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Arrighi, P., Di Molfetta, G., Marquez-Martin, I., & Perez, A. (2019). From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks. Sci Rep, 9, 10904–10pp.
Abstract: A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. In a previous paper, we showed that QWs over the honeycomb and triangular lattices can be used to simulate the Dirac equation. We apply a spacetime coordinate transformation upon the lattice of this QW, and show that it is equivalent to introducing spacetime-dependent local unitaries-whilst keeping the lattice fixed. By exploiting this duality between changes in geometry, and changes in local unitaries, we show that the spacetime-dependent QW simulates the Dirac equation in (2 + 1)-dimensional curved spacetime. Interestingly, the duality crucially relies on the non linear-independence of the three preferred directions of the honeycomb and triangular lattices: The same construction would fail for the square lattice. At the practical level, this result opens the possibility to simulate field theories on curved manifolds, via the quantum walk on different kinds of lattices.
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Arnault, P., Perez, A., Arrighi, P., & Farrelly, T. (2019). Discrete-time quantum walks as fermions of lattice gauge theory. Phys. Rev. A, 99(3), 032110–16pp.
Abstract: It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also ultralocal, i.e., the particle's speed is upper bounded, as in standard relativistic quantum field theories. The lattice chiral symmetry of staggered fermions, which corresponds to a translational invariance, is lost after the requirement of ultralocality of the evolution; this fact is an instance of Meyer's 1996 no-go results stating that no nontrivial scalar quantum cellular automaton can be translationally invariant [D. A. Meyer, J. Stat. Phys. 85, 551 (1996); Phys. Lett. A 223, 337 (1996)]. All results are presented in a single-particle framework and for a (1+1)-dimensional space-time.
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Marquez-Martin, I., Arnault, P., Di Molfetta, G., & Perez, A. (2018). Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks. Phys. Rev. A, 98(3), 032333–8pp.
Abstract: Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two steps of the evolution, we define a density current which is gauge invariant and conserved. In the continuum limit, the dynamics of the particle, under a suitable choice of the parameters, becomes the Dirac equation and the conserved current satisfies the corresponding conservation equation.
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Arrighi, P., Di Molfetta, G., Marquez-Martin, I., & Perez, A. (2018). Dirac equation as a quantum walk over the honeycomb and triangular lattices. Phys. Rev. A, 97(6), 062111–5pp.
Abstract: A discrete-time quantum walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in (2 + 1) dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice, both of interest in the study of quantum propagation on the nonrectangular grids, as in graphene-like materials. The latter, in particular, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.
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Marquez-Martin, I., Di Molfetta, G., & Perez, A. (2017). Fermion confinement via quantum walks in (2+1)-dimensional and (3+1)-dimensional space-time. Phys. Rev. A, 95(4), 042112–5pp.
Abstract: We analyze the properties of a two-and three-dimensional quantum walk that are inspired by the idea of a brane-world model put forward by Rubakov and Shaposhnikov [Phys. Lett. B 125, 136 (1983)]. In that model, particles are dynamically confined on the brane due to the interaction with a scalar field. We translated this model into an alternate quantum walk with a coin that depends on the external field, with a dependence which mimics a domain wall solution. As in the original model, fermions (in our case, the walker) become localized in one of the dimensions, not from the action of a random noise on the lattice (as in the case of Anderson localization) but from a regular dependence in space. On the other hand, the resulting quantum walk can move freely along the “ordinary” dimensions.
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Gomez-Vargas, G. A., Lopez-Fogliani, D. E., Muñoz, C., Perez, A. D., & Ruiz de Austri, R. (2017). Search for sharp and smooth spectral signatures of μnu SSM gravitino dark matter with Fermi- LAT. J. Cosmol. Astropart. Phys., 03(3), 047–23pp.
