Quantum Fest 2019

Eight Festival on Quantum Phenomena, Quantum Control and Quantum Optics.

Booklet of Abstracts . Preface

It is a pleasure to welcome all the participants to this Eight Festival on Quantum Phe- nomena, Quantum Control and Quantum Optics, organized by Centro de Investigaci´ony de Estudios Avanzados (Cinvestav), Unidad Profesional Interdisciplinaria en Ingenier´ıa y Tecnolog´ıasAvanzadas del I.P.N. (UPIITA-IPN), and the Bar Quantum.

The Quantum Fest is one of the results of the scientiﬁc and academic collaboration between the Physics Department of Cinvestav and UPIITA-IPN. The aim of this meeting is to bring together students and researchers which are engaged in the subjects of quantum phenomena, quantum control and quantum optics, from both theoretical and experimental approaches, in order to get lively discussions and to enable a closer contact between them.

The festival has been celebrated in the Physics Department of Cinvestav (2010, 2011, 2014), in the Tecn´ologicode Monterrey, Campus Estado de M´exico(2012, 2015), and in the UPIITA-IPN (2013, 2016).

This year, from October 28 to November 1, we celebrate de eight Quantum Fest in the Physics Department of Cinvestav. This festival would not have been possible without the valuable ﬁnancial and administrative support of Cinvestav, UPIITA-IPN, and the Bar Quan- tum.

We wish for a successful and enjoyable scientiﬁc meeting and acknowledge to all the participants whose attendance allows us to celebrate this event.

*Editorial note: The abstracts include only the name and institution(s) of the author who is registered as speaker of the related work. The complete list of authors (if there is more than one) will be provided by the speakers in the corresponding talk and/or poster.

i .

ii QUANTUM FEST ORGANIZATION

Organizing Committee

Sara Cruz y Cruz (UPIITA-IPN)

Nicol´asFern´andez(UPIITA-IPN)

Claudia Quintana (Physics Department, Cinvestav)

Oscar Rosas-Ortiz (Physics Department, Cinvestav)

Sponsors

The Quantum Fest 2019 has received ﬁnancial support from the following institutions and organizations:

Centro de Investigaci´ony de Estudios Avanzados (Cinvestav)

Unidad Profesional Interdisiplinaria en Ingenier´ıay Tecnolog´ıasAvanzadas del Instituto Polit´ecnicoNacional (UPIITA-IPN)

Bar Quantum

iii .

iv QuantumQuantum Fest 2019 Programme Fest 2019 Programme

Monday Tuesday Wednesday Thursday Friday October 28 October 29 October 30 October 31 November 1 09:30-10:00 Registration Registration Registration Haret- Opening Veronique Rosario Celia 10:00-11:00 Codratian Session Hussin Paredes Escamilla Rosu Kurt Bernardo Carlos Torres- Héctor Moya- C. Quintana/ V. Barrera/ 11:00-12:00 Wolf Torres Cessa P. Jiménez G. Morales

A. Jaimes/ Coffee Break/ Coffe Break/ Cofee Break/ Cofee Break/ 12:00-13:00 M. Enríquez K. Zelaya Mariana Vargas V.A. Vicente Z. Gress Heber Zepeda- (Colloquium Blas Manuel Gastón García- Fernández Vladislav 13:00-14:00 Physics Rodríguez Calderón (Seminar, Kravchenko Department) Lara HEP Group) 14:00-15:30 Lunch Lunch Lunch Lunch Closure Eduardo Roberto de J. 15:30-16:30 Eric Rowell Juan Rosales Nahmad León Montiel E. Barrios/ A. Contreras- F. Olivar/ Francisco 16:30-17:30 R. Castillo- Astorga/ Poster Session Delgado Pérez Z. Blanco Vladimir Víctor Piotr 17:30-18:30 Poster Session Rabinovich Velázquez Kielanowski

Chairpersons of the sessions:

• Monday 28 Nicol´asFern´andez(morning) and Kevin Zelaya (afternoon) • Tuesday 29 Oscar Rosas-Ortiz (morning) and Alfonso Jaimes (afternoon) • Wednesday 30 Alonso Contreras (morning) and Claudia Quintana (afternoon) • Thursday 31 V´ıctorBarrera (morning) and Fernando Olivar (afternoon) • Friday 1 Sara Cruz y Cruz (morning)

v .

vi Booklet Of Abstracts/Quantum Fest 2019 1

PLENARY TALKS

Elementary SU(2) operations to manipulate the entropy in large 2-level quantum systems

Francisco Delgado, Tecnol´ogicode Monterrey, Mexico

Email: [email protected]

Abstract: Under the SU(2) decomposition mechanism, we discuss procedures to manipulate the states of large quantum systems conformed by two-level systems. In this approach, the entropy manipulation is considered focal to reach such procedure. ————————————————————————————————————————–

Testing Bose-Einstein Condensates with Galaxy Rotation Curves

Celia Escamilla Rivera, Instituto de Ciencias Nucleares (ICN) –Universidad Nacional Aut´onomade M´exico(UNAM), Mexico

Email: [email protected]

Abstract: Scalar ﬁelds have been proposed as a possible explanation in the search for the fundamental nature of dark matter, among them, relativistic Bose gases is one of the best proposal for scalar ﬁeld candidates. Indeed, a black hole is a natural astrophysical phenomena that could lead to bound states for the relativistic Bose gas, in other words, we can extend Bose-Einstein condensate around a black hole. Using Tomas-Fermi approximation we study the density distribution of the Bose-Einstein condensates in galaxies, and using SPARC data sampler we perform statistical analyses of the parameters of the Bose gas: a mass parameter, a self-interaction coupling constant and the mass of the black hole (the only astrophysical parameter). We found that a Bose-Einstein condensate can be a strong candidate to explain the fundamental nature of dark matter. ————————————————————————————————————————–

Non-Hermitian resonance expansions and unitarity

GastónGarc´ıaCalderón, Instituto de F´ısica(IF) –Universidad Nacional Autónomade México(UNAM), Mexico

Email: gaston@ﬁsica.unam.mx

Abstract: After an introduction of the notion of resonance and of non-Hermitian resonance- state expansionsin quantum mechanics I address the problem of the time evolution of tun- neling decay to discuss the issue of unitarity, an indispensable physical requirement for a fundamental description of the decay process.It is shown that contrary to other approaches,a resonance expansion involving the full set of resonance states and complex energy eigenvalues satisﬁes the condition of unitarity. 2 Quantum Fest 2019/Booklet Of Abstracts

Ladder functions for classical and quantum exactly solvable systems

V´eroniqueHussin, Department of Mathematics and Statistics, University of Montr´eal, Canada

Email: [email protected]

Abstract: In recent years, ladder functions have been deﬁned in the context of the Hamil- tonian formalism of classical mechanics, and a strong correspondence has been observed for many systems between the classical and quantum objects in terms of their functional dependence on the canonical variables x and p. Indeed, ladder functions were constructed for a class of simple solvable classical systems and their form computed by analogy with the form of the corresponding well-known quantum objects.

This raised the question as to whether the analogy could be further pursued for more elaborated systems. In particular, the ladder functions of the one-dimensional classical and quantum systems known as Rosen-Morse II (RMII) and curved Kepler-Coulomb (KC) were missing in preceding approaches. We discovered that the ladder functions for these two systems are considerably more elaborate.

We will thus discuss the procedure to get them as product of two factor functions, in particular. In this way, we hope to complete the knowledge of this type of functions for the whole list of classical systems corresponding to the quantum systems solved by means of the factorization method. ————————————————————————————————————————– Symmetries of the renormalization group equations

Piotr Kielanowski, Physcs Department, Cinvestav, Mexico

Email: kiel@ﬁs.cinvestav.mx

Abstract: ————————————————————————————————————————–

Practical solution of forward and inverse one-dimensional spectral problems

Vladislav V. Kravchenko , Department of Mathematics, Cinvestav-Qu´eretaro,Mexico

Email: [email protected]

Abstract: The transmutation (transformation) operators are one of the main theoretical tools of the spectral theory [6-8]. In the talk a new approach is presented for solving the classical forward and inverse Sturm-Liouville problems on finite and infinite intervals. It is based on the Gel’fand-Levitan-Marchenko integral equations and recent results on the functional series representations for the transmutation (transformation) operator kernels [1-5]. New representations of solutions to the Sturm-Liouville equation are obtained revealing the following feature important for practical applications. Partial sums of the series admit estimates in- Booklet Of Abstracts/Quantum Fest 2019 3 dependent of the real part of the square root of the spectral parameter which makes them especially convenient for approximate solution of spectral problems. In particular, a new representation for so-called Jost solutions is obtained reducing all the calculations related to spectral and scattering data to finite intervals instead of the half line or the whole line. This is the case of the spectral density function as well as that of the reflection coefficient in the scattering problem. In a sense this reduction trivializes the classical spectral and scattering problems on infinite intervals previously considered as numerically challenging problems.

