A Space-Time Odyssey: Taming Exceptional Points in Elastodynamics for Sensitivity and Emissivity Enhancement

Geometric symmetries—such as translation, rotation, mirror, and fractal symmetries—are commonly found in nature and are utilized often in architecture and engineering as well as for realizing photonic crystals, phononic crystals, and metamaterials. The dynamical (hidden) symmetries—such as time-reversal symmetry and parity-time (PT) symmetry—however, are not apparent in the system geometry and instead require a careful analysis of the equations of motion describing the dynamic behavior of the system to recognize them. Incorporation of such dynamical symmetries and their violations at certain critical points—known as Exceptional Point Degeneracies (EPDs)—of the parameter space that control the system behavior can lead to intriguing and unusual consequences that have utility in engineering. The EPD is a spectral singularity where two or more eigenvalues and the corresponding eigenvectors of a non Hermitian system coalesce. One of the unique features of these EPDs is the sublinear approach of the modes towards the EPD. Hence, it has been exploited to create hypersensitive electronic, optical, microwave, acoustic, electromechanical, and elastodynamic sensors depending on the framework in which they are implemented. I will first present our studies on the character of EPD emergence where we examin PT-symmetric quasiperiodic, aperiodic, and fractal metastructures. They exhibit scale-free emergence of EPDs in their unfolding (fractal) spectra, suggesting that there are underlying universal rules that govern the emergence of EPDs in such non-Hermitian elastodynamic systems. These governing rules could facilitate the design and experimental realization of EPDs. Next. I will present a novel utilization of EPDs, where we demonstrate experimentally for the first time that the eigenvector degeneracy (EVD) associated with the EPDs can lead to an anomalous emissivity enhancement of a source when it is brought at the proximity of an EPD. Damping is commonly used as a design element to attenuate signals, i.e., mechanical waves and vibrations, in engineering systems. However, in this case, we use damping in an entirely passive system to amplify signals at the proximity to EPDs. Our study shows that incorporation of EPDs into mechanical systems such as MEMS resonators, nano-/AFM-indenters, and robotic actuators provides a new pathway to further boost the actuation power by four-fold while maintaining signal quality—importantly by entirely passive means with no gain/amplification elements.

Bio. Prof. Ramathasan Thevamaran received his B.Sc.Eng.(Hons.) (2008) in Civil Engineering from the University of Peradeniya, Sri Lanka, and his M.S. (2010) and Ph.D. (2015) in Mechanical Engineering from the California Institute of Technology, CA. Prior to joining the University of Wisconsin-Madison in 2017, he was a Postdoctoral Research Associate at the Department of Materials Science and Nanoengineering of Rice University, TX. His research focuses on (i) developing a fundamental understanding of the process-structure-property-function relations in structured materials, and (ii) creating innovative structured materials with superior specific properties and novel functionalities for extreme engineering applications. He is the recipient of 2022 Early Career Faculty Award from NASA, 2022 Innovation Award from the Wisconsin Alumni Research Foundation, and 2021 Ferdinand P. Beer and E. Russel Johnston, Jr. Outstanding New Mechanics Educator Award from the American Society for Engineering Education.

Karina Garay-Palmett (CICESE)

Quantum light sources and the implementation of an integrated photonic platform for quantum technology applications

The second quantum revolution is emerging. The era in which the principles of quantum mechanics are applied to developing new technology, such as quantum computing, communications, metrology, and simulation. It is recognized that photonic quantum systems play an essential role  in implementing this type of technology, which is why different photonic platforms are being proposed and demonstrated. This talk will focus on the processes that lead to generating and controlling nonclassical light, particularly single-photon, two-photon, and squeezed states, and the advances we have made in the experimental implementation of such light sources; the first studying the properties of single emitters and the last two exploiting the third-order nonlinearity of optical fibers and integrated waveguides. On the other hand, the advancements in developing photonic integrated circuits for applications in quantum technologies will be described. The proposed integrated platform is based on silicon nitride waveguides on silicon dioxide on a silicon substrate. The study includes theoretical, numerical, and experimental work and covers a research object that involves various areas, such as nonlinear optics, quantum optics, quantum information, materials science, and micro and nanofabrication. In the medium term, the goal is to demonstrate the generation of squeezed vacuum states and photonic qubits on a temporal mode basis and the implementation of quantum gates based on the frequency difference generation process.

