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de Vega, I., Bañuls, M. C., & Perez, A. (2010). Effects of dissipation on an adiabatic quantum search algorithm. New J. Phys., 12, 123010–19pp.
Abstract: According to recent studies (Amin et al 2008 Phys. Rev. Lett. 100 060503), the effect of a thermal bath may improve the performance of a quantum adiabatic search algorithm. In this paper, we compare the effects of such a thermal environment on the algorithm performance with those of a structured environment similar to the one encountered in systems coupled to an electromagnetic field that exists within a photonic crystal. Whereas for all the parameter regimes explored here, the algorithm performance is worsened by contact with a thermal environment, the picture appears to be different when one considers a structured environment. In this case we show that by tuning the environment parameters to certain regimes, the algorithm performance can actually be improved with respect to the closed system case. Additionally, the relevance of considering the dissipation rates as complex quantities is discussed in both cases. More specifically, we find that the imaginary part of the rates cannot be neglected with the usual argument that it simply amounts to an energy shift and in fact influences crucially the system dynamics.
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Hinarejos, M., Perez, A., & Bañuls, M. C. (2012). Wigner function for a particle in an infinite lattice. New J. Phys., 14, 103009–19pp.
Abstract: We study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a one-dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definition of the Wigner function in this case and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system, which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states and to their superpositions.
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Hinarejos, M., Perez, A., Roldan, E., Romanelli, A., & de Valcarcel, G. J. (2013). Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more. New J. Phys., 15, 073041–31pp.
Abstract: The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrodinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-dimensional Grover walks are presented.
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Hinarejos, M., Bañuls, M. C., & Perez, A. (2015). Wigner formalism for a particle on an infinite lattice: dynamics and spin. New J. Phys., 17, 013037–16pp.
Abstract: The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Banuls MC and Perez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included.
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Di Molfetta, G., & Perez, A. (2016). Quantum walks as simulators of neutrino oscillations in a vacuum and matter. New J. Phys., 18, 103038–8pp.
Abstract: We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in a vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing one to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, the simulation of neutrino oscillations with the help of quantum walks might be useful to illustrate these effects in extreme conditions, such as the solar interior or supernovae.
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Angles-Castillo, A., Bañuls, M. C., Perez, A., & De Vega, I. (2020). Prethermalization of quantum systems interacting with non-equilibrium environments. New J. Phys., 22(8), 083067–17pp.
Abstract: The usual paradigm of open quantum systems falls short when the environment is actually coupled to additional fields or components that drive it out of equilibrium. Here we explore the simplest such scenario, by considering a two level system coupled to a first thermal reservoir that in turn couples to a second thermal bath at a different temperature. We derive a master equation description for the system and show that, in this situation, the dynamics can be especially rich. In particular, we observe prethermalization, a transitory phenomenon in which the system initially approaches thermal equilibrium with respect to the first reservoir, but after a longer time converges to the thermal state dictated by the temperature of the second environment. Using analytical arguments and numerical simulations, we analyze the occurrence of this phenomenon, and how it depends on temperatures and coupling strengths. The phenomenology gets even richer if the system is placed between two such non-equilibrium environments. In this case, the energy current through the system may exhibit transient features and even switch direction, before the system eventually reaches a non-equilibrium steady state.
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Angles-Castillo, A., Perez, A., & Roldan, E. (2024). Bright and dark solitons in a photonic nonlinear quantum walk: lessons from the continuum. New J. Phys., 26(2), 023004–16pp.
Abstract: We propose a nonlinear quantum walk model inspired in a photonic implementation in which the polarization state of the light field plays the role of the coin-qubit. In particular, we take profit of the nonlinear polarization rotation occurring in optical media with Kerr nonlinearity, which allows to implement a nonlinear coin operator, one that depends on the state of the coin-qubit. We consider the space-time continuum limit of the evolution equation, which takes the form of a nonlinear Dirac equation. The analysis of this continuum limit allows us to gain some insight into the existence of different solitonic structures, such as bright and dark solitons. We illustrate several properties of these solitons with numerical calculations, including the effect on them of an additional phase simulating an external electric field.
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Kim, J. S., Lopez-Fogliani, D. E., Perez, A. D., & Ruiz de Austri, R. (2022). The new (g-2)(mu) and right-handed sneutrino dark matter. Nucl. Phys. B, 974, 115637–23pp.
Abstract: In this paper we investigate the (g – 2)(mu) discrepancy in the context of the R-parity conserving next-to minimal supersymmetric Standard Model plus right-handed neutrinos superfields. The model has the ability to reproduce neutrino physics data and includes the interesting possibility to have the right-handed sneutrino as the lightest supersymmetric particle and a viable dark matter candidate. Since right-handed sneutrinos are singlets, no new contributions for delta a(mu) with respect to the MSSM and NMSSM are present. However, the possibility to have the right-handed sneutrino as the lightest supersymmetric particle opens new ways to escape Large Hadron Collider and direct detection constraints. In particular, we find that dark matter masses within 10 less than or similar to m((upsilon) over tildeR) less than or similar to 600 GeV are fully compatible with current experimental constraints. Remarkably, not only spectra with light sleptons are needed, but we obtain solutions with m((mu) over tilde) greater than or similar to 600 GeV in the entire dark matter mass range that could be probed by new (g – 2)(mu) data in the near future. In addition, dark matter direct detection experiments will be able to explore a sizable portion of the allowed parameter space with mvR < 300 GeV, while indirect detection experiments will be able to probe a much smaller fraction within 200 less than or similar to m((nu)over tilde>R) less than or similar to 350 GeV.
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Perez, A. (2010). Information encoding of a qubit into a multilevel environment. Phys. Rev. A, 81(5), 052326–6pp.
Abstract: I consider the interaction of a small quantum system (a qubit) with a structured environment consisting of many levels. The qubit will experience a decoherence process, which implies that part of its initial information will be encoded into correlations between system and environment. I investigate how this information is distributed on a given subset of levels as a function of its size, using the mutual information between both entities, in the spirit of the partial-information plots studied by Zurek and co-workers. In this case we can observe some differences, which arise from the fact that I am partitioning just one quantum system and not a collection of them. However, some similar features, like redundancy (in the sense that a given amount of information is shared by many subsets), which increases with the size of the environment, are also found here.
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Hinarejos, M., Di Franco, C., Romanelli, A., & Perez, A. (2014). Chirality asymptotic behavior and non-Markovianity in quantum walks on a line. Phys. Rev. A, 89(5), 052330–7pp.
Abstract: We investigate the time evolution of the chirality reduced density matrix for a discrete-time quantum walk on a one-dimensional lattice. The matrix is obtained by tracing out the spatial degree of freedom. We analyze the standard case, without decoherence, and the situation in which decoherence appears in the form of broken links in the lattice. By examining the trace distance for possible pairs of initial states as a function of time, we conclude that the evolution of the reduced density matrix is non-Markovian, in the sense defined by Breuer, Laine, and Piilo [Phys. Rev. Lett. 103, 210401 (2009)]. As the level of noise increases, the dynamics approaches a Markovian process. The highest non-Markovianity corresponds to the case without decoherence. The reduced density matrix tends always to a well-defined limit that we calculate, but only in the decoherence-free case is this limit nontrivial.
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