
Spin systems
Spin systems serve as an interting and minimal testbed for studying quantum manybody systems, and quantum chaos. Such systems are very valuable to provide a link between general ideas, and real live scenarios, where one must really search conditions under which these ideas can be realized.
In particular, we often use a kicked set of spin 1/2 particles that can be coupled in a very flexible way. This has allowed us recently to study several indicators of complexity, and even though we found large regions where such indicators are inconsistent [1]. We have also used such systems as nonconventional environments to study the effects of nested environments, of the evolution of entanglement under decoherence.
 C. GonzálezGutiérrez, E. Villaseñor, C. Pineda, and T. ~H. Seligman, “Stabilizing coherence with nested environments: a numerical study using kicked Ising models,” Phys. Scr., vol. 91, iss. 8, pp. 83001, 2016.
[Bibtex]@ARTICLE{2015arXiv151207683G, author={Gonz\'alezGuti{\'e}rrez, C. and Villase{\~n}or, E. and {Pineda}, C. and Seligman, T.~H.}, title = "{Stabilizing coherence with nested environments: a numerical study using kicked Ising models}", journal = {Phys. Scr.}, note = {arXiv:1512.07683}, primaryClass = "quantph", keywords = {Quantum Physics}, volume={91}, doi = {10.1088/00318949/91/8/083001}, number={8}, pages={083001}, url={http://stacks.iop.org/14024896/91/i=8/a=083001}, year={2016}, adsurl = {http://adsabs.harvard.edu/abs/2015arXiv151207683G}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }
 C. Pineda, T. Prosen, and E. Villaseñor, “Two dimensional kicked quantum Ising model: dynamical phase transitions,” New Journal of Physics, vol. 16, iss. 12, pp. 123044, 2014.
[Bibtex]@article{136726301612123044, author={C Pineda and T Prosen and E Villaseñor}, title={Two dimensional kicked quantum Ising model: dynamical phase transitions}, journal={New Journal of Physics}, volume={16}, number={12}, pages={123044}, url={http://stacks.iop.org/13672630/16/i=12/a=123044}, year={2014} }
 C. Pineda and T. Prosen, “Nonuniversal level statistics in a chaotic quantum spin chain,” Phys. Rev. E, vol. 76, pp. 61127, 2007.
[Bibtex]@article{PP2007, Adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System}, Adsurl = {http://adsabs.harvard.edu/cgibin/nphbib_query?bibcode=2007quant.ph..2164P&db_key=PRE}, Author = {Pineda, C. and Prosen, T.}, DateModified = {20080915 11:01:34 +0200}, Doi = {10.1103/PhysRevE.76.061127}, Eid = {061127}, Eprint = {quantph/0702164}, Journal = {Phys. Rev. E}, Keywords = {chaos; Ising model; matrix algebra; quantum computing; quantum theory; random processes}, Pages = {061127}, Publisher = {APS}, Title = {Nonuniversal level statistics in a chaotic quantum spin chain}, Volume = {76}, Year = {2007}, BdskUrl1 = {http://link.aps.org/abstract/PRE/v76/e061127}, BdskUrl2 = {http://dx.doi.org/10.1103/PhysRevE.76.061127}}
 C. GonzálezGutiérrez, E. Villaseñor, C. Pineda, and T. ~H. Seligman, “Stabilizing coherence with nested environments: a numerical study using kicked Ising models,” Phys. Scr., vol. 91, iss. 8, pp. 83001, 2016.

Random matrices in quantum information
Random matrices are a very powerful tool. They have been used to describe the nuclei, chaotic systems, the economy and many other things. We are pioneers in trying to capture the complexity of quantum information systems. We have used this tool to describe the decoherence that affects one, two and an arbitrary number of qubits. We have also used is to fight decoherence. Presently we continue working in a better description of decoherence with random matrix models, and we are starting to use random matrices to describe
density matrices.
Recently we have use them to explore fundamental ideas in quantum metrology. Surprisingly, the developments in quantum metrology assume that we already know the parameter to formulate the best way to measure it. We have uncovered the best way to obtain information about a parameter encoded in a quantum system, without knowing beforehand the value of such parameter.
