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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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Guo, J. J., Sun, F. X., Zhu, D. Q., Gessner, M., He, Q. Y., & Fadel, M. (2023). Detecting Einstein-Podolsky-Rosen steering in non-Gaussian spin states from conditional spin-squeezing parameters. Phys. Rev. A, 108(1), 012435–7pp.
Abstract: We present an experimentally practical method to reveal Einstein-Podolsky-Rosen (EPR) steering in non-Gaussian spin states by exploiting a connection to quantum metrology. Our criterion is based on the quantum Fisher information, and uses bounds derived from generalized spin-squeezing parameters that involve measurements of higher-order moments. This leads us to introduce the concept of conditional spin-squeezing parameters, which quantify the metrological advantage provided by conditional states, as well as detect the presence of an EPR paradox.
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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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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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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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