Types Of Coherent States Research Articles

Coherent state excitations and string-added coherent states in gauge-gravity correspondence

We analyze detailed properties of BPS coherent states and their connection to gravity. We interpret the group integral coherent state as a path integral over auxiliary variables coupled to the elementary letters of the theory. The eigenvalues of coherent state amplitudes can be viewed as collective coordinates of giant gravitons. Inspired by the above coherent states and by the integrability, we construct a new type of coherent states in the SL(2) sectors and their cousin PSU(1,1|2) sectors, analogous to the aforementioned coherent states. The large spin and small spin limits can be obtained by varying coherent state amplitudes. We add string words onto the BPS coherent states, and this gives rise to string-added coherent states. The insertions of string multi-words can be viewed as operator-insertions in this path integral. We describe BPS states and near BPS states building upon these coherent states in gauge-gravity correspondence. For example, string-added coherent states and their near BPS spectra are analyzed. This approach is particularly convenient for heavy excited states.

Towards generation of indistinguishable coherent states

We have addressed the characteristic distinguishability of coherent states in the temporal domain from a directly modulated quantum well-based gain-switched laser diode. We identify adjustable parameters to generate indistinguishable coherent states from an electrically pumped semiconductor laser using small-signal and large-signal models. The experiment confirms the generation of indistinguishable signal and decoy coherent states as predicted by the numerical simulation. In addition, the potential for indistinguishability has been explored in different types of coherent states.

GENERALIZED KLAUDER-PERELOMOV COHERENT STATES IN THE FRAME OF DIAGONAL OPERATORS ORDERING TECHNIQUE

In the paper we constructed and examined the properties of Klauder–Perelomov type coherent states (KP-CSs) for an arbitrary quantum system , using the technique of normal ordering of diagonal operators (DOOT). This is a generalization of the technique of integration with an ordered product (IWOP) introduced by Hong-yi Fan and applied very successfully in the case of canonical operators in quantum optics . The two examples (applications) in the last part (the one-dimensional harmonic oscillator , as well as a family of Pöschl–Teller type potentials) lead to both known and new results. This demonstrates the validity and effectiveness of the DOOT technique.

Superposition type coherent states in all dimensional loop quantum gravity

We propose a new kind of coherent state for the general $SO(D+1)$ formulation of loop quantum gravity in the $(1+D)$-dimensional space-time. Instead of Thiemann's coherent state for $SO(D+1)$ gauge theory, our coherent spin-network state is given by constructing proper superposition over quantum numbers of the spin-networks with vertices labelled by the coherent intertwiners. Such superposition type coherent states are labelled by the so-called generalized twisted geometric variables which capture the geometric meaning of discretized general relativity. We study the basic properties of this kind of coherent states, i.e., the completeness and peakedness property. Moreover, we show that the superposition type coherent states are consistent with Thiemann's coherent state for $SO(D+1)$ gauge theory in large $\eta$ limit.

Coherent state superpositions, entanglement, and gauge/gravity correspondence

We focus on two types of coherent states, the coherent states of multi-graviton states and the coherent states of giant graviton states, in the context of gauge/gravity correspondence. We conveniently use a phase shift operator and its actions on the superpositions of these coherent states. We find N-state Schrödinger cat states, which approach the one-row Young tableau states, with fidelity between them asymptotically reaching 1 at large N. The quantum Fisher information of these states is proportional to the variance of the excitation energy of the underlying states and characterizes the localizability of the states in the angular direction in the phase space. We analyze the correlation and entanglement between gravitational degrees of freedom using different regions of the phase space plane in bubbling AdS. The correlation between two entangled rings in the phase space plane is related to the area of the annulus between the two rings. We also analyze two types of noisy coherent states, which can be viewed as interpolated states that interpolate between a pure coherent state in the noiseless limit and a maximally mixed state in the large noise limit.

Generalised effective cosmology from group field theory

We extend various recent results regarding the derivation of effective cosmological Friedmann equations from the dynamics of group field theory (GFT). Restricting ourselves to a single GFT field mode (or fixed values of Peter–Weyl representation labels), we first consider dynamics given by a quadratic Hamiltonian, which takes the form of a squeezing operator, and then add a quartic interaction that can be seen as a toy model for interactions in full GFT. Our derivation of effective Friedmann equations does not require a mean-field approximation; we mostly follow a general approach in which these equations in fact hold for any state. The resulting cosmological equations exhibit corrections to classical Friedmann dynamics similar to those of loop quantum cosmology, leading to generic singularity resolution, but also involve further state-dependent terms. We then specify these equations to various types of coherent states, such as Fock coherent states or Perelomov–Gilmore states based on the su(1, 1) structure of harmonic quantum cosmology. We compute relative uncertainties of volume and energy in these states, clarifying whether they can be interpreted as semiclassical. In the interacting case, both analytical and numerical approximations are used to obtain modified cosmological dynamics. Our results clarify how effective cosmological equations derived from GFT can provide reliable approximations to the full dynamics.