 E. Martinez, C. Pineda, F. Leyvraz, and P. BarberisBlostein, “Quantum estimation of unknown parameters,” ArXiv eprints, 2016.
[Bibtex]@ARTICLE{2016arXiv160607899M, author = {{Martinez}, E. and {Pineda}, C. and {Leyvraz}, F. and {BarberisBlostein}, P. }, title = "{Quantum estimation of unknown parameters}", journal = {ArXiv eprints}, archivePrefix = "arXiv", eprint = {1606.07899}, primaryClass = "quantph", keywords = {Quantum Physics}, year = 2016, month = jun, adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160607899M}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }
 C. Pineda and T. ~H. Seligman, “Random density matrices versus random evolution of open system,” J. Phys. A, vol. 48, pp. 425005, 2015.
[Bibtex]@ARTICLE{2014arXiv1407.7052P, author = {{Pineda}, C. and {Seligman}, T.~H.}, title = "{Random density matrices versus random evolution of open system}", journal = {J. Phys. A}, volume = {48}, pages = {425005}, archivePrefix = "arXiv", doi = {10.1088/17518113/48/42/425005}, eprint = {1407.7052}, primaryClass = "quantph", keywords = {Quantum Physics}, year = 2015, month = jul, adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1407.7052P}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }
 J. Amaro and C. Pineda, “Multipartite entanglement dynamics in a cavity,” Phys. Scr., vol. 90, pp. 68019, 2015.
[Bibtex]@ARTICLE{2014arXiv1410.3281A, author = {{Amaro}, J. and {Pineda}, C}, title = "{Multipartite entanglement dynamics in a cavity}", journal = {Phys. Scr.}, volume = {90}, pages = {068019}, doi = {10.1088/00318949/90/6/068019}, archivePrefix = "arXiv", eprint = {1410.3281}, primaryClass = "quantph", keywords = {Quantum Physics}, year = 2015, month = oct, adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1410.3281A}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }
 T. Gorin, C. Pineda, and T. H. Seligman, “Decoherence of an $n$qubit quantum memory,” Phys. Rev. Lett., vol. 99, pp. 240405, 2007.
[Bibtex]@article{GPS2007, Author = {T. Gorin and C. Pineda and T. H. Seligman}, Doi = {10.1103/PhysRevLett.99.240405}, Eid = {240405}, Eprint = {arXiv:quantph/0703190}, Journal = {Phys. Rev. Lett.}, Pages = {240405}, Title = {Decoherence of an $n$qubit quantum memory}, Volume = {99}, Year = {2007}, BdskUrl1 = {http://dx.doi.org/10.1103/PhysRevLett.99.240405}}
 H. Kohler, I. E. Smolyarenko, C. Pineda, T. Guhr, F. Leyvraz, and T. H. Seligman, “Surprising Relations between Parametric Level Correlations and Fidelity Decay,” Phys. Rev. Lett., vol. 100, pp. 190404, 2008.
[Bibtex]@article{KSPGLS2008, Author = {H. Kohler and I. E. Smolyarenko and C. Pineda and T. Guhr and F. Leyvraz and T. H. Seligman}, DateAdded = {20080624 19:11:22 +0200}, DateModified = {20080915 10:58:56 +0200}, Doi = {10.1103/PhysRevLett.100.190404}, Eid = {190404}, Eprint = {arXiv:0712.3370}, Journal = {Phys. Rev. Lett.}, Numpages = {4}, Pages = {190404}, Publisher = {APS}, Title = {Surprising Relations between Parametric Level Correlations and Fidelity Decay}, url = {http://link.aps.org/abstract/PRL/v100/e190404}, Volume = {100}, Year = {2008}, BdskUrl1 = {http://link.aps.org/abstract/PRL/v100/e190404}, BdskUrl2 = {http://dx.doi.org/10.1103/PhysRevLett.100.190404}}
 T. Gorin, C. Pineda, H. Kohler, and T. H. Seligman, “A random matrix theory of decoherence,” New J. Phys., vol. 10, pp. 115016, 2008.