Numerical methods based on the proposed approach for solving forward problems allow one to compute large sets of eigendata with a nondeteriorating accuracy. Solution of the inverse problems reduces directly to a system of linear algebraic equations. In the talk some numerical illustrations will be presented.

[1] V. V. Kravchenko, L. J. Navarro and S. M. Torba, Representation of solutions to the one- dimensional Schr¨odingerequation in terms of Neumann series of Bessel functions. Applied Mathematics and Computation, v. 314 (2017) 173-192.

[2] V. V. Kravchenko, Construction of a transmutation for the one-dimensional Schrodinger operator and a representation for solutions. Applied Mathematics and Computation, v. 328 (2018) 75-81.

[3] V. V. Kravchenko, On a method for solving the inverse scattering problem on the line. Mathematical Methods in the Applied Sciences 42 (2019) 1321-1327.

[4] V. V. Kravchenko, On a method for solving the inverse Sturm-Liouville problem. Journal of Inverse and Ill-Posed Problems, 27 (2019), 401-407.

[5] B. B. Delgado, K. V. Khmelnytskaya, V. V. Kravchenko, A representation for Jost solutions and an eﬃcient method for solving the spectral problem on the half line. Mathematical Methods in the Applied Sciences, to appear.

[6] B. M. Levitan, Inverse Sturm-Liouville problems, VSP, Zeist, 1987.

[7] V. A. Marchenko, Sturm-Liouville Operators and Applications. Birkhauser, Basel, 1986.

[8] V. A. Yurko, Introduction to the theory of inverse spectral problems. Moscow, Fizmatlit, 2007, 384pp. (Russian). ————————————————————————————————————————– Coupled harmonic oscillators in classical and quantum systems: operator techniques

H´ectorMoya-Cessa, INAOE, Mexico

Email: [email protected]

Abstract: 4 Quantum Fest 2019/Booklet Of Abstracts

Nonlinear Spectroscopy with Quantum Light

Roberto de J. León-Montiel, Instituto de Ciencias Nucleares (ICN) –Universidad Nacional Autónomade México(UNAM), Mexico

Email: [email protected]

Abstract: Entangled two-photon absorption spectroscopy has been widely recognized as a powerful tool for revealing relevant information about the structure of complex molecular systems. However, to date, experimental implementation of this technique has remained elusive, mainly because of the need to performing multiple experiments with two-photon states diﬀering in temporal correlations, which translates in the necessity to have at the experi- menter?s disposal tens, if not hundreds, of entangled-photon sources. In this talk, I will describe an experimentally-feasible scheme, developed in my group, which successfully over- comes this limitation. By making use of a temperature-controlled entangled-photon source, I will show that the two-photon absorption signal, recorded as a function of the temperature of the nonlinear crystal that generates the paired photons, and a controllable delay between them, carries all information about the electronic structure of the absorbing medium, which can be revealed by a simple Fourier transformation. ————————————————————————————————————————–

Is a Deterministic and Local Interpretation of Quantum Mechanics Possible?. . . First steps

Eduardo Nahmad-Achar, Instituto de Ciencias Nucleares (ICN) –Universidad Nacional Aut´onomade M´exico(UNAM), Mexico

Email: [email protected]

Abstract: Quantum states in superposition cannot be observed, suggesting that they merely embody information on possible measurement results. Yet, we think of them as describing physical systems that evolve in time according to given mathematical equations. Furthermore, evolution takes place in physical space-time, and local causality is imposed on space-time by Special Relativity (a sequence of cause and effect that constitutes a fundamental principle by which we think about and do scientific work).?It is therefore strange that there is non-locality and violation of causality embedded in Quantum Mechanics. We try to give here a first step to see whether a deterministic and local interpretation is possible. We will show that Bell?s inequality in not conclusive about the non-local nature of Quantum Mechanics, in that there exists an interpretation of reality (which we put forward) which is local and in which Bell?s inequality cannot be derived. Assuming determinism and locality a new Bell-like inequality is derived, which is always satisfied by Quantum Mechanics and which allows for local hidden variables [1].

[1] N. Sanchez-Kuntz and E. Nahmad-Achar, Found. Phys. 48, 27 (2018) Booklet Of Abstracts/Quantum Fest 2019 5

Nonconventional superﬂuidity in ultracold dipolar gases

Rosario Paredes Gutiérrez, Instituto de F´ısica(IF) –Universidad Nacional Autónomade México(UNAM), Mexico

Email: rosario@ﬁsica.unam.mx

Abstract: In this seminar we discuss the emergence of p-wave superfluidity in a dipolar Fermi gas confined in a double layer array of parallel optical lattices in two dimensions. The dipole moments of the molecules placed at the sites of the optical lattices, separated a distance L and pointing in opposite directions, produce an effective attractive interaction among them, except between those dipoles situated one on top of the other. Such interaction between dipoles is precisely the origin of the non conventional superfluid state. We first argue on the two body physics and then, we present the analysis for the ground state of the many-body system within the mean field scheme. In particular, we study the stable regions, as a function of the system parameters, namely the effective interaction between dipoles c and the filling factor n, for which the superfluid state can exist. Following the BKT scheme we estimate the critical temperature of the superfluid state. ————————————————————————————————————————–

Composite Phase Control in the Optomechanical State Transfer Protocol

Blas Manuel Rodr´ıguezLara, Tecnol´ogicode Monterrey, Mexico

Email: [email protected]

Abstract: State transfer in optomechanical systems uses a mean ﬁeld enhancement of bare couplings. However, this process, as well as any other mischaracterization, can be a source of noise that takes us away from optimal state transfer. We propose a control scheme based in composite phase driving sequences to minimize the eﬀect of the noise. This provides robust state transfer under reasonable random variations in the system parameters. ————————————————————————————————————————–

Fractional calculus applied to electromagnetics waves

Juan J. Rosales Garc´ıa, DICIS-Universidad de Guanajuato, Mexico

Email: [email protected], [email protected]

Abstract: In this talk, we give an introduction to the fractional calculus considering some definitions, such as Riemann-Liouville, Caputo, Caputo-Fabrizio fractional derivative and integrals, as well as, the conformable derivative. In particular, we will consider the propagation of electromagnetic waves in an infinitely extended homogeneous media at rest, characterized by the permittivity ε and permeability µ. Two types of the fractional differential equations will be examined separately; with fractional time derivative and the spatial fractional derivative. The parameters σt and σx are introduced which characterize the existence of the fractional time and space components, respectively. It is shown that in the first case 6 Quantum Fest 2019/Booklet Of Abstracts

there is a relation between σt and the period T0 of the wave given by the order γ of the fractional differential equation, and in the second case the relation is between σx and the wavelength λ. Due to these relations the solutions of the corresponding fractional differential equations are given in terms of the Mittag-Leffler function depending only on the parameter γ ————————————————————————————————————————–

Spectral properties of one-dimensional Dirac operators with ﬁnite and inﬁnite sets of delta- interaction

Vladimir Rabinovich, ESIME-IPN, Mexico

Email: [email protected]

Abstract: We consider the Dirac operator on R of the form d Du(x) = J + Q + Q u(x), x ∈ dx s R

u(1) 0 −1 where u = is a two-dimensional distribution on , J = , u(2) R 1 0

p(x) + r(x) q(x) Q(x) = , p, q, r ∈ L∞( ) q(x) −p(x) + r(x) R is a regular potential, X Qs(x) = Γ(y)δ(x − y) y∈Y ∞ is a singular potential, Γ(y) = (γi,j(y))i,j=1,2 is a 2 × 2-matrix with elements γi,j ∈ l (Y), i, j = 1, 2, and Y ⊂ R is a ﬁnite or inﬁnite discrete set. We associate with the formal Dirac operator D the unbounded operator D in the Hilbert 2 2 d space L (R, C ) deOned by the Dirac operator DQ = J dx + Q with regular potential Q and the point interaction conditions

