Generalized Susskind-Glogower coherent states
- URL: http://arxiv.org/abs/2011.10303v1
- Date: Fri, 20 Nov 2020 09:55:49 GMT
- Title: Generalized Susskind-Glogower coherent states
- Authors: Jean-Pierre Gazeau, V\'eronique Hussin, James Moran, and Kevin Zelaya
- Abstract summary: We introduce two new families of Susskind-Glogower-I and Susskind-Glogower-II coherent states.
For completeness, the optical properties related to the new families of coherent states are explored and compared with respect to some well-known optical states.
- Score: 0.3149883354098941
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Susskind-Glogower coherent states, whose Fock expansion coefficients include
Bessel functions, have recently attracted considerable attention for their
optical properties. Nevertheless, identity resolution is still an open
question, which is an essential mathematical property that defines an
overcomplete basis in the Fock space and allows a coherent state quantization
map. In this regard, the modified Susskind-Glogower coherent states have been
introduced as an alternative family of states that resolve the identity
resolution. In the present manuscript, the quantization map related to the
modified Susskind-Glogower coherent states is exploited, which naturally leads
to a particular representation of the $\mathfrak{su}(1,1)$ Lie algebra in its
discrete series. The latter provides evidence about further generalizations of
coherent states, built from the Susskind-Glogower ones by extending the indexes
of the Bessel functions of the first kind and, alternatively, by employing the
modified Bessel functions of the second kind. In this form, the new families of
Susskind-Glogower-I and Susskind-Glogower-II coherent states are introduced.
The corresponding quantization maps are constructed so that they lead to
general representations of elements of the $\mathfrak{su}(1,1)$ and
$\mathfrak{su}(2)$ Lie algebras as generators of the SU$(1,1)$ and SU$(2)$
unitary irreducible representations respectively. For completeness, the optical
properties related to the new families of coherent states are explored and
compared with respect to some well-known optical states.
Related papers
- Separability of Graph Laplacian Quantum States: Utilizing Unitary
Operators, Neighbourhood Sets and Equivalence Relation [1.6190746208019742]
This article delves into an analysis of the intrinsic entanglement and separability feature in quantum states as depicted by graph Laplacian.
We show that the presence or absence of edges in the graph plays a pivotal role in defining the entanglement or separability of these states.
arXiv Detail & Related papers (2024-01-04T14:15:12Z) - Covariant operator bases for continuous variables [0.0]
We work out an alternative basis consisting of monomials on the basic observables, with the crucial property of behaving well under symplectic transformations.
Given the density matrix of a state, the expansion coefficients in that basis constitute the multipoles, which describe the state in a canonically covariant form that is both concise and explicit.
arXiv Detail & Related papers (2023-09-18T18:00:15Z) - Chiral topologically ordered states on a lattice from vertex operator
algebras [0.0]
We show that the states are well-defined in the thermodynamic limit and have exponential decay of correlations.
It also gives candidates for bosonic states in non-trivial invertible phases, including the $E_8$ phase.
arXiv Detail & Related papers (2023-01-20T17:33:12Z) - Characterizing generalized axisymmetric quantum states in $d\times d$
systems [0.0]
We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions.
We solve the separability problem for a subspace of these states and show that a sizable part of the family is bound entangled.
Our results allow us to estimate entanglement properties of arbitrary states, as general states can be symmetrized to the considered family by local operations.
arXiv Detail & Related papers (2022-02-22T17:09:18Z) - Coherent States for infinite homogeneous waveguide arrays: Cauchy coherent states for $E(2)$ [0.0]
Perelomov coherent states for infinite homogeneous waveguide arrays with Euclidean E(2) symmetry are defined.
It is shown that Perelomov coherent states for the Eucliean E(2) group have a simple and natural physical realization.
arXiv Detail & Related papers (2021-12-01T22:51:53Z) - Complete entropic inequalities for quantum Markov chains [17.21921346541951]
We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality.
We also establish the first general approximateization property of relative entropy.
arXiv Detail & Related papers (2021-02-08T11:47:37Z) - On the Local Linear Rate of Consensus on the Stiefel Manifold [39.750623187256735]
We restrict the convergence of properties of the Stfelian gradient over the Stiefel problem (for an un connected problem)
The main challenges include (i) developing a technical for analysis, and (ii) to identify the conditions (e.g., suitable step-size and under which the always stays in the local region) under which the always stays in the local region.
arXiv Detail & Related papers (2021-01-22T21:52:38Z) - Finite-Function-Encoding Quantum States [52.77024349608834]
We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions.
We investigate some of their structural properties.
arXiv Detail & Related papers (2020-12-01T13:53:23Z) - Local optimization on pure Gaussian state manifolds [63.76263875368856]
We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm.
The method is based on notions of descent gradient attuned to the local geometry.
We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
arXiv Detail & Related papers (2020-09-24T18:00:36Z) - Cumulant-free closed-form formulas for some common (dis)similarities
between densities of an exponential family [38.13659821903422]
In this work, we report (dis)similarity formulas which bypass the explicit use of the cumulant function.
Our method requires only to partially factorize the densities canonically of the considered exponential family.
arXiv Detail & Related papers (2020-03-05T07:46:22Z) - Gaussian Process States: A data-driven representation of quantum
many-body physics [59.7232780552418]
We present a novel, non-parametric form for compactly representing entangled many-body quantum states.
The state is found to be highly compact, systematically improvable and efficient to sample.
It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
arXiv Detail & Related papers (2020-02-27T15:54:44Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.