[Bibtex]@article{GPKS2008, author={T. Gorin and C. Pineda and H. Kohler and T. H. Seligman}, title={A random matrix theory of decoherence}, journal= {New J. Phys.}, volume={10}, Eprint = {arXiv:0807.4913}, pages={115016}, doi = {10.1088/13672630/10/11/115016}, url={http://stacks.iop.org/13672630/10/115016}, year={2008}, abstract={Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantumchaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix arising from the ensemble induced, in contrast to previous studies where the average values of purity, concurrence and entropy were considered; we further discuss when one or the other approach is relevant. The two approaches agree in the limit of large environments. Analytic results for the average density matrix and its purity are presented in linear response approximation. The twoqubit system is analysed, mainly numerically, in more detail.} }
 L. Kaplan, F. Leyvraz, C. Pineda, and T. H. Seligman, “A trivial observation on timereversal in random matrix theory,” J. Phys. A, vol. 40, pp. F1063F1068, 2007.
[Bibtex]@article{KLPS2007, Abstract = {It is commonly thought that a statedependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is timereversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models.}, Author = {L. Kaplan and F. Leyvraz and C. Pineda and T. H. Seligman}, DateModified = {20080915 10:59:22 +0200}, Eprint = {arXiv:0709.3353}, Journal = {J. Phys. A}, Pages = {F1063F1068}, Doi = {10.1088/17518113/40/49/F04}, Title = {A trivial observation on timereversal in random matrix theory}, Url = {http://stacks.iop.org/17518121/40/F1063}, Volume = {40}, Year = {2007}, BdskUrl1 = {http://stacks.iop.org/17518121/40/F1063}}
 C. Pineda, T. Gorin, and T. H. Seligman, “Decoherence of twoqubit systems: a random matrix description,” New J. Phys., vol. 9, pp. 106, 2007.
[Bibtex]@article{PGS2007, Author = {C. Pineda and T. Gorin and T. H. Seligman}, Doi = {10.1088/13672630/9/4/106}, Eprint = {arXiv:quantph/0702161}, Issn = {13672630}, Journal = {New J. Phys.}, Month = {April}, Pages = {106}, Publisher = {Institute of Physics Publishing}, Title = {Decoherence of twoqubit systems: a random matrix description}, Volume = {9}, Year = {2007}, BdskUrl1 = {http://dx.doi.org/10.1088/13672630/9/4/106}}
 E. Martinez, C. Pineda, F. Leyvraz, and P. BarberisBlostein, “Quantum estimation of unknown parameters,” ArXiv eprints, 2016.

Markovianity in quantum systems
The advent of quantum information and quantum technology has pushed us back to a deeper understanding of the basics of quantum mechanics. Various fundamental aspects, like equilibration, simulability, and even foundations, among others, have been revised with its help. This new framework has provided both valuable insight into the foundations and new technological achievements. But theory and its related experiments have advanced asymmetrically mainly due to the impossibility to isolate completely the experimental setup, leaving the system open and exposed to decoherence.
The equations that rule the dynamics of quantum open systems are rather involved but many problems can be solved after some assumptions are made. The widely used BornMarkov approximation, that has been successfully applied to describe many physical situations, is associated with both a memoryless environment and a weak coupling between system and environment. However, recently, interest in quantum open systems where this assumption no longer applies — usually called nonMarkovian (NM) evolution — has flourished.
We have studied when, and to what extend, deviations from the ideal Markovian approximation appear. This has been done with the aid of very general tools, like random matrix theory (so as to study a quantum environment) or with the aid of classical chaos (to study the effect of coupling to a generic, but classical environment).
Several questions still remain open. We are currently working on understanding the transition from generic nonmarkovianity of a strongly coupled system, to generic markovianity predicted in the weak coupling regime. We are also looking forward for experimental insight with a group in Brazil.
 C. Pineda, T. Gorin, D. Davalos, D. A. Wisniacki, and I. Garc’iaMata, “Measuring and using nonMarkovianity,” Phys. Rev. A, vol. 93, pp. 22117, 2016.
[Bibtex]@ARTICLE{pineda:definitions:nm:2015, title = {Measuring and using nonMarkovianity}, author = {Pineda, Carlos and Gorin, Thomas and Davalos, David and Wisniacki, Diego A. and Garc\'{\i}aMata, Ignacio}, journal = {Phys. Rev. A}, volume = {93}, issue = {2}, pages = {022117}, numpages = {8}, year = {2016}, month = {Feb}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.93.022117}, url = {http://link.aps.org/doi/10.1103/PhysRevA.93.022117} }
 N. Garrido, T. Gorin, and C. Pineda, “Transition from nonMarkovian to Markovian dynamics for generic environments,” Phys. Rev. A, vol. 93, pp. 12113, 2016.