Benoit Seron (Uni-Freiburg)

Multiphoton interference, boson sampling, and boson bunching

Abstract: One of the most well publicized feats of quantum information is the achievement of a "quantum advantage" by photonic experiments. In this talk, we will introduce the concepts of multiphoton interference, with particular interest to the subtleties of photonic distinguishability. A natural application, called boson sampling and its extensions will be discussed. It presents a direct quantum equivalent to table-top Galton board experiment. A surprising result, at the interface between the mathematical theory of matrix permanents and bosonic physics will be discussed in detail as an example of the concepts introduced in this talk: against a commonly held rule of thumb, we will show that boson bunching is not maximized by indistinguishable particles.

Bio. Benoit Seron is postdoctoral researcher at the Albert-Ludwigs-Universität Freiburg, in the group of Quantum Optics and Statistics, under the supervision of Prof. Andreas Buchleitner. I finished my PhD in the University of Brussels, under the supervision of Prof. Nicolas Cerf. I studied applied mathematics in the University of Cambridge, and theoretical physics in the University of Brussels

Gernot Alber (TU Darmstadt)

Detection of typical bipartite quantum correlations by local generalized measurements

Detection of genuine quantum correlations, such as entanglement or steerability, by quantum measurements, which can possibly be performed locally by far distant observers, are of particular interest for applications in quantum information processing, in particular for quantum key distribution and quantum communication. In this context the natural question arises how does the effectiveness of detecting such genuine quantum correlations depend on the nature of local quantum measurements  and on the dimensionality of the quantum systems involved for typical, randomly selected quantum states. In this talk current activities are discussed which address this question. In particular, recent results [1,2] are presented which address this question by exploring basic properties of commonly used sufficient conditions for entanglement- and steerability-detection of arbitrary dimensional bipartite quantum systems  based on correlation matrices and joint probaility distributions [3]. In order to explore characteristic features of their dependence on the nature of the local quantum measurements generalized quantum measurements based on informationally complete positive operator valued measures(POVMs)  of the so called (N,M)-type are discussed. These recently introduced .(N,M)-POVMs [4] are capable of describing various important generalized quantum measurements in a unified way, including mutually unbiased measurements and symmetric informationally complete measurements and their generalizations. It turns out that  symmetry properties of (N,M)-POVMs imply that sufficient conditions for bipartite entanglement- or steerability-detection exhibit characteristic scaling properties which relate different equally efficient local quantum correlation detection scenarios. In order to access the effectiveness of local entanglement- or steerability-detection for bipartite quantum states of different dimensions numerical results on Euclidean volume ratios between locally detectable entangled or steerable states and all bipartite quantum states are presented, which are based on a recently developed hit-and-run Monte-Carlo algorithm [5,6].

Bio. Gernot Alber is a professor of Theoretical Physics at the Technische Universit ̈at Darmstadt since 2002. He got his PhD and Habilitation at the Universität Innsbruck, and was Assistant Professor in the University of Freiburg. He has more than 150 publications and his fields of specialization are Theoretical Quantum Optics, Quantum Information Theory, and Foundations of Quantum Theory.

Jorge Garza Olguín (DQ-UAM-I)

Software ad-hoc to analyze the electronic structure of confined systems

It is recognized that the electronic structure of atoms and molecules is modified when physical restrictions confine such systems. Unfortunately, the computational tools developed for free systems are inadequate for these problems since the corresponding boundary conditions are not incorporated correctly, or they were not considered in developing the software. Thus, in our laboratory, we have been designing software to study the electronic structure of confined atoms enclosed by hard or soft walls. Such techniques solve Hartree-Fock or Kohn-Sham equations to obtain electron density, orbitals, and total energy. Additionally, we have developed software to determine intermolecular interactions formed between molecules and cages involved in the confinement. In this talk, some details of the mentioned software are mentioned, and the applications aborded until now are discussed. Perspectives about confined systems are also mentioned at the end of the talk.