Coherent States of the Generalized Heisenberg Algebra with $$\varvec{k-1}$$ Isolated States

In this paper we construct the generalized Heisenberg algebra with \( k-1 \) isolated states. We use this algebra to construct three types of coherent states. Finally we discuss the non-classical properties related to the coherent states.

Coherent Polariton Modes and Lasing in ZnO Nano‐ and Microwires

This article presents a topical literature survey on types of coherent states in bare and functionalized ZnO nano‐ and microwire microcavities, together with own new approaches of the authors. By optical excitation, coherent emission from electron–hole plasma and from exciton‐polariton Bose–Einstein condensates, both up to room temperature, have been observed by various research groups. The impact of the interplay between the excitation properties and geometry of the structures as well as of the charge carrier dynamics on the emission behavior of the structures has been discussed. For different cavity types spectrally tunable mono‐/dual‐mode laser operation as well as propagation of coherent polariton states have been demonstrated. Further functionalization of the bare structures in hybrid systems allows optimization and engineering of the cavity as well as the polariton mode structure and the design of sophisticated light–matter states.

Introduction to the Coherent States Approach for Solving Non-linear Physical Problems

We summarize some crucial results from mathematical models that help us understand the relevance of gener-alized coherent states (GCS), a fundamental method used for the description of non-linear problems in physics. We mainly concentrate our review in the following models: ferromagnetism, nonlinear Schr¨odinger equation with external potential, nonlinear quantum oscillators, Bose - Einstein condensation (BEC) and the DNA quasi-spin model. Such models and some applications of the wide variety these involve are outlined. As variational trial states, the coherent states (CS) allow the estimation of the ground state energies and properties, yielding results which become exact in a number of nonlinear differential equations for dynamical variable of each model. Mainly we concentrate our review on two types of coherent states, The first one are based on the Heisenberg - Weyl group where it is applied the bosonization effect. The second one is based on the SU(2)/U(1) Lie group. For this case when the Hamiltonian and all physical operators are constructed by the elements of a Lie algebra, the generalized coherent states approach is directly applied without bozonization.

Construction of the Barut-Girardello type of coherent states for Pöschl-Teller potential

The Pöschl-Teller (PT) potential occupies a privileged place among the anharmonic oscillator potentials due to its applications from quantum mechanics to diatomic molecules. For this potential, a polynomial su(1, 1) algebra has been constructed previously. So far, the coherent states (CSs) associated with this algebra have never appeared. In this paper, we construct the coherent states of the Barut-Girardello coherent states (BG-CSs) type for the PT potentials, which have received less attention in the scientific literature. We obtain these CSs and demonstrate that they fulfil all conditions required by the coherent state. The Mandel parameter for the pure BG-CSs and Husimi’s and P-quasi distributions (for the mixed-thermal states) is also presented. Finally, the exponential form of the BG-CSs for the PT potential has been presented and enabled us to build Perelomov type CSs for the PT potential. We point out that the BG-CSs and the Perelomov type coherent states (PCSs) are related via Laplace transform.

Pöschl-Teller Hamiltonian: Gazeau-Klauder type coherent states, related statistics, and geometry

This work mainly addresses a construction of Gazeau-Klauder type coherent states (CSs) for a Pöschl-Teller model. Relevant characteristics are investigated. Induced geometry and statistics are studied. Then, the Berezin-Klauder-Toeplitz quantization of the classical phase space observables is presented.

Noncommutative quantum mechanics in a time-dependent background

We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time-dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional canonical variables. We employ the Lewis-Riesenfeld method of invariants to construct explicit analytical solutions for the corresponding time-dependent Schroedinger equation. The eigenfunctions are expressed in terms of the solutions of variants of the nonlinear Ermakov-Pinney equation and discussed in detail for various types of background fields. We utilize the solutions to verify a generalized version of Heisenberg's uncertainty relations for which the lower bound becomes a time-dependent function of the background fields. We study the variance for various states including standard Glauber coherent states with their squeezed versions and Gaussian Klauder coherent states resembling a quasi-classical behaviour. No type of coherent states appears to be optimal in general with regard to achieving minimal uncertainties, as this feature turns out to be background field dependent.

Restriction on types of coherent states due to gauge symmetry

From the viewpoint of the SU(2) coherent states (CS) and their path integrals (PI) labeled by a full set of Euler angles (ϕ, θ, ψ) which we developed in the previous paper, we study the relations between gauge symmetries of Lagrangians and allowed quantum states; We investigate permissible types of fiducial vectors (FV) in the full quantum dynamics in terms of SU(2) CS for typical Lagrangians. We propose a general framework for a Lagrangian having a certain gauge symmetry with respect to one of the Euler angles ψ. We find that for the case FV are so restricted that they belong to the eigenstates of Ŝ3or to the orbits of them under the action of the SU(2); And the strength of a fictitious monopole, which appears in the Lagrangian, is a multiple of ½. In this case Dirac strings are permitted. Our formulations and results deepen those of the preceding work by Stone that has piloted us; We illustrate the relation between the two methods. The reasoning here does not work for a Lagrangian without the gauge symmetry. This suggests a new possibility about monopole charge quantization. Besides analogies to field theory and entanglements in quantum information (QI) are briefly mentioned.