[Bibtex]@article{2015arXiv150702529G, title = {Transition from nonMarkovian to Markovian dynamics for generic environments}, author = {Garrido, Nephtal\'{\i} and Gorin, Thomas and Pineda, Carlos}, journal = {Phys. Rev. A}, volume = {93}, issue = {1}, pages = {012113}, numpages = {9}, year = {2016}, month = {Jan}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.93.012113}, url = {http://link.aps.org/doi/10.1103/PhysRevA.93.012113} }
 M. Znidaric, C. Pineda, and I. GarciaMata, “NonMarkovian Behavior of Small and Large Complex Quantum Systems,” Phys. Rev. Lett., vol. 107, pp. 80404, 2011.
[Bibtex]@article{ZPG2011, pages = {080404}, numpages = {4}, month = {Aug}, volume = {107}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.107.080404}, author = {Znidaric, Marko and Pineda, Carlos and GarciaMata, Ignacio}, title = {NonMarkovian Behavior of Small and Large Complex Quantum Systems}, year = {2011}, doi = {10.1103/PhysRevLett.107.080404}, issue = {8}, journal = {Phys. Rev. Lett.}, publisher = {American Physical Society} }
 I. GarcíaMata, C. Pineda, and D. Wisniacki, “NonMarkovian quantum dynamics and classical chaos,” Phys. Rev. A, vol. 86, pp. 22114, 2012.
[Bibtex]@article{PhysRevA.86.022114, title = {NonMarkovian quantum dynamics and classical chaos}, author = {GarcíaMata, Ignacio and Pineda, Carlos and Wisniacki, Diego}, journal = {Phys. Rev. A}, volume = {86}, issue = {2}, pages = {022114}, numpages = {5}, year = {2012}, month = {Aug}, doi = {10.1103/PhysRevA.86.022114}, url = {http://link.aps.org/doi/10.1103/PhysRevA.86.022114}, publisher = {American Physical Society} }
 I. GarcíaMata, C. Pineda, and D. A. Wisniacki, “Quantum nonMarkovian behavior at the chaos border,” J. Phys. A, vol. 47, iss. 11, pp. 115301, 2014.
[Bibtex]@article{175181214711115301, author={Ignacio GarcíaMata and Carlos Pineda and Diego A Wisniacki}, title={Quantum nonMarkovian behavior at the chaos border}, journal={J. Phys. A}, volume={47}, number={11}, pages={115301}, url={http://stacks.iop.org/17518121/47/i=11/a=115301}, year={2014} }
 C. Pineda, T. Gorin, D. Davalos, D. A. Wisniacki, and I. Garc’iaMata, “Measuring and using nonMarkovianity,” Phys. Rev. A, vol. 93, pp. 22117, 2016.

Relativistic quantum information
We are studying several aspects of relativity within the framework of quantum information. On the one hand, a big discussion about the very meaning of the partial trace in the context of particles with internal degrees of freedom is ongoing in the literature. With Gibran Valdez we are studying its status and making some progress. On the other hand, Dirac’s equation is well suited to describe electrons under certain circumstances. Exploring the relation between this equation and tight binding models has enable us to get a deeper insight in its properties (joined work with Emerson Sadurni and Alex Franco).
 A. S. Rosado, J. A. FrancoVillafañe, C. Pineda, and E. Sadurn’i, “SternGerlach splitters for lattice quasispin,” Phys. Rev. B, vol. 94, pp. 45129, 2016.