A(y)u(y + 0) = B(y)u(y − 0), y ∈ Y

1 1 deﬁned by the singular potential Qs, where A(y) = 2 Γ(y) − J, B(y) = − 2 Γ(y) + J . 2 2 We give conditions for the operator D to be self-adjoint in L (R, C ). Moreover we study the Fredholm properties and the essential spectrum of unbounded operator D We consider the band-gap structure of spectra of Dirac operator D with periodic regular and singular potentials, and the inﬂuence of slowly oscillating perturbations of regular potentials Q on the essential spectrum of periodic Dirac operators. Booklet Of Abstracts/Quantum Fest 2019 7

Factorizations of Diﬀerential Equations in Mathematical Physics

Haret-Codratian Rosu Barbus, IPICyT, Mexico

Email: [email protected]

Abstract: I review some of the factorizations of diﬀerential equations I have been working with over the years, some of them old, others more recent ones, with emphasis on their applications. Some of the latter are new having the status of work in progress. ————————————————————————————————————————–

Anyons and Beyond: The Mathematics of Topological Phases

Eric Rowell , Department of Mathematics, Texas A&M University, USA

Email: [email protected]

Abstract: By now anyons have been deeply studied from various theoretical points of view, but interesting physical realizations remain elusive. The promise of topological quantum computation has driven much of this research. Yet other, less familiar topologicalphases of matter are less well-studied, and may also be of signiﬁcant technological value. One lesson that we have learned from anyons is that category theory is a very convenient convenient language to for modeling such systems. (Indeed, category theory is becoming more accepted as a framework for many areas of science, see Forbes Magazine July 29, 2019.) In this talk I will illustrate this principle, by showing how they allow us to understand anyons and then how we hope to extend to other topologicalmaterials. ————————————————————————————————————————–

Exploration of the North Pole exhibited by Magnetic Nanoparticles

Carlos Torres-Torres, ESIME-IPN,Mexico

Email: [email protected]; [email protected]

Abstract: The magnetism as a relativistic electricity has resulted in the development of diverse applications related to quantum phenomena, nanophotonics and ultrafast plasmonic processes among others. Magnetic nanoparticles have proven to be very powerful tools that derive their potential from excitations remarkably influenced by quantum confinement. The Surface Plasmon Resonance of metal nanoparticles is responsible for the enhancement of many of their light-controlled low-dimensional functions. This presentation describes particular experimental principles of nonlinear optics and physical mechanisms originated by multi-photonic processes. The importance of the temporal regime of electromagnetic interactions from the order of nanoseconds to femtoseconds will be discussed. Some fascinating physical effects that can contribute to the gyroscopic behavior of magnetic nanoparticles will be also pointed out. 8 Quantum Fest 2019/Booklet Of Abstracts

Quantum chaos in time series of single photons as a superposition of local and non-local states

V´ıctorVelázquez, Facultad de Ciencias (FC) –Universidad Nacional Autónomade México (UNAM), Mexico

Email: [email protected]

Abstract: In this talk we show that it is possible to obtain time series of photons with “on demand” statistics. In particular, we analyze the time series of photons that have quantum chaos. We show experimentally that we can redeﬁne quantum chaos in time series of photons as the superposition of photon states of the two behaviors wave and particle, in the same proportion. ————————————————————————————————————————–

From free motion on a 3-sphere to the Zernike system of wavefronts inside a circular pupil

Kurt Bernardo Wolf, Instituto de Ciencias F´ısicas(ICF) –Universidad Nacional Aut´onoma de M´exico(UNAM), Mexico

Email: bwolf@ﬁs.unam.mx

Abstract: The Zernike system stems from free motion on a 3-sphere, properly projected on the 2-dimensional manifold of the unit disk. This exhibits separability in a variety of coordinate systems, polynomial solutions, finite on the disk boundary. These correspond to Zernike’s classification of aberrations of wavefronts in circular pupils. The interbasis expansion coefficients include discrete Hahn polynomials that are a particular subset of Clebsch-Gordan coefficients. Booklet Of Abstracts/Quantum Fest 2019 9

CONTRIBUTION TALKS

Design and Construction of Homodyne Detectors for the Study of Quantum Optical States

Erick Barrios Barocio, Facultad de Ciencias (FC) –Universidad Nacional Aut´onomade M´exico(UNAM), and UPIITA-IPN, Mexico

Email: [email protected]

Abstract: Nowadays the fields of Quantum Optics and Quantum Information are experi- encing a mayor development worldwide, and in particular in the experimental arena. The reason for this great development relies in the potential future applications of this technology in fields of computing, security, telecommunications and metrology. However, in order to be part and contribute in the development and research in these fields, we must be able to design and construct the electronic devices suitable for the study of light with quantum features, as well as the software needed to analyze the experimental data obtained. In this talk, I will present a general overview of the theory, applications and design of one of such devices called Homodyne Detector that allows us to study light at quantum level and to develop quantum communications and quantum metrology techniques. ————————————————————————————————————————–

Quantum states of light in a non linear Mach-Zehnder interferometer.

Zurika Blanco, Physics Department, Cinvestav, Mexico

Email: iblanco@ﬁs.cinvestav.mx

Abstract: We propose, as initial state, a linear combination of Fock states that permits the recovering of already studied states; for example, Glauber coherent states, optimized binomial states, or nonlinear coherent states. Then, we analyze the classicalness of these states using a beam splitter and the Mandel parameter. We addressed our attention to the nonlinear coherent states because such states have nonclassical properties than can be exhibited with the help of a beam splitter although their P-representation is a delta function. We injected this linear combination of Fock states in a Mach-Zehnder interferometer with a nonlinear optical medium in one of his arms, as proposed by Dunningham. This device can improve the measurement precision by reaching the Heisenberg limit. The main idea is that this device permits the manipulation of the photon-states that are injected in the nonlinear Mach-Zehnder interferometer. 10 Quantum Fest 2019/Booklet Of Abstracts

On the spectra of one-dimensional Schrdinger operators with countably inﬁnite point interactions

V´ıctorBarrera-Figueroa, SEPI-UPIITA-IPN, Mexico

Email: [email protected]

Abstract: In this talk we consider formal Schrdinger operators

d2 S u (x) = − + q (x) u (x) , x ∈ , (1) q dx2 R

∞ with potentials q = q0 + qs consisting of a regular part q0 ∈ L (R) and a singular part qs with support on a countably inﬁnite set Y ⊂ R. We construct a self-adjoint extensionH of operator(1) given in terms of only the regular potential q0 and certain matrix conditions at every point of Y. We analyse the esential spectrum of H under quite general conditions, and derive a dispersion relation in a closed form when the set Y is isomorphic to Z. Such dispersion relation leads to a precise way to calculate the edges of the spectral bands of Schrdinger operators with periodic regular potentials and periodic matching conditions at the points of Y' Z. ————————————————————————————————————————–

The method of fundamental solutions with Bergmann kernel in eigenvalue problems

R. Castillo-P´erez, ESIME-IPN, Mexico

Email: [email protected]

Abstract: The Method of Fundamental Solutions (MFS) has been employed for the solution of boundary value problems long ago [1]. However, when used for the solution of eigenvalue problems its most simple version shows some limitations because it employs the determinant (which decreases very fast) for the detection of the eigenvalues [2]. This makes it diﬃcult to locate them, specially for non trivial geometries. Several methods have been proposed in order to overcome this and other drawbacks still using the MFS [3]. Here we propose and analyze the performance of a method in which the Bergman kernel [4] is constructed based on a complete system of fundamental solutions, which turns the eigenvalue problem into a problem of locating simple poles of a function based on the computed Bergman kernel and having a more reasonable scale.

[1] Kupradze V. D., and Aleksidze M. A. The Method of Functional Equations for the Approximate Solution of Certain Boundary Value Problems. Z. Vych. Mat. 1964, 4, pp. 683-715.

[2] Aleksidze M. A. Fundamental Functions in Approximate Solutions of Boundary Value Problems, Nauka, Moscow, Russia, 1991 (in Russian).

[3] Alves C. J. S. and Antunes P. R. S. The Method of Fundamental Solutions Applied to the Calculation of Eigenfrequencies and Eigenmodes of 2D Simply Connected Shapes. CMC 2005, Vol. 2, No. 4 pp. 251-265.