Bio. Jorge Garza received his Ph.D. in chemistry from the Universidad Autónoma Metropolitana Campus Iztapalapa. As part of his academic background, Jorge Garza was involved in two important projects for quantum chemistry: a) NWChem, from the Pacific Northwest National Laboratory in the USA. b) CRYSTAL, from the Università degli Studi di Torino in Italy. The aim of these projects is related to parallel programming techniques. Jorge Garza has published more than 120 JCR articles, which have received more than 5000 cites, and in the last years, he has developed quantum chemistry programs using GPUs.

Emerson Sadurní (IFUAP)

Controlling superconducting qubits for quantum computing

Quantum computers have the potential to solve complex problems efficiently. However, to unleash their full capability, complex quantum systems have to be manufactured, manipulated and measured with unprecedented accuracy and precision. In this presentation I will focus on superconducting qubits as one of the most promising platforms for quantum computing. To enhance their quantum processing capabilities we have systematically optimized the material parameters and reached several hundred microseconds coherence times. Furthermore, we have investigated optimal control methods and demonstrated high-fidelity single and two-qubit gates. Finally, by simultaneously coupling multiple qubits we could realize multi-qubit operations to efficiently create many-body entangled state. As a specific example I will demonstrate a fractional state transfer protocol on a chain of superconducting qubits and discuss its potential use case for quantum simulations and parity readout.

Bio. Stefan Filipp has been appointed Professor in Technical Physics at the Technical University of Munich and Director of the Walther-Meissner-Institute of the Bavarian Academy of Sciences and Humanities in 2020. Before he has led the superconducting qubit team at the IBM Research – Zurich Laboratory to develop architectures for quantum computing based on superconducting circuits. He has joined IBM in 2014 as permanent research staff member of the experimental quantum computing team at IBM T.J. Watson Research lab in Yorktown Heights, NY, US. His degree in physics he has received from the Vienna University of Technology, Austria, and the Uppsala University, Sweden for his studies on quantum geometric phases effects, for which he was awarded the Victor-Hess Award. He then worked as Postdoc and later Senior Researcher on quantum computing, quantum simulation and quantum optics with superconducting circuits at the ETH Zurich. In 2020 he has been nominated as co-chair of the 'Quantencomputing' expert panel of the German Chancellery. He is currently leading a collaborative research project on building a German quantum computer based on superconducting qubits as part of the Munich Quantum Valley.  

Eduardo Gómez García (IF-UASLP)

Towards Mexican Quantum Technologies 

Over the last 4 years there has been a systematic discussion on the most effective way for Mexico to enter the Quantum Technologies market within the Quantum Information Division of the Mexican Physical Society, which resulted in the Mexican Quantum Technologies Initiative. It takes into account the capabilities and existing infrastructure in the country to identify niches where we can make a relevant contribution. An example of this is the case of atomic gravimetry that has applications in underground exploration and monitoring of seismic, vulcanological and structual risk, all of them of particular interest for the country. The existing scientific community in Mexico is mature enough to make the transition towards generating novel Quantum Technologies. 

Bio. Since 2018, I am an Associate Professor at the Chemistry Faculty at the National Autonomous University of Mexico (UNAM) with eight years of experience in the study of transport theory of low dimensional systems. After getting the PhD degree in Physics at the UNAM in 2013, I worked three years as a postdoc at the Catalan Institute of Nanoscience and Nanotechnology in Barcelona (ICN2) under the supervision of Prof. Dr. Habil. Stephan Roche. After those years, I got a FONDECyT postdoctoral fellowship at the University of Chile under the supervision of Dr. Luis E. F. Foa Torres. Now, I am actively involved in research projects concerning Floquet Topological Insulators, Higher order Topological Insulators and Non-Hermitian Topological Insulators.