[Bibtex]@article{PhysRevB.94.045129, title = {SternGerlach splitters for lattice quasispin}, author = {Rosado, A. S. and FrancoVillafa\~ne, J. A. and Pineda, C. and Sadurn\'{\i}, E.}, journal = {Phys. Rev. B}, volume = {94}, issue = {4}, pages = {045129}, numpages = {10}, year = {2016}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.94.045129}, url = {http://link.aps.org/doi/10.1103/PhysRevB.94.045129} }
 S. Hacyan and R. Jáuregui, “A relativistic study of Bessel beams,” J Phys. B, vol. 39, iss. 7, pp. 1669, 2006.
[Bibtex]@article{09534075397009, author={S Hacyan and R Jáuregui}, title={A relativistic study of Bessel beams}, journal={J Phys. B}, volume={39}, number={7}, pages={1669}, doi={10.1088/09534075/39/7/009}, year={2006} }
 A. S. Rosado, J. A. FrancoVillafañe, C. Pineda, and E. Sadurn’i, “SternGerlach splitters for lattice quasispin,” Phys. Rev. B, vol. 94, pp. 45129, 2016.

Rank dynamics
Many complex phenomena, from the selection of traits in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which may eventually lead to stratified structures such as the wealth distribution worldwide. However, it is still unclear whether the road to hierarchical complexity is determined by the particularities of each phenomena, or if there are universal mechanisms of stratification common to many systems. Human sports and games, with their (varied but simplified) rules of competition and measures of performance, serve as an ideal test bed to look for universal features of hierarchy formation, as well al languages for which a huge data base provided by google. With this goal in mind, we have analysed the behaviour of players and team rankings over time for several sports and games and word use over centuries. Even though, for a given time, the distribution of performance ranks varies, we find statistical regularities in the dynamics of ranks. Specifically the rank diversity, a measure of the number of elements occupying a given rank over a length of time, has the same functional form in sports and games as in languages, another system where competition is determined by the use or disuse of grammatical structures. Our results support the notion that hierarchical phenomena may be driven by the same underlying mechanisms of rank formation, regardless of the nature of their components.
 J. A. Morales, S. Sánchez, J. Flores, C. Pineda, C. Gershenson, G. Cocho, J. Zizumbo, R. F. Rodríguez, and G. Iñiguez, “Generic temporal features of performance rankings in sports and games,” EPJ Data Science, vol. 5, iss. 1, pp. 33, 2016.
[Bibtex]@ARTICLE{cochodos, author="Morales, Jos{\'e} A. and S{\'a}nchez, Sergio and Flores, Jorge and Pineda, Carlos and Gershenson, Carlos and Cocho, Germinal and Zizumbo, Jer{\'o}nimo and Rodr{\'i}guez, Rosal{\'i}o F. and I{\~{n}}iguez, Gerardo", title="Generic temporal features of performance rankings in sports and games", journal="EPJ Data Science", year="2016", volume="5", number="1", pages="33", issn="21931127", doi="10.1140/epjds/s136880160096y", url="http://dx.doi.org/10.1140/epjds/s136880160096y" }
 G. Cocho, J. Flores, C. Gershenson, C. Pineda, and S. Sánchez, “Rank Diversity of Languages: Generic Behavior in Computational Linguistics,” PLoS ONE, vol. 10, iss. 4, pp. e0121898, 2015.
[Bibtex]@ARTICLE{cocho:idiomas, author = {Cocho, Germinal AND Flores, Jorge AND Gershenson, Carlos AND Pineda, Carlos AND Sánchez, Sergio}, journal = {PLoS ONE}, publisher = {Public Library of Science}, title = {Rank Diversity of Languages: Generic Behavior in Computational Linguistics}, year = {2015}, month = {04}, volume = {10}, url = {http://dx.doi.org/10.1371%2Fjournal.pone.0121898}, pages = {e0121898}, abstract = { Statistical studies of languages have focused on the rankfrequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution
rank diversity . We calculate this diversity for books published in six European languages since 1800, and find that it follows a universal lognormal distribution. Based on the mean and standard deviation associated with the lognormal distribution, we define three different word regimes of languages: “heads” consist of words which almost do not change their rank in time, “bodies” are words of general use, while “tails” are comprised by contextspecific words and vary their rank considerably in time. The heads and bodies reflect the size of language cores identified by linguists for basic communication. We propose a Gaussian random walk model which reproduces the rank variation of words in time and thus the diversity. Rank diversity of words can be understood as the result of random variations in rank, where the size of the variation depends on the rank itself. We find that the core size is similar for all languages studied. }, number = {4}, doi = {10.1371/journal.pone.0121898} }
 J. A. Morales, S. Sánchez, J. Flores, C. Pineda, C. Gershenson, G. Cocho, J. Zizumbo, R. F. Rodríguez, and G. Iñiguez, “Generic temporal features of performance rankings in sports and games,” EPJ Data Science, vol. 5, iss. 1, pp. 33, 2016.