[4] Campos H. M., Castillo-Perez R., Kravchenko V. V. Construction and application of Bergman-type reproducing kernels for boundary and eigenvalue problems in the plane. Complex Variables and Elliptic Equations, 2012, Vol. 57, No. 7-8, pp. 787-824. Booklet Of Abstracts/Quantum Fest 2019 11

Photonic systems with two-dimensional landscapes of complex refractive indexvia time-dependent supersymmetry

Alonso Contreras Astorga, Physics Department, Cinvestav, Mexico

Email: acontreras@ﬁs.cinvestav.mx

Abstract: We present a framework for the construction of solvable models of optical settings with genuinely two dimensionallandscapes of refractive index. Solutions of the associated non- separable Maxwell equations inparaxial approximation are found using the time-dependent supersymmetry. We discuss peculiar theoreticalaspects of the construction. In particular, we focus on the existence of localized solutions specific for thenew systems. Sufficient conditions for their existence are discussed. Localized solutions vanishing for large |x|, which we call light dots, as well as the guided modes that vanish exponentially outside the wave guides,are constructed. We consider different definitions of the parity operator and analyze general properties of the PT-symmetric systems, e.g., presence of localized states or existence of symmetry operators. Despite themodels with parity-time symmetry are of the main concern, the proposed framework can serve for constructionof non-PT -symmetric systems as well. We explicitly illustrate the general results on a number of physicallyinteresting examples, e.g., wave guides with periodic fluctuation of refractive index or with a localized defect, curved wave guides, two coupled wave guides, or a uniform refractive index system with a localized defect. ————————————————————————————————————————–

New families of analytical solvable time-dependent radiation ﬁelds for one qubit

Marco Enr´ıquez, Tecnol´ogicode Monterrey–CEM, Mexico

Email: [email protected]

Abstract: Exactly solvable models are valuable in quantum mechanics even though the number of cases is very limited. In this talk we present a method to generate families of time-dependent two-level Hamiltonians for which the correspondent evolution operator can be disentangled in an exact way via the Wei-Norman formalism. It is shown that the Hamil- tonian oﬀ-diagonal elements are connected with the Ermakov equation and the dynamics is sensitive to the nature of its solutions. A physical model is discussed in the context of the nuclear magnetic resonance phenomenon. 12 Quantum Fest 2019/Booklet Of Abstracts

Propagation of Hermite-Gaussian modes in a parabolic medium

Zulema Gress Mendoza, Universidad Aut´onomadel Estado de Hidalgo, Mexico

Email: [email protected]

We analyze the light propagation processes in a weakly inhomogeneous optical media with a quadratic refractive index profile. The factorization method is applied to construct ladder operators for the Hermite-Gaussian modes. These operators allow to show that the su(1,1) and su(2) algebras generate the spectrum of propagation constants at any fixed transversal plane. We also construct the corresponding families of coherent states for these algebras as solutions of differential equations admitting separation of variables. ————————————————————————————————————————–

Self-healing of structured light: Can you cover a light beam with a ﬁnger?

Alfonso Jaimes N´ajera, CICESE Monterrey, Mexico

Email: [email protected]

Abstract: Self-healing is the ability of light to self-reconstruct after being partially blocked by an opaque obstacle during free-space propagation. It is well-known that Bessel beams possess that ability, and its physical mechanism is well understood. In recent years, it has been shown that Laguerre-Gauss beams also have self-healing properties. However, a clear physical mechanism that explains this phenomenon has not been presented to the best of our knowledge. In this talk we show that the Laguerre and Hermite Gaussian beams can be constituted of traveling waves that are capable of describing the self-healing process in physical terms. Additionally, measurable predictions in the laboratory can be made, which would in turn constitute a physical proof of the existence of these traveling waves. ————————————————————————————————————————–

Lindblad master equation in Lie algebra representation

Pedro Jim´enez, Physics Department, Cinvestav, Mexico

Email: rjimenez@ﬁs.cinvestav.mx

Abstract: The density matrix that represents the state of a Markovian quantum system is in general a semigroup member. In turn, the Liouvillian that deﬁnes the related Lindblad master equation (LME) is the generator of a contraction semigroup. If the complete positive and trace preserving map associated with these master equation can be written in Kraus representation it turns out in the analytical solution of the problem. In this work we analyze when that Kraus representation can be handle as a Lie algebra channel, i.e., in terms of a representation of some compact and semi simple Lie algebra. Then, we analyze the general physical properties of the dynamical evolution of open systems. Booklet Of Abstracts/Quantum Fest 2019 13

Unitary operators over quantum systems of several levels.

Guillermo Morales-Luna, Computer Science Department, Cinvestav, Mexico

Email: [email protected]

Abstract: High-dimensional quantum states generalise multi-valued logics. The analogous of Pauli transforms acting on these quantum states determine a subgroup structure in U(n) and in SU(n), which acts over the maximally entangled Bell states. The resulting properties are suitable to produce superdense coding communication protocols. ————————————————————————————————————————–

A fractional formulation for some relevant equations of mathematical physics

Fernando Olivar Romero, Physics Department, Cinvestav, Mexico

Email: folivar@ﬁs.cinvestav.mx

Abstract: Using derivatives of all positive orders between 1 and 2, we study a fractional space-time partial differential equation that connects the heat and wave equation through the -order of its fractional time-derivative (1 ≤ α ≤ 2) and the β-order of its space derivative (1 ≤ β ≤ 2). The notion of Caputo for the time derivative and the Riesz pseudo-differential operator for the space derivative are adopted. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The Cauchy problem associated to this model is solved for delta and Gaussian initial disturbances. As a first generalization of this model, we add a term proportional to the solution function which permits the study of a fractional differential equation that intermediates between the Klein-Gordon equation and a modified heat equation with radiation losses. Another generalization arises from the introduction of a fractional damping term into the initial equation, which leads to the fractional damped wave equation. ————————————————————————————————————————–

On the master equation for entangled bipartite qubit systems coupled to photon baths

Claudia Quintana, Physics Department, Cinvestav, Mexico

Email: lquintana@ﬁs.cinvestav.mx

Abstract:The time-evolution of pure states (ρ2 = ρ) associated with a closed bipartite system S = SA + SB is unitary and obeys the Heisenberg equation. By summing the degrees of freedom of the subsystem B we obtain the reduced state ρA of subsystem A, which is a mixed 2 state (ρA 6= ρA) in general. One may consider SA as an open system that interacts with SB in controlled form. The law of motion for SA is not represented by the Heisenberg equation anymore, so that a master equation is necessary. We consider a closed tetra-partite system S composited by two entangled qubits and two quantized single-mode radiation fields; two isolated QED cavities contain a pair (qubit + field) each one. Our interest is addressed to investigate the master equation for the different configurations of subsystems SA and SB that can be obtained from S. 14 Quantum Fest 2019/Booklet Of Abstracts

First measurement of the neutrino-induced phase shift in the BAO spectrum (Colloquium of the Physics Department))

Mariana Vargas Magaa, IF-UNAM, Mexico

Email: mmaganav@ﬁsica.unam.mx

Abstract: In this talk, I will present how we can use galaxy redshift surveys to constrain properties of neutrinos and other light relics. Neutrinos were a dominant component of the energy density in the early universe and, therefore, played an important role in the evolution of cosmological perturbations. In particular neutrinos imprint a temporal phase of sound waves in the primordial plasma. I will present the ﬁrst constraint on this neutrino-induced phase shift in the spectrum of baryon acoustic oscillations of the BOSS DR12 data. ————————————————————————————————————————–

Complete orthogonal systems of solutions for the d-dimensional radial Schrodinger equation transformations

V´ıctorA. Vicente Ben´ıtez, Department of Mathematics, Cinvestav-Qu´eretaro,Mexico

Email: [email protected]

Abstract: The aim of this talk is to present an explicit construction of an orthogonal complete system of solutions for the radial Schrdinger equation. We consider in a star- d shaped domain Ω of the Euclidean space R (with dimension d > 2) the equation of the form Su(x) := (4d − q (kxk)) u(x) = 0 for x ∈ Ω, (2) where q is a C1 function that only depends of the radial component r = kxk.

