit where N goes to infinity and the discrete oscillator approaches the standard harmonic oscillator, the polynomials tend to 2 × 2 matrix orthogonal polynomials and the squeezed-coherent states tend to those of the standard oscillator.

Applied Physics B, 2020

In this paper, at first we consider special type of entangled states named "entangled squeezed coherent states" by using squeezed coherent states. Next, we study the entanglement characteristics of these entangled states by evaluating concur-rence. In the continuation, we investigate some of their nonclassical properties such as quantum statistics which contained sub-Poissonian photon statistics and the oscillatory photon number distribution, second-order correlation function and quad-rature squeezing for different squeezing values of two modes. In addition, we compare the results of the "entangled squeezed coherent states" with those of the common entangled states such as "entangled coherent states", "entangled squeezed vacuum states" and "entangled squeezed one-photon states". Finally, using the proposed theoretical scheme in the previous works, we will generate the entangled squeezed coherent states with different initial conditions. In this scheme, a Λ-type three-level atom interacts with the two-mode quantized field in the presence of two strong classical fields.

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

Quantum Information Processing, 2019

In this paper, we introduce quasi-Bell states as a result of two-mode superposition of two "Near" coherent states, � , ⟩ , shifted in phase by and 2 , where the latter introduced by Othman et al. as a new class of quantum states attached to the simple harmonic oscillator which generated via a Mach-Zehnder interferometer. To gain insight into useful attributes to quantum information theory, we present a general analysis of non-classical properties such as photon counting probability, photon statistics, squeezing effect and quantum polarization. We also derive the concurrence measure to quantify entanglement of these states and look for conditions that provide information on which these become maximally entangled. Comparing with some cases already discussed in the literature, we find that the phase angle plays an important role in nonclassical effects. We also get a connection between entanglement and the polarization degree of the introduced states.

Journal of the Optical Society of America B, 1987

The multiphoton squeezed states defined in this paper are generalizations of the conventional coherent (Glauber) and squeezed (Yuen) states previously discussed by many authors. We define multiphoton generalizations of the latter by a unified class of states that includes the Holstein-Primakoff realizations of SU(2) and SU(1, 1) as well as the standard harmonic oscillator coherent states (Weyl-Heisenberg group) and squeezed states in a general framework that allows also non-Hermitian realizations. We determine the squeezing properties of these states in a unified formalism and study numerically their dependence on the parameter classifying the states.

Optics Communications, 2007

Nonclassical features of the superposition of two coherent states which are p/2 out of phase are discussed, such as sub-Poissonian photon statistics and quadrature squeezing, as well as negativity of the Wigner function. Special nonclassicality is found in the special state where the relative phase of superposition has relationship with the average photon number. The analysis of the amount of entanglement is also presented for the related two-mode entangled coherent states.

1996

It is certified that the work contained in this thesis entitled Coherent and Squeezed angular momentum states in Schwinger representation with applications to quantum optics by Abir Bandyopadhyay has been carried out under my supervision and that this work has not been submitted elsewhere for a degree.