Other topics

Interaction of Matter and Structured Light
Microscopical shaping of light beams has opened the possibility of their use in devices for the manipulation of cold atoms: predesigned structured light could play the role for cold matter that crystals or material cavities play for light. Advances have been done towards the use of light beams as wave guides for atom transport; ringshaped optical lattices have been shown to yield appropriate potentials for studying quasionedimensional physical systems with closedboundary conditions. We are specially interested in the detailed description of BECs and thermal clouds interacting with propagation invariant beams. The idea is to identify the effects of structured light both in internal and center of mass motion of the atoms. We are also interested in correlations and general properties through the BardeenCooperSchrieffer (BCS) BoseEinsteincondensate (BEC) crossover.
 R. Jauregui and P. ~A. QuintoSu, “Natural focusing of symmetric Airy beams,” ArXiv eprints, 2014.
[Bibtex]@ARTICLE{2014arXiv1407.7418J, author = {{Jauregui}, R. and {QuintoSu}, P.~A.}, title = "{Natural focusing of symmetric Airy beams}", journal = {ArXiv eprints}, archivePrefix = "arXiv", eprint = {1407.7418}, primaryClass = "physics.optics", keywords = {Physics  Optics}, year = 2014, month = jul, adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1407.7418J}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }
 M. Bienert and P. BarberisBlostein, “Optomechanical laser cooling with mechanical modulations,” Phys. Rev. A, vol. 91, pp. 23818, 2015.
[Bibtex]@article{PhysRevA.91.023818, title = {Optomechanical laser cooling with mechanical modulations}, author = {Bienert, Marc and BarberisBlostein, Pablo}, journal = {Phys. Rev. A}, volume = {91}, issue = {2}, pages = {023818}, numpages = {9}, year = {2015}, month = {Feb}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.91.023818}, url = {http://link.aps.org/doi/10.1103/PhysRevA.91.023818} }
 P. BarberisBlostein and O. AguilarLoreto, “Propagation of a probe pulse inside a Bose–Einstein condensate under conditions of electromagnetically induced transparency,” Physica Scripta, vol. 90, iss. 6, pp. 68008, 2015.
[Bibtex]@article{14024896906068008, author={Pablo BarberisBlostein and Omar AguilarLoreto}, title={Propagation of a probe pulse inside a Bose–Einstein condensate under conditions of electromagnetically induced transparency}, journal={Physica Scripta}, doi = {10.1088/00318949/90/6/068008}, volume={90}, number={6}, pages={068008}, url={http://stacks.iop.org/14024896/90/i=6/a=068008}, year={2015}, abstract={We obtain a partial differential equation for a pulse travelling inside a Bose–Einstein condensate under conditions of electromagnetically induced transparency. The equation is valid for a weak probe pulse. We solve the equation for the case of a threelevel BEC in Λ configuration with one of its ground state spatial profiles initially constant. The solution characterizes, in detail, the effect that the evolution of the condensate wave function has on pulse propagation, including the process of stopping and releasing it.} }
 M. Bolaños and P. BarberisBlostein, “Algebraic solution of the Lindblad equation for a collection of multilevel systems coupled to independent environments,” Journal of Physics A: Mathematical and Theoretical, vol. 48, iss. 44, pp. 445301, 2015.