Using the approach of transmutation operators theory, we consider the fact of any solution of (2) can be written in the form

Z 1 T f(x) = f(x) + σd−1G(r, 1 − σ2)f(σ2x)dσ. (3) 0 where h is an harmonic function in Ω [1]. Employing the properties of T , we obtain an orthogonal complete system of solutions S for (2), that generalizes the concept of harmonic homogeneous polynomial. The completeness of the system S in the sense of the uniform convergence on compact subsets of Ω, and in the L2- norm, will be shown. In addition, we develop an algorithm to the explicit construction of the system S. Finally, we study an d application to the solution of the Dirichlet problem in the unit ball B . [1] R. P. Gilbert, K. Atkinson, Integral operator methods for approximating solutions of Dirichlet problems. ISMN Vol. 15, Birkhuser, Basel, 1970. Booklet Of Abstracts/Quantum Fest 2019 15

Time-dependent exactly solvable potentials generated by point transformations

Kevin Zelaya, University of Montreal, Canada, and Physics Department, Cinvestav, Mexico

Email: kdzelaya@ﬁs.cinvestav.mx

Abstract: The proper form-preserving point transformation is introduced to deform a given solvable stationary Schr¨odingerequation into a new one with explicit dependence on time. Given that the inner-product is preserved, a set of orthogonal solutions is then inherited from the initial system. The constants of motion (invariant operators) of the new system are extracted in a straightforward form by simply performing the appropriate mapping and by exploiting the preservation of the ﬁrst integrals available in the initial system. In particular, it is shown that the parametric oscillator can be seen as a deformation of the harmonic oscillator. Lastly, a new family of time-dependent potentials is generated by combining the Darboux and point transformations. ————————————————————————————————————————–

Study and characterization for the conﬁguration: scintillator material+SiPM and its application to medical physics (Seminar, HEP Group)

Heber Zepeda-Fern´andez, Facultad de Ciencias F´ısico-Matem´aticas-BUAP, Mexico

Email: [email protected]

Abstract: The use of Silicon Photomultiplier (SiPM) has been used more frequently in the last years compared to Photomultiplier Tubes (PMT), due to its low cost, low voltage for its operation, and most useful, its smaller size, which can be 1mmX1mm. In this talk I will show the studies I have done on characterization of scintillating materials Bc404 and Bc422 + SiPM. The main study is its time resolution, this to be used as a trigger Level 0 for the Multi-Pirpose Detector (MPD) experiment for the Joint Institute for Nuclear Research laboratory in Dubna, Russia. The studies of this conﬁguration can be extended in the charge deposition (energy) and can be used in dose control to be administered to a patient. Finally, I talk about of a proposal of this conﬁguration for a Positron Emission Tomography (PET). 16 Quantum Fest 2019/Booklet Of Abstracts

. Booklet Of Abstracts/Quantum Fest 2019 17

POSTERS

A study of Generalized uncertainty principle and the eﬀects on coherent and squeezed states

Pranjal Agarwal, Shiv Nadar University, India, and UPIITA-IPN, Mexico

Email: [email protected]

Abstract: In this work we discuss the recent Generalized uncertainty principle, brieﬂy see one of its rough derivations and that it implies existence of minimal uncertainty in position. We’ll end by taking a quick look at the modiﬁed uncertainties of few quantum mechanical states under this new framework. ————————————————————————————————————————–

Random walks and photon statistics

Gustavo Armend´aris Pe˜na, Facultad de Ciencias, UNAM, Mexico

Email: ﬁsher [email protected]

Abstract: In this work, we studied the diffraction pattern of a photon entering a network of beam splitters. Besides, we add random noise to study decoherence in the diffracted light. By a numerical simulation we show that the more probable output port of the network, in which we can find the photon, is near the extreme ports of the network and the probability decays towards the center ports. ————————————————————————————————————————–

Using the energy distribution as a benchmarking among models for adiabatic quantum processing in the protein folding problem

Alan Anaya, Tecnol´ogicode Monterrey , Mexico

Email: [email protected]

Abstract: Network site-penalizing and turn-encoding models for quantum adiabatic processing in the protein folding problem are recreated to get their respective energy distribution and then it is used to benchmark their tentative performance. 18 Quantum Fest 2019/Booklet Of Abstracts

Featuring causal order in teleportation of two quantum teleportation channels

Carlos Cardoso Isidoro, Tecnol´ogicode Monterrey, Mexico

Email: [email protected]

Abstract: Causal order has been considered to improve the ﬁdelity of communication in quantum channels, ﬁrst showing as a depolarizing channel becomes transparent as a result of interference in the causal order. This approach has been applied to teleportation generating similar results. In this work, causal order in teleportation is revisited to improve the quantum information transmission. ————————————————————————————————————————–

Analysis of a stratiﬁed quantum waveguide with interactions at planes

Raymundo Conde V´azquez, UPIITA-IPN, Mexico

Email: [email protected]

Abstract: In this work it is studied a stratified quantum waveguide in a three-dimensional 3 system of rectangular coordinates x = (x1, x2, x3) ∈ R . This quantum waveguide is modeled by the stationary Schrödingerequation with a potential function q = qr + qs depending on only the vertical coordinate x3, which consists of two parts: a regular part representing an attractive potential  0, x < 0  3 qr (x3) = V, 0 < x3 < h ,  0, x3 > h 0 0 where V < 0, and a singular part qs (x3) = α0δ (x3) + β0δ (x3) + α1δ (x3 − h) + β1δ (x3 − h), αi, βi ∈ R, i = 0, 1, supported at the planes x3 = {0, h}. These planes represent interfaces of the waveguide between the core at x3 ∈ (0, h) and the cladding at x3 ∈ (−∞, 0) ∪ (h, ∞). For the regularization of the Schrödingerequation with a singular potential, we construct a self-adjoint extension of the Schrödingeroperator based on the work of Kurasov [4]. It follows that the action of the singular potential is represented by certain boundary conditions at the planes x3 = {0, h} given in a matrix form. The Green’s function of the waveguide is obtained as a superposition of the bound and scattering states. Asymptotic expressions of the Green function are obtained by means of the stationary phase method [1-3].

[1] Barrera-Figueroa V, Rabinovich V S. Asymptotics of the far ﬁeld generated by a modulated point source in a planarly layered electromagnetic waveguide. Math. Method Appl. Sci., 2014. 38: 1970-1989.

[2] Fedoryuk M V. Asymptotic Analysis. Linear Ordinary Diﬀerential Equations. Springer-Verlag: Moscow, 1983.

[3] Kravchenko VV, Porter RM. Spectral parameter power series for Sturm-Liouville problems. Wiley InterScience, 2010. 33: 459–468.

[4] Kurasov P. Distribution theory for discontinuous test functions and diﬀerential operators with generalized coeﬃcients. J. of Math. Anal. and App., 1996. 201: 297-323. Booklet Of Abstracts/Quantum Fest 2019 19

Semi-quantum game of life

Hugo Iv´anFern´andezCid, CIC-IPN , Mexico

Email: [email protected]

In the present work we implemented a semi-quantum version of Conway?s Game of Life cellular automaton which presents superposition and interference phenomena. Rules are implemented as non- reversible operators acting on each cell according to its neighbors liveness, ie., the sum of the probability amplitudes for measuring the cells on the alive state, considering a Moore-neighborhood. We reproduced classical patterns, like stills and oscillators, and some interesting new patterns which represents the evolution of probability amplitudes for measuring cell states in two possible base states: alive and dead. ————————————————————————————————————————–

Phase-space properties of position dependent mass quantum oscillators

Jonatan Gamboa, Physics Department, Cinvestav, Mexico

Email: jgamboa@ﬁs.cinvestav.mx

Abstract: The quantum systems with a mass which is a function of the position represent an interface between theoretical and experimental physics. The best known example is the notion of eﬀective mass arising in the study of electrons in semiconductors. A major problem is that the self-adjointness of the Hamiltonian depends on the ordering of the mass and the momentum in the kinetic term. In this work we study the form to solve such an ordering and show the way in which the variable mass problem is transformed into an eigenvalue problem of constant mass and we use a phase-space formulation to construct the Wigner function for an oscillator of variable mass and show that such function is a deformed version of the conventional one. We also show that the Bialynicki-Birula inequality is satisﬁed by such oscillator. ————————————————————————————————————————–

Entanglement in photosynthetic light-harvesting complexes: an introductory review based on master equations modelling

Bruno Gonz´alezSoria, Tecnol´ogicode Monterrey, Mexico

Email: [email protected]

Abstract:We review the modelling of photosynthetic light-harvesting in plants and bacteria under open-systems master equations to get valuable information in their entanglement re- laxation while they undergo into thermal equilibrium. 20 Quantum Fest 2019/Booklet Of Abstracts

Spatial control of structured photon pairs

Dalia Guti´errezL´opez, ICN-UNAM, Mexico

Email: [email protected]

Abstract: The spatial properties of photon pairs produced by the process of spontaneous parametric down-conversion (SPDC), with an apertured zeroth-order Bessel-Gauss beam, were studied in theory and experiment. We developed a method that modiﬁes the structured pump beam with the rotation of a half-plane aperture, that allows the selection of either one or a portion of the two individual cones that form an SPDC dual-cone angular spectrum and also, determine the shape and orientation of the conditional angular spectrum. This control of the SPDC spatial properties can be useful for quantum information processing protocols. ————————————————————————————————————————–

Towards noiseless quantum computation using anticoherent states

Christian Louis Hanotel Pinz´on, Instituto de Ciencias Nucleares-UNAM, Mexico

Email: [email protected]