Pedro Pereyra Padilla  (CB-UAM-A)

The Theory of Finite Periodic Systems

I will start with a brief reflection on the Bloch Theory drawbacks and some specific high-resolution experimental results on transport and optoelectronic properties in superlattices. I will then present the general formalism of the Theory of Finite Periodic Systems, closed analytical expressions in the quasi-one-dimensional limit, and specific calculations using this approach to explain the experimental results.

Bio. Pedro Pereyra Padilla is a distinguished professor at UAM. Ph.D. from UNAM, Mexico, post-doctorate at Max-Planck Institut für Kernphysik, Heidelberg. Coauthor of the Theory of Nuclear Reaction, the Poisson distribution of Scattering Matrices. Coauthor of the Multichannel Approach to Disordered Conductors, the DMPK Equation. Author of important extensions to the Theory of Finite Periodic Systems and of several publications devoted to electronic transport and optoelectronics.

Rafael A. Méndez (ICF-UNAM)

Emulating Molecular and Condensed Matter Physics with coupled-resonator elastic structures

The coupled-resonator elastic structures, introduced some years ago by our group, consist of resonators coupled through finite phononic crystals. These structures are called elastic meta-atoms when the normal-mode frequency of a resonators falls within a forbidden band of the couplers. In this case the elastic waves localize in the resonators and decay evanescently through the couplers. The trapped vibrations mimic the quantum-mechanical p_z orbitals and are called atomic elastic meta-orbitals. This phenomenology of the meta-atoms emulates the tight-binding regime of Condensed Matter Physics and the Hückel model of Molecular Physics. When some elastic meta-atoms are coupled through the finite phononic crystals the elastic meta-molecules are obtained and the atomic elastic meta-orbitals couple one to each other resulting in molecular elastic meta-orbitals. In this talk novel applications of the coupled-resonator elastic structures in linear and aromatic molecules will be presented. Topological states, equivalent to those of Solid State Physics, also emerge in the tight-binding elastic regime.

Bio. Dr. Rafael Mendez is Professor at Instituto de Ciencias Fisicas, UNAM in Cuernavaca Morelos. He made his studies at Facultad de Ciencias, UNAM at CMDX obtaining the Alfonso Caso Medal for his Ph. D. He realized a posdoc at the University of Essen and a sabbatical stay at the Universidad Politecnica de Valencia. He obtained, the 2003 UAM research medal by a collaboration with Dr. Gabriela Baez. He is expert in absorption and coupling of waves with the exterior. He created the Laboratory of Waves and Metamaterials and is founder of the Multi-institutional group of the same name

Hans-Jürgen Stöckmann 

(Universität Marburg)

A spectral duality in graphs and microwave networks

Quantum graphs have been proposed by Kottos, Smilansky [1] as an ideal tool to study the spectral statistics of chaotic systems. There is a one-to-one correspondence between a quantum graph and a correspondingly shaped microwave network, which had been used by Sirko and coworkers [2] in a number of papers for the study of spectral statistics and fluctuation properties of graphs. In our own group we used a microwave graph with a particular symmetry mimicking a spin 1/2 to study the spectral statistics of the Gaussian symplectic ensemble [3]. In a three-terminal graph we studies transport properties and compared them with random matrix predictions [4].  Nobody doubted that the spectral properties of graphs are correctly described by random matrix theory, when we recently came across a phenomenon casting serious doubts on this assumption. Depending on the boundary conditions at the vertices there are Neumann and Dirichlet graphs, the first ones realized in experiments and assumed in most theoretical studies. Dirichlet graphs, on the other hand, correspond to completely disintegrated graphs with spectra being the superposition of the spectra of the individual bonds with Dirichlet boundary conditions at both ends. Due to the interlacing theorem [5] Neumann and Dirichlet spectra are strongly correlated, with the consequence that contrary to widespread belief the statistics of the Neumann spectrum is not correctly described by random matrix theory but adopts features of the interlacing Dirichlet spectrum [6]. This is illustrated by microwave studies and numerics.