[Bibtex]@article{175181214844445301, author={Marduk Bolaños and Pablo BarberisBlostein}, title={Algebraic solution of the Lindblad equation for a collection of multilevel systems coupled to independent environments}, journal={Journal of Physics A: Mathematical and Theoretical}, volume={48}, number={44}, pages={445301}, url={http://stacks.iop.org/17518121/48/i=44/a=445301}, doi = {10.1088/17518113/48/44/445301}, year={2015}, abstract={We consider the Lindblad equation for a collection of multilevel systems coupled to independent environments. The equation is symmetric under the exchange of the labels associated with each system and thus the opensystem dynamics takes place in the permutationsymmetric subspace of the operator space. The dimension of this space grows polynomially with the number of systems. We construct a basis of this space and a set of superoperators whose action on this basis is easily specified. For a given number of levels, M , these superoperators are written in terms of a bosonic realization of the generators of the Lie algebra ##IMG## [http://ej.iop.org/images/17518121/48/44/445301/jpa520185ieqn1.gif] {${\mathfrak{sl}}({M}^{2}).$} In some cases, these results enable finding an analytic solution of the master equation using known Liealgebraic methods. To demonstrate this, we obtain an analytic expression for the state operator of a collection of threelevel atoms coupled to independent radiation baths. When analytic solutions are difficult to find, the basis and the superoperators can be used to considerably reduce the computational resources required for simulations.} }
 C. Sabín, P. BarberisBlostein, C. Hernández, R. B. Mann, and I. Fuentes, “Effects of threebody collisions in a twomode BoseEinstein condensate,” Journal of Mathematical Physics, vol. 56, iss. 11, 2015.
[Bibtex]@article{:/content/aip/journal/jmp/56/11/10.1063/1.4936314, author = "Sabín, Carlos and BarberisBlostein, Pablo and Hernández, Cristopher and Mann, Robert B. and Fuentes, Ivette", title = "Effects of threebody collisions in a twomode BoseEinstein condensate", journal = "Journal of Mathematical Physics", year = "2015", volume = "56", number = "11", eid = 112102, pages = "", url = "http://scitation.aip.org/content/aip/journal/jmp/56/11/10.1063/1.4936314", doi = "http://dx.doi.org/10.1063/1.4936314" }
 F. PoncianoOjeda, S. HernándezGómez, O. LópezHernández, C. MojicaCasique, R. Col’inRodr’iguez, F. Ram’irezMart’inez, J. FloresMijangos, D. Sahagún, R. Jáuregui, and J. JiménezMier, “Observation of the 5p_3/2 to 6p_3/2 electricdipoleforbidden transition in atomic rubidium using opticaloptical doubleresonance spectroscopy,” Phys. Rev. A, vol. 92, pp. 42511, 2015.
[Bibtex]@article{PhysRevA.92.042511, title = {Observation of the 5p_3/2 to 6p_3/2 electricdipoleforbidden transition in atomic rubidium using opticaloptical doubleresonance spectroscopy}, author = {PoncianoOjeda, F. and Hern\'andezG\'omez, S. and L\'opezHern\'andez, O. and MojicaCasique, C. and Col\'{\i}nRodr\'{\i}guez, R. and Ram\'{\i}rezMart\'{\i}nez, F. and FloresMijangos, J. and Sahag\'un, D. and J\'auregui, R. and Jim\'enezMier, J.}, journal = {Phys. Rev. A}, volume = {92}, issue = {4}, pages = {042511}, numpages = {6}, year = {2015}, month = {Oct}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.92.042511}, url = {http://link.aps.org/doi/10.1103/PhysRevA.92.042511} }
 R. Jauregui and P. ~A. QuintoSu, “Natural focusing of symmetric Airy beams,” ArXiv eprints, 2014.

Bosonic and Fermionic Channel Capacities
The notion of quantum channel capacity is central to quantum Shannon theory. Early development from the seventies was a starting point to an impressive amount of knowledge that has been acquired in the last two decades. The capacity informs us about the ability of a channel to transmit classical or quantum correlations. More precisely, consider a sender who has, in principle, at his disposal an optimal encoder producing a classical or quantum code, and a receiver able to process the channel output and recover the transmitted information (that is, to decode) with an arbitrarily high precision. In this way, the information can be transmitted at the rate given by the capacity and cannot be better by any other choice of encoding. Various additional conditions or restrictions might be added, for instance if privacy is required or some sort of assistance is available in terms of other quantum or classical resources available to the communicating parties. This leads to a countless number of important capacity definitions relevant under given circumstances and one might even try to characterize the whole capacity multidimensional regions in which the axes correspond to various available resources. We analyze the quantum capacities of bosonic and fermionic systems that interact so that a Bogoliubov transformed phase space describes them in an approximate way.
 K. Brádler and R. Jáuregui, “Entanglement enhancement and postselection for two atoms interacting with thermal light,” J. Phys. B, vol. 40, iss. 4, pp. 743, 2007.