Abstract: When a quantum system traces a cycle in quantum state space it acquires a geometric phase that does not depend on the parametrization of the cyclic path, but do depend on the path itself. In the presence of noise that deforms the path, the phase gets aﬀected, compromising the robustness of possible applications, e.g., in quantum computing. We show that for a special class of states (anticoherent states) and for paths that correspond to ro- tations, the phase only depends on topological characteristics of the path and is therefore immune to noise. ————————————————————————————————————————–

Quantum photon entanglement

Hern´andezHern´andezEduardo, FC-UNAM, Mexico

Email: [email protected]

Abstract: In this work the congruence of the Copenhagen interpretation of quantum mechanics with the experimental results obtained was corroborated, this was done by discov- ering the non-locality of the system, in order to indicate this, the coefficient ζ = (45, 45) + (45, 45)/((0, 90) + (90, 0)) that relates the number of matches to different polarization angles, so if the coefficient is 1, the system is non-local, on the contrary, if the coefficient is 1/2 the system is local. Finally, a coefficient with a value of 0.83040.0235 and an error of 16.96% with respect to the theoretical value was obtained, concluding that the system is not local, and corresponds to that proposed by the Copenhagen interpretation, however, the result could be closer to 1 if an assembly is made with greater precision. Booklet Of Abstracts/Quantum Fest 2019 21

Why to construct quantum wave packets from widely diﬀerent distribution functions?

Luis Alberto Jaramillo Ben´ıtez , ESFM-IPN, Mexico

Email: [email protected]

Abstract: It is frequently, in quantum mechanics books, the mention of the wave packets which is a solution of Schr odinger equation. However, reasons for choosing the distribution to build wave packets are little explored. What is the difference between use one distribution instead another one? What are the consequences of this choice? Detailed descriptions about this choice are scarce. We analyze the consequences of using different distributions: Sinc function, Gaussian function and Lorentz function; to build wave packets, as different features able to be used in favor of our purposes. ————————————————————————————————————————–

On the fundamentals of Quantum Mechanics and the impact of Feynman?s interpretation

Brenda E. Jim´enez-Ramos, ESFM-IPN, Mexico

Email: [email protected]

Abstract: Quantum mechanics (QM) admits diﬀerent interpretations, however, one of the most useful to understand, how it works, and how to calculate with, is Feynman’s interpretation. In addition, we take into account, from the beginning, the QM postulates. These postulates are a very useful tool to develop calculations and give us the opportunity to get into the mathematical principles that conform QM. Without this fundamental structure, it becomes, even more, diﬃcult to understand QM. Feynman is well known for his gift for explanation. He could make hard, mathematical, subjects, easier to understand to many student and professors that attended his lectures. In this work, we follow his steps and reasoning, and we follow closely his physics lectures and provide simple examples on how to construct the quantum mechanics amplitude and probability for processes and trajectories were bosons and fermions are involved, either individually or collectively.

We also know that indistinguishable particles can be made distinguishable if we tag them. Once they are tagged, appears an observable and a series of QM operations can be carried out on them. The results on one type of particles and on the other type of particles are quite diﬀerent. We stress those diﬀerences. Feynman gives us clear and easy rules (addition or subtraction of amplitudes) to work out the quantum mechanics amplitude of bosons and fermions under scattering processes (trajectories and energies). We compile and summarise those rules. We have not found any other simple treatment of these rules. This treatment allows a better working scheme in research and with novice students that are entering this beautiful area of physics. 22 Quantum Fest 2019/Booklet Of Abstracts

Singularities and internal rotational dynamics of electron beams

Gerardo Jim´enezTrejo, UPIITA-IPN, Mexico

Email: [email protected]

Abstract: In this work we make an analysis of a pair of phase singularities immersed in wave functions having the behavior of Laguerre-Gaussian beams. The cases to be treated are static and dynamic singularities. We consider the composition of canonical and kinetic currents and the velocities on each momentum state. We compare the behavior of time-dependent and stationary systems and obtain the topological charge numbers that characterize the rotation of currents around the singularities. Finally, we present some analytical and numerical results to illustrate our model. ————————————————————————————————————————–

Study of the Quantum-to-Classical Transition in a Statistical Mixture of Biphoton SPDC and Coherent States

Diego Lara, Facultad de Ciencias, UNAM, Mexico

Email: godie [email protected]

Abstract: The Quantum to Classical transitions be an open problem in quantum theory. This work consist in two parts, in the ﬁrst one develop experimentallystatistical mixture, we propose the statistical mixture starting with the classical experiment ofanti correlation for pair of photons SPDC, plus a coherent beam passing along the same optical path to ensureindistinguishability. The statistical weights of this two states were modulates by their corresponding intensities. The second part it consisted in the develop of atheoreticalde- scription of thetransition viadensity matrix. We obtain a smooth transition in terms of the second order correlation function through the proposed density matrix. The experimental data andtheoretical description seem to be in concordance. ————————————————————————————————————————–

On the dispersion properties of the Zakharov-Shabat system

Samantha Loredo-Ram´ırez, UPIITA-IPN, Mexico

Email: [email protected]

Abstract: The Zakharov-Shabat system [5]

∂xn1 (x) − λn1 (x) = U (x) n2 (x) , (4a)

∂xn2 (x) + λn2 (x) = −U (x) n1 (x) , (4b) consists of two coupled first-order linear differential equations, where U is a potential function, > (n1, n2) is a vector-valued solution with complex entries, and λ ∈ C is a parameter. This system has several applications in quantum mechanics, and applied mathematics, among others. Let q := iU [4], hence the previous system leads to the following uncoupled Schrödinger Booklet Of Abstracts/Quantum Fest 2019 23 equations

2 2 −∂x + V (x) u (x) = −λ u (x) (5a) 2 2 −∂x + W (x) v (x) = −λ v (x) (5b) 2 2 where V (x) := q − ∂xq, and W (x) := −∂xq − q are their corresponding potentials, and

u := n1 + in2, v := n1 − in2. We identify equations (5) as supersymmetric partners. Note that the construction of supersymmetric partners can also be done by means of the Darboux transformation [1,2]. In this work we analyse the dispersion states and the resonance states of system (5) by means of the Spectral Parameter Power Series method [3] and we link this spectral information with the Zakharov-Shabat system (4).

[1] Cooper F, Khare A, Sukhatme U. Supersymmetry and quantum mechanics. World Scientiﬁc Publishing Co. ELSEVIER: Singapore, 2001.

[2] Kravchenko V V, Torba S M. Transmutations for Darboux transformed operators with applications. Journal of physics A: Mathematical and Theorical; 45: 1-21,2012.

[3] Kravchenko V V, Porter R M. Spectral parameter power series for Sturm–Liouville problems. Math. Method App. Sci. 33: 459-468, 2010.

[4] Kravchenko V V, Velasco G U. Dispersion equation and eigenvalues for the Zakharov-Shabat system using spectral parameter power series. Journal of mathematical of physics; 52: 063517 1-063517 8, 2011.

[5] Zakharov V E, Shabat A B. Exact theory of two-dimensional self-focusing and one-dimensional self- modulation of waves in nonlinear media. Soviet Physics JETP, 34: 62-69, 1972. ————————————————————————————————————————–

Beam propagation in anisotropic inhomogeneous media

Juan L´opez, Physics Department, Cinvestav, Mexico

Email: jlopez@ﬁs.cinvestav.mx

Abstract: Anisotropic media have electromagnetic or mechanical properties that depend on the direction of propagation of some perturbation, or wave, inside them. In this work we are interested in the case of optical anisotropy, that is, roughly saying, in studying media whose refraction index is not rotary invariant.