Bio. Professor Hans-Jürgen Stöckmann studied physics at Heidelberg University , received his doctorate there in 1972, and got his habilitation in 1978. Since 1979, he has been a Professor at the University of Marburg, now retired. He has fostered the field of quantum chaos and the development of microwave experimental techniques for its study. He received the Leopoldo García-Colín Medal in 2016.

César Cabrera (UHH)

Quantum simulation with ultracold Fermi gases

Quantum simulation with ultra-cold atomic gases has emerged as a powerful tool for studying complex quantum phenomena and addressing fundamental questions in condensed matter physics. In the first part of my talk, I will provide an overview to understand the fundamental principles of quantum simulation and why cold atoms are the ideal platform for these experiments. I will introduce the different cooling techniques used to bring atoms to ultracold temperatures, enabling us to observe quantum effects. In the second part, I will focus on ultracold Fermi gases as a platform for studying the evolution of a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. I will present recent measurements of the low-energy excitation spectrum of strongly interacting Fermi gases and the rich physics of imbalanced Fermi gases in low dimensions. 

Bio. Dr. Cabrera earned his Ph.D. in photonics from ICFO - The Institute of Photonic Sciences in Barcelona, under the supervision of Prof. Leticia Tarruell. During his doctoral research, he pioneered the field of quantum simulation in Spain using ultracold quantum gases. His significant contributions include the design and construction of a quantum simulator and the first observation of a Bose-Einstein condensation (BEC) in Spain. Additionally, he achieved the observation of a dilute quantum liquid droplet in a two-component BEC, which opened a new research direction in the field of ultracold quantum gases. Following his Ph.D., Dr. Cabrera moved for a postdoctoral position at the Max Planck Institute of Quantum Optics in Munich, Germany, working in the group led by Prof. Monika Aidelsburger and Prof. Immanuel Bloch. During this time, he took a leading role in the development of a quantum gas microscope capable of imaging and controlling individual atoms in an optical lattice. Throughout his career, Dr. Cabrera has made notable contributions to the field, resulting in impactful research papers published in esteemed journals, such as Nature and Science. His accomplishments have earned him various awards and fellowships, including the Best ICFO PhD thesis award in 2018 and the prestigious Marie Curie postdoctoral Fellowship. Presently, Dr. Cabrera serves as the coordinator of the CUI graduate school at the University of Hamburg and holds the position of senior scientist in the group led by Prof. Henning Moritz. In his current role, he leads research efforts focused on the study of ultracold Lithium Fermi gases in low dimensions.

Salvador Venegas Andraca (ITESM CEM)

Fuzzy Measurements and Coarse Graining in Many-Body Quantum Systems

We investigate fuzzy measurements and coarse graining in many-body systems from a quantum perspective, utilizing the concept of imperfect detectors. In order to address these issues, we employ the language of quantum channels, whose foundations will be reviewed during the presentation. We demonstrate how to consider various geometries adaptable to a wide range of experimental situations. Furthermore, we characterize these channels and find that the observable state space contracts dramatically with the number of particles. If time allows, we will discuss relevant advancements pertaining to the observed effective dynamics and the entropy associated with observable states.

Bio. Carlos Pineda is a professor at the Institute of Physics, UNAM. He did his bachelor in physics at the National University of Colombia and his Master and Ph.D. studies at UNAM, where he gained the Alfonso Caso Medal. He was the recipient of the Marcos Moshinsky Fellowship in 2016. Among others, his lines of research include quantum optics, quantum information, many body systems, decoherence, and complex systems.