[Bibtex]@article{09534075404009, author={K Brádler and R Jáuregui}, title={Entanglement enhancement and postselection for two atoms interacting with thermal light}, journal={J. Phys. B}, volume={40}, number={4}, pages={743}, doi={10.1088/09534075/40/4/009}, year={2007} }
 K. Brádler and R. Jáuregui, “Entanglement enhancement and postselection for two atoms interacting with thermal light,” J. Phys. B, vol. 40, iss. 4, pp. 743, 2007.

Atomic Manipulation
The goal is to study how to manipulate quantum states at will. This has applications in quantum information processing. The topics that are studied related with the general goal are: quantum optics, cold atoms interacting with cavity quantum electrodynamics, decoherence and quantum information.
 R. Jáuregui, “Control of atomic transition rates via laserlight shaping,” Phys. Rev. A, vol. 91, pp. 43842, 2015.
[Bibtex]@article{PhysRevA.91.043842, title = {Control of atomic transition rates via laserlight shaping}, author = {J\'auregui, R.}, journal = {Phys. Rev. A}, volume = {91}, issue = {4}, pages = {043842}, numpages = {18}, year = {2015}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.91.043842}, url = {http://link.aps.org/doi/10.1103/PhysRevA.91.043842} }
 R. Jáuregui, “Control of atomic transition rates via laserlight shaping,” Phys. Rev. A, vol. 91, pp. 43842, 2015.
Older topics
Some topics that we have touched long ago, but are not of main interest now are the following.

Fermionic Quantum Circuits
The equations of motion for a quantum mechanical system has long been known. That does not mean that we understand the behavior of the quantum mechanical system. This is also true for system with simpler evolution laws, as classical systems and cellular automata. Understanding quantum manybody systems is a challenge for the brave. A full understanding of such systems would allow to explain, say, high temperature superconductivity. Several techniques (such as density functional theory, renormalization group methods, path integration etc) have been developed. Still the problem of fermions in two dimensions remained elusive.
One promising method is the quantum circuit method, in which the wave function is represented via a circuit that prepares it. If one allows for a small number of one and two qubit gates, this method may describe just a small corner of Hilbert space, but that is the interesting corner.
We are currently working in a fermionic implementation that would allow to describe multidimensional lattices. We have proposed a method [1], [2], and we are currently implementing for squeezing the numbers that people ask for.
 T. Barthel, C. Pineda, and J. Eisert, “Contraction of fermionic operator circuits and the simulation of strongly correlated fermions,” Phys. Rev. A, vol. 80, pp. 42333, 2009.
[Bibtex]@article{BPE2009, author = {Barthel, T. and Pineda, C. and Eisert, J.}, title = {Contraction of fermionic operator circuits and the simulation of strongly correlated fermions}, year = {2009}, journal = {Phys. Rev. A}, volume = {80}, eid = {042333}, numpages = {12}, eprint = {arXiv:0907.3689}, pages = {042333}, keywords = {fermion systems; quantum computing; quantum entanglement; renormalisation}, url = {http://link.aps.org/abstract/PRA/v80/e042333}, doi = {10.1103/PhysRevA.80.042333} }
 C. Pineda, T. Barthel, and J. Eisert, “Unitary circuits for strongly correlated fermions,” Phys. Rev. A, vol. 81, pp. 50303, 2010.
[Bibtex]@ARTICLE{PBE2010, author = {{Pineda}, C. and {Barthel}, T. and {Eisert}, J.}, title = "{Unitary circuits for strongly correlated fermions}", journal = {Phys. Rev. A}, keywords = {Quantum computation, Quantum statistical mechanics, Strongly correlated electron systems; heavy fermions}, year = 2010, month = may, volume = 81, pages = {050303}, doi = {10.1103/PhysRevA.81.050303}, surl = {http://adsabs.harvard.edu/abs/2010PhRvA..81e0303P}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} eprint = {arXiv:0905.0669} }
 T. Barthel, C. Pineda, and J. Eisert, “Contraction of fermionic operator circuits and the simulation of strongly correlated fermions,” Phys. Rev. A, vol. 80, pp. 42333, 2009.