Abstract: The μnu SSM solves the μproblem of supersymmetric models and reproduces neutrino data, simply using couplings with right-handed neutrinos nu's. Given that these couplings break explicitly R parity, the gravitino is a natural candidate for decaying dark matter in the μnu SSM. In this work we carry out a complete analysis of the detection of μnu SSM gravitino dark matter through gamma-ray observations. In addition to the two-body decay producing a sharp line, we include in the analysis the three-body decays producing a smooth spectral signature. We perform first a deep exploration of the low-energy parameter space of the μnu SSM taking into account that neutrino data must be reproduced. Then, we compare the gamma-ray fluxes predicted by the model with Fermi-LAT observations. In particular, with the 95% CL upper limits on the total diffuse extragalactic gamma-ray background using 50 months of data, together with the upper limits on line emission from an updated analysis using 69.9 months of data. For standard values of bino and wino masses, gravitinos with masses larger than about 4 GeV, or lifetimes smaller than about 10(28) s, produce too large fluxes and are excluded as dark matter candidates. However, when limiting scenarios with large and close values of the gaugino masses are considered, the constraints turn out to be less stringent, excluding masses larger than 17 GeV and lifetimes smaller than 4 x 10(25) s.
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Bru, L. A., de Valcarcel, G. J., Di Molfetta, G., Perez, A., Roldan, E., & Silva, F. (2016). Quantum walk on a cylinder. Phys. Rev. A, 94(3), 032328–7pp.
Abstract: We consider the two-dimensional alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or “hidden” extra dimension. If one starts from localized initial conditions on the lattice, the dynamics of the quantum walk that is obtained after tracing out the small dimension shows the contribution of several components which can be understood from the study of the dispersion relations for this problem. In fact, these components originate from the contribution of the possible values of the quasimomentum in the closed dimension. In the continuous space-time limit, the different components manifest as a set of Dirac equations, with each quasimomentum providing the value of the corresponding mass. We briefly discuss the possible link of these ideas to the simulation of high-energy physical theories that include extra dimensions. Finally, entanglement between the coin and spatial degrees of freedom is studied, showing that the entanglement entropy clearly overcomes the value reached with only one spatial dimension.
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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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Hinarejos, M., Bañuls, M. C., Perez, A., & de Vega, I. (2017). Non-Markovianity and memory of the initial state. J. Phys. A, 50(32), 335301–17pp.
Abstract: We explore in a rigorous manner the intuitive connection between the non-Markovianity of the evolution of an open quantum system and the performance of the system as a quantum memory. Using the paradigmatic case of a two-level open quantum system coupled to a bosonic bath, we compute the recovery fidelity, which measures the best possible performance of the system to store a qubit of information. We deduce that this quantity is connected, but not uniquely determined, by the non-Markovianity, for which we adopt the Breuer-Laine-Piilo measure proposed in Breuer et al (2009 Phys. Rev. Lett. 103 210401). We illustrate our findings with explicit calculations for the case of a structured environment.
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Gomis, P., & Perez, A. (2016). Decoherence effects in the Stern-Gerlach experiment using matrix Wigner functions. Phys. Rev. A, 94(1), 012103–11pp.
Abstract: We analyze the Stern-Gerlach experiment in phase space with the help of the matrix Wigner function, which includes the spin degree of freedom. Such analysis allows for an intuitive visualization of the quantum dynamics of the device. We include the interaction with the environment, as described by the Caldeira-Leggett model. The diagonal terms of the matrix provide us with information about the two components of the state that arise from interaction with the magnetic field gradient. In particular, from the marginals of these components, we obtain an analytical formula for the position and momentum probability distributions in the presence of decoherence that shows a diffusive behavior for large values of the decoherence parameter. These features limit the dynamics of the present model. We also observe the decay of the nondiagonal terms with time and use this fact to quantify the amount of decoherence from the norm of those terms in phase space. From here, we can define a decoherence time scale, which differs from previous results that make use of the same model. We analyze a typical experiment and show that, for that setup, the decoherence time is much smaller than the characteristic time scale for the separation of the two beams, implying that they can be described as an incoherent mixture of atoms traveling in the up and down directions with opposite values of the spin projection. Therefore, entanglement is quickly destroyed in the setup we analyzed.
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