A very ﬁrst example of anisotropic medium that we usually ﬁnd is the calcite. Some ex- periences with calcite show that we have to distinguish between ordinary and extraordinary polarization. Light propagation in calcite can be described by considering it as a homogeneous medium. Although the homogeneous case is well known, this is not the case for inhomogeneous optical anisotropy. Some exceptions consider ray optics approach. In this work, we construct solutions to Maxwell equations for an inhomogenous anisotropic medium whose refraction index is to be determined as part of the solution of the problem. This is done by using usual techniques of mathematical physics. 24 Quantum Fest 2019/Booklet Of Abstracts

How complex is the nucleus? Entropy of nuclear states as a tool for a viable response

Leonardo L´opez Hern´andez, Facultad de Ciencias, UNAM, Mexico

Email: leonardo.physic [email protected]

Atomic nuclei are chaotic systems according to the statistics of their energy spectrum. The behavior of such a spectrum of energies as a time series is characterized by the power spectrum 1/f ratio , however, these chaotic properties can also be observed in the behavior of the entropy of information of the probability amplitudes of the basis states. This exercise is shown here. ————————————————————————————————————————–

Bound states in the continuum in Darboux-deformed potentials

Leonardo L´opez Mejia, UPIITA-IPN, Mexico

Email: [email protected]

A general method for constructing von Neumann-Wigner potentials is presented. The method consists in using a scattering solution of an arbitrary short range potential as a transformation function in a degenerated version of the second order Darboux transformation. After the continuity of the solutions is guaranteed, it is shown that the resulting system, in addition to its set of bound and scattering states, contains a square integrable wave function associated to an energy eigenvalue belonging to the continuous part of the spectrum. In the last part of this work, the nature of the bound state in the continuum is investigated. ————————————————————————————————————————–

Geometric approach to the three-qubit system entanglement

Salvio Luna Hern´andez, Physics Department, Cinvestav, Mexico

Email: sluna@ﬁs.cinvestav.mx

Abstract: We revisited the entanglement three-qubit polytope formalism, where non-local properties are studied from a purely geometric perspective. For instance, information about entanglement is encoded in the elements of this polytope, such as vertices, edges and facets. In this sense, we accomplished a numerical identification of the Acn classes with some specific regions of such a 3D convex body. This framework is also useful to show that the eigenvectors of a pairwise Ising interaction Hamiltonian exhibit only three different types of entanglement. Finally, we briefly discuss the possibility of identifying some elements of the polytope with a class representative state in the correspondent Hilbert space. Booklet Of Abstracts/Quantum Fest 2019 25

Finite-diﬀerences derivative for non-equidistant points and exact for the exponential function

Armando Mart´ınezP´erez, Physics Department, Cinvestav, Mexico

Email: jmartinezp@ﬁs.cinvestav.mx

Abstract: We use a new approach for the discrete derivative on a finite mesh. This proposal is such that it is also an aproximation to the derivative of a function, just as with the usual finite differences method, but with the characteristic that it is exact for a function of our choice. We illustrate the use of the method with the eigenfunction of the derivative which is the exponential function. This last feature is an advantage for defining a discrete operator which acts on vectors defined on a mesh. This proposal is applied in the quantum realm in order to have a meaningful discrete quantum momentum operator. ————————————————————————————————————————–

Quantum chaos in time series of single photons

Benjam´ınMendoza Zarate, FC-UNAM, Mexico

Email: Mithrandir Mz [email protected]

Abstract: ————————————————————————————————————————–

On the spectrum of one-dimensional Schrodinger operators with periodic delta Dirac interactions

Leticia Olivera, UPIITA-IPN, Mexico

Email: [email protected]

Abstract: ————————————————————————————————————————–

Diﬀerential operators with white-noise

Carlos G. Pacheco, Department of Mathematics, Cinvestav, Mexico

Email: [email protected]

Abstract: We study differential operators with random coefficients in terms of the white noise; this includes an operator with a random potential. Using bilinear forms we propose finding explicitly the Green kernel of these operators. To do so we appeal to theory of Sturm- Liouville. 26 Quantum Fest 2019/Booklet Of Abstracts

Electromagnetic analogue of atomic Rabi oscillations

Emmanuel Prez Jaramillo, Secretaria de Marina, Mexico

Email:

Abstract: The formal equivalence between the Helmholtz equation in the paraxial regime and the time-dependent Schrdinger equation is considered in order to explore the possibility of constructing an electromagnetic analogue of atomic Rabi oscillations by means of a curved, multimodal waveguide. This construction would be the ﬁrst step in the design of some low cost laboratory tools, based on optical components, in order to simulate, in practice, this quantum phenomenon. ————————————————————————————————————————–

Electromagnetic propagation in spectrally designed open waveguides

Rub´enRazo Ch´avez, UPIITA-IPN, Mexico

Email: razo [email protected]

Abstract: The analogy between Classical Optics and Quantum Mechanical phenomena is discussed. The optical intensity and the optical intensity current carried by a light beam are identified with the probability density and the probability density current in quantum mechanics. The continuity and the square integrability conditions in the Helmholtz equation are fulfilled under some circumstances. The analysis of short-range potentials, and the deter- mination of the bound, scattering and resonance states, and their optical analogous, namely the guided, radiation and leaky modes of waveguides is presented. Finally, as illustrative examples, the cases of the some cut-off quantum mechanical potentials and diverse graded index optical waveguides are analyzed. ————————————————————————————————————————–

Description of quantum systems in terms of an analogy with electromagnetic signals within a stratiﬁed medium

Alejandro Romero, Physics Department, Cinvestav, Mexico

Email: aromero@ﬁs.cinvestav.mx

Abstract: In this work we explore the relation between two systems inherently distinct: electromagnetic propagation and absorption/scattering by a quantum potential well. These, respectively classical and quantum systems, may be understood one in terms of the other by a simple analogy. The study of this analogy, interesting as it is, has the additional motivation of providing a mean to verify quantum phenomena using classic experiments which are easier to set up in a laboratory. Booklet Of Abstracts/Quantum Fest 2019 27

Chemical Synthesis of lanthanide doped BiFeO3-based perovskite photocatalyst for dyes degradation applications

Daniela Vargas Romero, ESIQUIE-IPN, Mexico

Email: [email protected]

Abstract: Bismuth ferrite (BiFeO3 or BFO) it is one of the most studied perovskites due to its properties . In this work we are going to evaluate the inﬂuence of the microwave assisted- hydrothermal synthesis method on the microstructural characteristics of the BFO and its doping with Ce, Pr and Nd, as well as the metal deposition approach looking forward to its application in heterogeneous photocatalysis. Structural and microstructural features will be characterized using X-ray diﬀraction (XRD), scanning electron microscopy (SEM) and elemental mapping (EDS). The rhodamine-B (RhB) and methyl orange degradation reaction under visible radiation conditions was monitoring with UV-Vis spectrometry. ————————————————————————————————————————–

The Quantum Signature of Fundamental Symmetries in Magnetic Spectroscopic Measure- ments

Ver´onicaVillegas, UPIITA-IPN, Mexico

Email: [email protected]

Abstract: Quantum, as well as, classical physics phenomena, can reveal, in measurements, fundamental symmetries as rotation, translation, parity and spin characteristics. If a change x to x + ∆x, or a t to t + ∆t, or a θ to θ + ∆θ is performed on a quantum system, then a change in its wave function is or is not realized, then the quantum system is invariant under such transformation, or it is not. Magnetic systems such as nanomagnets, spin qbits, su- perconducting electron pairs, monolithic sets of magnetic moments show particular, complex behaviors of their wave functions and energies when they are rotated by an θ angle, be it small or a complete 2π turn, or 2πn turns. In particular, the 2π rotation about an azimuthal axis should leave invariant the quantum magnetic state due to the topology of this regular 3 − D space we live in. In addition to rotation symmetry, there exists also the anisotropic response of a magnetic quantum system, since the vector magnetization (or spin magnetic moment) interacts, strongly, anisotropically with ﬁrst, second, third order neighbouring magnetic moments and intrinsic and extrinsic electromagnetic ﬁelds.

Both, rotational symmetry and anisotropic interactions are strongly tangled in magnetic materials beyond any structural arrangement of atoms (and structural symmetry), since both appear in absolutely random solid state arrangements of magnetic atoms. Here we show FMR measurements that show the presence of strong axial anisotropy and at the same time invariance of the quantum state under 2π azimuthal rotation for amorphous magnetic micrometric cylindrical materials. We also show the apparent breaking of this rotational symmetry in other amorphous magnetic samples. The anisotropic behaviour is the same in both types of samples. Both eﬀects are disentangled, their quantum signatures are indicated clearly and interpretation of the apparent 2π rotation symmetry breaking is build upon the existence of low laying, long lived, metaestable magnetization states. 28 Quantum Fest 2019/Booklet Of Abstracts

. Booklet Of Abstracts/Quantum Fest 2019 29

ATTENDANTS

Aguilar Mirn Alberto (IPN)

Ak Kob Rodrguez Alix (IPN)

Albarran Gandara Jess Eduardo (IPN) lvarez Alejandro (UPIITA-IPN) lvarez Lizeth (ESIME-IPN) lvarez Morales Jorge Luis (UPIICSA-IPN) lvarez Julio (UPIITA-IPN)

Andrade Hidalgo y Costilla David Emigdio (UNAM)

Angeles Ballesteros Andrea Carolina (ENCB-IPN)