José Luis Hernández Pozos (DF-UAM-I)

 From the traditional Paul trap to a linear trap at the turn of one parameter: A generalization of the trapping potential in electrodynamic ion trap 

From the original Paul trap with hyperbolic electrodes developed in the 1950´s a long way has been covered to include in the description of the trap (e.g) the misalignment of the electrodes or variations in the electrode's shape which leads to the need of including additional octupole or higher order terms in the trapping potential, etc.  These studies have addressed the influence in the stability of the trapped ions and its motional frequencies as the geometry of the trap is changed and , its influence in the use of these devices as mass spectrometers,  tools for ultrahigh resolution spectroscopy and more recently, for the physical implementation of quantum computers. Here we present a generalization of the trapping potential that can encompass most of the different geometry variations studied in the last fifty years for Paul traps and  numerically study the stability zones for this potential when varying a parameter that modifies the geometry of the trap and that can be continuously varied from a normal trap with hyperbolic electrodes to a “squared” trap or an elliptical trap. We present the results of our simulations and the possible implications for the different applications of these kind of devices.

María Gabriela Báez Juárez  (UAM-A)

Tight-binding models for torsional waves in high-quality coupled-resonator phononic metamaterials

Tight-binding models (TBM) were developed in the field of Solid State Physics for the approximate calculation of the electronic band structure of atomic crystals, among other more complex solids. Recently, the validity of these TB-models for obtaining the frequency spectra of certain structured elastic systems has been demonstrated. These consist of arrays of elastic resonators,linked together by locally periodic structures, called coupled resonator phononic metamaterials (CRPM). These elastic wave systems are a type of classical analogue to emulate wave properties of atomic crystals. In this talk presents the model and analytical expressions for the dispersion relationship and the velocity of the group of torsional waves. The results suggest that almost any material described by the tight junction model of solid state physics can be emulated with CRPMs.

Antonio A. Fernández Marín (Tec. Nal. Tehúacan)

Quantum transport quantities: Cross section versus time delay and trapping probability

In this talk, we discuss the behavior of the s-wave partial cross section, the Wigner-Smith time delay, and the trapping probability as function of the wave number $k$. The s-wave central square well is used for concreteness, simplicity, and to elucidate the controversy whether it shows true resonances. It is shown that, except for very sharp structures, the resonance part of the cross section, the trapping probability, and the time delay, reach their local maxima at different values of $k$. In addition, we show numerically that the time delay is positive at its local maxima, occurring just before the resonant part of the cross section reaches its local maxima. We will conclude that different closely related scattering functions do not in general peak at the same $k$ values as the resonant part of the cross section and hence their study offers complementary information about the resonance properties of the system under study.

Bryan Manjarrez Montañez 

Wave transport in elastic metamaterials

Metamaterials have novel physical properties that make them special. We present the design of a 2D metamaterial formed by two small rectangles coupled by a small beam. Using the COMSOL Multiphysics software, we obtain diverse band structures of the metamaterial as a function of the symmetric and antisymmetric positions of the beam that couples both plates. An anisotropic group velocity is obtained around approximately 20 kHz. Managing to control the directionality and speed of propagation of a wave packet. Finally, a metamaterial of finite size is designed, allowing experimental collaborators to experimentally measure the property of the metamaterial.

Hugo Alberto Lara García

Moiré-induced non-linearities: From multi-photon resonance to translational symmetry breaking in driven-dissipative moiré systems

Moiré lattices formed from semiconductor bilayers host tightly localised excitons that simultaneously couple strongly to light and possess a large electric dipole moment. In this talk, we will show that the moiré platforms enable the realization of a new form of polaritons that exhibit strong optical non-linearities controlled by the underlying discrete character of the matter excitations. We will demonstrate the emergence of multi-photon resonances, “discrete” bi-stabilities, the appearance of states with broken translational symmetry, and discuss the role of free carriers on the optical response.

Bio. I graduated with a Bachelor's degree in Physics from UNAM. I pursued my Master's and Ph.D. degrees in the Graduate Program in Physical Sciences under the guidance of Dr. Rosario Paredes. Subsequently, I carried out postdoctoral research at the University of Aarhus in Denmark and the University of Cambridge in the United Kingdom. My areas of expertise lie at the intersection of atomic physics, condensed matter, and quantum optics, with a particular interest in many-body systems and exotic phases of matter in the quantum regime.