Squeezed states and Hermite polynomials in a complex variable

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pure Appl. Math. 14, 187 (1961)].

An observation of quadratic algebra, dual family of nonlinear coherent states and their non-classical properties, in the generalized isotonic oscillator

In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra, we obtain Heisenberg algebra. From the algebra, we define two non-unitary and one unitary displacement type operators. While the action of one of the non-unitary type operators reproduces the original nonlinear coherent states, the other one fails to produce a new set of nonlinear coherent states (dual pair). We show that these dual states are not normalizable. For the nonlinear coherent states, we evaluate the parameter A3 and examine the non-classical nature of the states through quadratic and amplitude-squared squeezing effect. Further, we derive analytical formula for the P-function, Q-function, and the Wigner function for the nonlinear coherent states. All of them confirm the non-classicality of the nonlinear coherent states. In addition to the above, we obtain the harmonic oscillator type coherent states from the unitary displacement operator.

Spin foams with timelike surfaces

Spin foams of 4D gravity were recently extended from complexes with purely spacelike surfaces to complexes that also contain timelike surfaces. In this paper, we express the associated partition function in terms of vertex amplitudes and integrals over coherent states. The coherent states are characterized by unit 3-vectors which represent normals to surfaces and lie either in the 2-sphere or in the 2D hyperboloids. In the case of timelike surfaces, a new type of coherent state is used and the associated completeness relation is derived. It is also shown that the quantum simplicity constraints can be deduced by three different methods: by weak imposition of the constraints, by restriction of coherent state bases and by the master constraint.

GENERALIZED DEFORMED HARMONIC OSCILLATORS IN THE FRAMEWORK OF UNIFIED (q; α, β, γ; ν)-DEFORMATION

The aim of this paper is the study of the generalized deformed quantum oscillators in the framework (q; α, β, γ; ν)-deformed of oscillator algebra. By selecting the special values of deformation parameters, we have separated a generalized deformed oscillator connected with generalized discrete Hermite II polynomials. By these means we have constructed Barut–Girardello type coherent states of this oscillator. We have found the conditions on the (q; α, β, γ; ν)-deformation parameters at which the free (q; α, β, γ; ν)-deformed oscillator approximate the usual anharmonic oscillator in the homogeneous Kerr medium.

Gazeau-Klauder type coherent states for hypergeometric type operators

Abstract Hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitely described in the general case. Some additional shape invariant operators depending on several parameters are defined in a natural way by starting from this general factorization. The mathematical properties of the eigenfunctions and eigenvalues of the operators thus obtained depend on the values of the parameters involved. We study the parameter dependence of orthogonality, square integrability and monotony of the eigenvalue sequence. The results obtained allow us to define certain systems of Gazeau-Klauder type coherent states and to describe some of their properties. Our systematic study recovers a number of well-known results in a natural, unified way and also leads to new findings.

Schwinger representation approach to the Lipkin model

The Schwinger representation and the Marumori–Yamamura–Tokunaga boson expansion are used to describe the Lipkin model in terms of generalized coherent states. The groundstate, first excited state and RPA energies are obtained within several variant types of coherent states. It has been found that generalized coherent states defined in consonance with the parity symmetry of the model describe particularly well the transition from weak to strong coupling, providing a remarkable improvement of the mean-field description of the transition zone.

Higher-order uncertainty relations

Using the non-negativity of Gram determinants of arbitrary order, we derive higher-order uncertainty relations for the symmetric uncertainty matrices of corresponding order n > 2 to n Hermitean operators (n = 2 is the usual case). The special cases of third-order and fourth-order uncertainty relations are considered in detail. The obtained third-order uncertainty relations are applied to the Lie groups SU(1,1) with three Hermitean basis operators (K 1,K 2,K 0) and SU(2) with three Hermitean basis operators (J 1,J 2,J 3) where, in particular, the group-coherent states of Perelomov type and of Barut–Girardello type for SU(1,1) and the spin or atomic coherent states for SU(2) are investigated. The uncertainty relations for the determinant of the third-order uncertainty matrix are satisfied with the equality sign for coherent states and this determinant becomes vanishing for the Perelomov type of coherent states for SU(1,1) and SU(2). As an example of the application of fourth-order uncertainty relations, we consider the canonical operators (Q 1,P 1,Q 2,P 2) of two boson modes and the corresponding uncertainty matrix formed by the operators of the corresponding mean deviations, taking into account the correlations between the two modes. In two mathematical appendices, we prove the non-negativity of the determinant of correlation matrices of arbitrary order and clarify the principal structure of higher-order uncertainty relations.