Arce Ontiveros Arturo (ESIME-IPN) vila Snchez Christian (ESCOM-IPN)

Becerra Garca Eduardo (Physics Department, Cinvestav)

Bucio Ibarra Aldo Misael (UPIITA-IPN)

Camarena Rodrguez Alberto (UPIITA-IPN)

Campos Quiroz Angeles (UPIITA-IPN)

Canseco Jimnez Sahory Andrea (IF-UNAM)

Cantera Jose (FC-UNAM)

Carbajal Gasca Alin Denis (ESIME-IPN)

Carbajal Gmez Karime Bertha (ESIME-IPN)

Carmona Cruz Mariana (UPIITA-IPN)

Carrillo Garca Axel (ESFM-IPN)

Cosme Trujillo Tunnik (UPIBI-IPN)

Castaon Mndez Rodrigo (CIC-IPN)

Espinosa Rodrguez Jos Luis (ESIME-IPN)

Fajardo Granados Dayra Gabriela (UPIITA-IPN)

Fernndez Lizrraga Mariana del Carmen (ENCB-IPN)

Galvn lvarez Aketzali (UPIBI-IPN)

Gamboa Vzquez Ariel (Tecnolgico de Monterrey)

Garca lvarez Vctor Fernando (ESE-IPN)

Garca Merino Jair (ESM-IPN) 30 Quantum Fest 2019/Booklet Of Abstracts

George Jurez Bibiana Ivett (UPIITA-IPN)

Graca Beltrn Geselle (ESIME-IPN)

Graca Villa Esbeydy Elizabeth (ESIME-IPN)

Gonzlez Ayala Marcos (UPIITA-IPN)

Gonzlez Martnez Miguel de Jess (ICN-UNAM)

Gonzlez Serrano Luis (UPIITA-IPN)

Gonzlez Pardo Adrian (ESCOM-IPN)

Gudio Fabela Jos Esteban (UPIITA-IPN)

Guzmn Boris (ESIQUIE-IPN)

Gutirrez Lpez Gerardo Jess (ESIA-IPN)

Hernndez Salvador Gallardo* (Physics Department, Cinvestav)

Hernndez Cristopher (FC-UNAM)

Hernndez Amador Mauro Killary (ESIME-IPN)

Hernndez Ramrez Mario (ESIME-IPN)

Herrera Fernando (ESIME-IPN)

Huerta Bobadilla Leslie Beln (IPN)

Hurtado Aviles Eric Abraham (ESIME-IPN)

Ixtepan Samantha (ESIME-IPN)

Jacome Carlos (ESIME-IPN)

Jaimes Najera Jonathan (ESFM-IPN)

Jorge Coto Eylin (UPIICSA-IPN)

Leana Amaro Jessica (ESIA-IPN)

Lluis Aceﬀ Esteban (FC-UNAM)

Lpez Frida (IPN)

Luna Martnez Mayra Margarita (UPIBI-IPN)

Magos Cortes Daniela (Physics Department, Cinvestav)

Maldonado Sifuentes Christian (CIC-IPN)

Martnez Gonzlez Andrea (ESIME-IPN)

Martnez Sptimo Abissaid (ESIQUIE-IPN)

Matas Lpez Jess (UPIICSA-IPN)

Mayrn Francisco (ESIME-IPN) Booklet Of Abstracts/Quantum Fest 2019 31

Melendrez Cedillo Javier (ESIME-IPN)

Mendoza Arango Ivn Manuel (UPIICSA-IPN)

Mercado Mario Alberto (CIDETEC-IPN)

Mireles Prez Maria Caridad (UPIBI-IPN)

Montes Gmez Edgar Adhair (ESIME-IPN)

Morales Meza Lourdes Georgina (ESIA-IPN)

Morelos Garnica Loreley Araceli (ENCB-IPN)

Mundo Franco Katia (ENCB-IPN)

Muoz Ruiz Ulises (UPIITA-IPN)

Neri Cruz Juan Ernesto (ENCB-IPN)

Olguin Garca Alma Patricia (ESIME-IPN)

Olvera Vldez Marycruz (ESIQUIE-IPN)

Onofre Soto Ana Laura (UPIITA-IPN)

Parada Ortega Luis Enrique (ESIME-IPN)

Peralta Mendoza Jennifer Daniela (UPIITA-IPN)

Prez Garca Jos de Jess (ESIME-IPN)

Prez Mendoza Alan (IPN)

Prez Rodrguez Diana Paola (UAM-Xochimilco)

Pia Spezia Horacio (ESIQUIE-IPN)

Proa Cintia (UPIBI-IPN)

Rabadan Ortiz Adrian (UPIITA-IPN)

Ramos Gmez Elisa (ESCOM-IPN)

Ramrez Montalvo Irene Berenice (ESCOM-IPN)

Ramrez Reyna Omar (ESIME-IPN)

Ramrez Torrijos Mauricio (ENMH-IPN)

Ros Prado Rosario (UPIITA-IPN)

Rivero Salgado Gloria Manuela (ENCB-IPN)

Roa Bohrquez Karol Lizbeth (CICATA-IPN)

Rodrguez Martnez Claudia (ENCB-IPN)

Rodrguez Rodrguez Alejandro (CICATA-IPN)

Rojas Guerrero Diana Laura (ENCB-IPN) 32 Quantum Fest 2019/Booklet Of Abstracts

Rueda Maria (ESFM-IPN)

Snchez Caldern Jess (ESIME-IPN)

Surez Gerardo (Physics Department, Cinvestav)

Luis Fernando Subieta (UPIITA-IPN)

Tinoco Silva Ana Isabel (UPIICSA-IPN)

Tamayo Celada Diana Nadia (ENCB-IPN)

Urbano Altamirano Francisco (Physics Department, Cinvestav)

Valencia Hernndez Joel Eduardo (IPN)

Vldez Melani (ESCOM-IPN)

Vargas lvarez Vctor Emiliano (ENCB-IPN)

Vargas Axel (UPIITA-IPN)

Vega Vzquez Dario (ESIME-IPN)

Zuiga Martnez Montserrat de Jess (ESIME-IPN)

*(Faculty) Index Alan Anaya, 15 Kevin Zelaya, 14 Alejandro Romero, 22 Kurt Bernardo Wolf, 8 Alfonso Jaimes Nájera,11 Alonso Contreras Astorga, 10 Leonardo López Hernández,20 Armando Mart´ınezPérez, 20 Leticia Olivera, 21 Attendants, 23 Luis Alberto Jaramillo Ben´ıtez,18

Benjam´ınDavid Mendoza Zarate, 21 Marco Enr´ıquez,11 Blas Manuel Rodr´ıguez Lara, 5 Mariana Vargas Magaa, 13 Brenda E. Jimenez-Ramos, 18 Pedro Jiménez, 12 Bruno GonzálezSoria, 17 Piotr Kielanowski, 2 Plenary talks, 1 Carlos Cardoso Isidoro, 15 Posters, 15 Carlos G. Pacheco, 21 Pranjal Agarwal, 15 Carlos Torres-Torres, 7 Celia Escamilla Rivera, 1 R. Castillo-Prez, 9 Christian Louis Hanotel Pinzón,17 Raymundo Conde Vazquez, 16 Claudia Quintana, 13 Roberto de J. Len-Montiel, 4 Contribution talks, 8 Rosario Paredes Gutirrez , 5 RubénRazo Chávez, 22 Dalia GutiérrezLópez, 17 Daniela Vargas Romero, 22 Salvio Luna Hernández,20 Diego Lara, 19 Samantha Loredo, 19

Eduardo Nahmad-Achar, 4 VéroniqueHussin, 2 Emmanuel Prez Jaramillo, 21 V´ıctorA. Vicente Ben´ıtez,13 Eric Rowell, 7 V´ıctorBarrera-Figueroa, 9 Erick Barrios Barocio, 8 V´ıctorVelázquez,7 VerónicaVillegas, 23 Fernando Olivar Romero, 12 Vladimir Rabinovich, 6 Francisco Delgado, 1 Vladislav V. Kravchenko, 2

GastónGarc´ıaCalderón,1 Zulema Gress Mendoza, 11 Gerardo JiménezTrejo, 18 Zurika Blanco, 8 Guillermo Morales-Luna, 12 Gustavo ArmendárisPea, 15

H´ectorMoya-Cessa, 4 Haret Rosu, 6 Heber Zepeda-Fernndez, 14 Hugo Ivan Fernndez Cid, 16

Jonatan Gamboa, 16 Juan J. Rosales Garc´ıa,6 Juan L´opez, 19