Roberto Quezada Batalla (DM-UAM-I)

Weyl moments in quantum Gaussian states

The well known analytical approach to quantum Gaussian states has a combinatorial counterpart, where moments of the field operator (Weyl moments) play a central role. We will discuss on the equivalence of these two approaches to gaussianity in the one-dimensional case, i.e., for the one-mode Weyl representation of the CCR’s. Examples of Gaussian states and channels will be presented.

Bio. Roberto Quezada graduated at the Mathematical Institute of the Polish Academy of Sciences in 1990.  His is currently interested in Quantum Probability and Quantum Markov Semigroups, which are semigroups of completely positive trace-preserving maps.

Thomas W. Stegmann (ICF-UNAM)

Controlling the current flow in 2D materials 

We will discuss several strategies on how to control locally the current flow in 2D materials. In the first part of the talk, we will show that the current in twisted bilayer graphene can be steered through the twist angle and electrostatic gating. The steering is explained by the trigonal shape of the energy bands beyond the van Hove singularity. In the second part of this talk, we will show how to guide the current flow on arbitrary pathways by means of Kekulé-O engineering.  

Bio. Thomas Stegmann did Doctoral Studies at the University Duisburg-Essen in Germany. In 2014 he came as a postdoc to México, working with Thomas Seligman at the Instituto de Ciencias Físicas of the UNAM in Cuernavaca. Since 2016 he is professor for physics at the same institute. His research interests are focuses on the electronic transport in nanostructures.

David Villaseñor (IIMAS-UNAM)

Chaos in a dissipative radiation-matter system 

Quantum technologies are based on quantum-mechanical principles. A paradigmatic system where these principles can be studied is an interacting radiation-matter system. Moreover, an intriguing topic is how chaos affects the quantum systems and the possible repercussions over the quantum applications. In this talk, we will explain the way to characterize the onset of chaos in a dissipative radiation-matter system, the open Dicke model, when dissipation is due to cavity losses. We analyze two case studies where the classical isolated system shows regularity and where chaos appears. To characterize the open Dicke model as regular or chaotic, we study regions of its complex spectrum arranged by the increasing absolute value of its eigenvalues. Our results agree with the Grobe-Haake-Sommers (GHS) conjecture for Markovian dissipative quantum systems, which seem to be universal results for this kind of systems.

José G. Santiago G. 

Spectral deformations with non-orthogonal orbitals

By considering overlaps between nearest-neighbor isolated atomic states, a description of deformed spectra is achieved for systems that range from a dimeric configuration of potential wells up to aperiodic structures with specific spectra, passing through translationally invariant arrays. For the first system, a comparison is made between predictions from a tight-binding model with non-orthogonal orbitals and the experimental spectrum of a pair of ceramic disks succeeding in correctly describing the phenomenon of asymmetric splitting of energy levels. Wannier functions are investigated in this context and are calculated for both the dimeric and periodic cases. The freedom of phase for localization adjustment of the latter functions is illustrated with a pair of examples. A secular equation for the deformed spectrum of a compact set of potential wells enables the engineering of nearly equispaced energy eigenvalues. Then, the concept of an all-electronic clock is briefly discussed and the coherent evolution of wavepackets is presented for a particular aperiodic configuration. Finally, a numerical method for thestudy of transport properties of one-dimensional shifted potentials is introduced. These considerations may be relevant in the miniaturization of artificial crystals as well as in the fabrication of an isochronous electronic device which is estimated to work at higher frequencies than current quartz oscillators.

J. E. Barrios Vargas (FQ-UNAM)

Nanostructured pumped-corner state in a Kagome lattice

Bulk-boundary correspondence establishes the connection between the topological properties of the bulk and the edge states when a boundary is present. However, the boundary can be tailored to tune the appearance of the edge states. Using a higher-order topological Hamiltonian, we engineered the appearance of a one-corner state that can be translated between corners with a periodic parameter. As a result, we established that this is a pumping mechanism. The one-corner state is characterized using the inverse participation ratio, and we establish that the state has a topological invariant associated. Consequently, the state is topologically protected. 

John Alexander Franco