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Wuensch, W., Degiovanni, A., Calatroni, S., Korsback, A., Djurabekova, F., Rajamaki, R., et al. (2017). Statistics of vacuum breakdown in the high-gradient and low-rate regime. Phys. Rev. Accel. Beams, 20(1), 011007–11pp.
Abstract: In an increasing number of high-gradient linear accelerator applications, accelerating structures must operate with both high surface electric fields and low breakdown rates. Understanding the statistical properties of breakdown occurrence in such a regime is of practical importance for optimizing accelerator conditioning and operation algorithms, as well as of interest for efforts to understand the physical processes which underlie the breakdown phenomenon. Experimental data of breakdown has been collected in two distinct high-gradient experimental set-ups: A prototype linear accelerating structure operated in the Compact Linear Collider Xbox 12GHz test stands, and a parallel plate electrode system operated with pulsed DC in the kV range. Collected data is presented, analyzed and compared. The two systems show similar, distinctive, two-part distributions of number of pulses between breakdowns, with each part corresponding to a specific, constant event rate. The correlation between distance and number of pulses between breakdown indicates that the two parts of the distribution, and their corresponding event rates, represent independent primary and induced follow-up breakdowns. The similarity of results from pulsed DCto 12GHz rf indicates a similar vacuum arc triggering mechanism over the range of conditions covered by the experiments.
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Arnault, P., Pepper, B., & Perez, A. (2020). Quantum walks in weak electric fields and Bloch oscillations. Phys. Rev. A, 101(6), 062324–12pp.
Abstract: Bloch oscillations appear when an electric field is superimposed on a quantum particle that evolves on a lattice with a tight-binding Hamiltonian (TBH), i.e., evolves via what we call an electric TBH; this phenomenon will be referred to as TBH Bloch oscillations. A similar phenomenon is known to show up in so-called electric discrete-time quantum walks (DQWs) [C. Cedzich et al., Phys. Rev. Lett. 111, 160601 (2013);] this phenomenon will be referred to as DQW Bloch oscillations. This similarity is particularly salient when the electric field of the DQW is weak. For a wide, i.e., spatially extended, initial condition, one numerically observes semiclassical oscillations, i.e., oscillations of a localized particle, for both the electric TBH and the electric DQW. More precisely, the numerical simulations strongly suggest that the semiclassical DQW Bloch oscillations correspond to two counterpropagating semiclassical TBH Bloch oscillations. In this work it is shown that, under certain assumptions, the solution of the electric DQW for a weak electric field and a wide initial condition is well approximated by the superposition of two continuous-time expressions, which are counterpropagating solutions of an electric TBH whose hopping amplitude is the cosine of the arbitrary coin-operator mixing angle. In contrast, if one wishes the continuous-time approximation to hold for spatially localized initial conditions, one needs at least the DQW to be lazy, as suggested by numerical simulations and by the fact that this has been proven in the case of a vanishing electric field [F. W. Strauch, Phys. Rev. A 74, 030301(R) (2006)].
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Arnault, P., Di Molfetta, G., Brachet, M., & Debbasch, F. (2016). Quantum walks and non-Abelian discrete gauge theory. Phys. Rev. A, 94(1), 012335–6pp.
Abstract: A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1) Maxwell fields and SU(N) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs.
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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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Martone, G. I., Larre, P. E., Fabbri, A., & Pavloff, N. (2018). Momentum distribution and coherence of a weakly interacting Bose gas after a quench. Phys. Rev. A, 98(6), 063617–21pp.
Abstract: We consider a weakly interacting uniform atomic Bose gas with a time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov treatment we investigate the time evolution of several observables, including the momentum distribution, the degree of coherence in the system, and their dependence on dimensionality and temperature. We rigorously prove that the low-momentum Bogoliubov modes remain frozen during the whole evolution, while the high-momentum ones adiabatically follow the change in time of the interaction strength. At intermediate momenta we point out the occurrence of oscillations, which are analogous to Sakharov oscillations. We identify two wide classes of time-dependent behaviors of the coupling for which an exact solution of the problem can be found, allowing for an analytic computation of all the relevant observables. A special emphasis is put on the study of the coherence property of the system in one spatial dimension. We show that the system exhibits a smooth “light-cone effect,” with typically no prethermalization.
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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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Vnuchenko, A., Esperante Pereira, D., Gimeno, B., Benedetti, S., Catalan Lasheras, N., Garlasch, M., et al. (2020). High-gradient testing of an S-band, normal-conducting low phase velocity accelerating structure. Phys. Rev. Accel. Beams, 23(8), 084801–13pp.
Abstract: A novel high-gradient accelerating structure with low phase velocity, v/c = 0.38, has been designed, manufactured and high-power tested. The structure was designed and built using the methodology and technology developed for CLIC 100 MV/m high-gradient accelerating structures, which have speed of light phase velocity, but adapts them to a structure for nonrelativistic particles. The parameters of the structure were optimized for the compact proton therapy linac project, and specifically to 76 MeV energy protons, but the type of structure opens more generally the possibility of compact low phase velocity linacs. The structure operates in S-band, is backward traveling wave (BTW) with a phase advance of 150 degrees and has an active length of 19 cm. The main objective for designing and testing this structure was to demonstrate that low velocity particles, in particular protons, can be accelerated with high gradients. In addition, the performance of this structure compared to other type of structures provides insights into the factors that limit high gradient operation. The structure was conditioned successfully to high gradient using the same protocol as for CLIC X-band structures. However, after the high power test, data analysis realized that the structure had been installed backwards, that is, the input power had been fed into what is nominally the output end of the structure. This resulted in higher peak fields at the power feed end and a steeply decreasing field profile along the structure, rather than the intended near constant field and gradient profile. A local accelerating gradient of 81 MV/m near the input end was achieved at a pulse length of 1.2 μs and with a breakdown rate (BDR) of 7.2 x 10(-7) 1 /pulse/m. The reverse configuration was accidental but the operating with this field condition gave very important insights into high-gradient behaviour and a comprehensive analysis has been carried out. A particular attention was paid to the characterization of the distribution of BD positions along the structure and within a cell.
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Woolley, B., Burt, G., Dexter, A. C., Peacock, R., Millar, W. L., Catalan Lasheras, N., et al. (2020). High-gradient behavior of a dipole-mode rf structure. Phys. Rev. Accel. Beams, 23(12), 122002–11pp.
Abstract: A normal-conducting, X-band traveling wave structure operating in the dipole mode has been systematically high-gradient tested to gain insight into the maximum possible gradients in these types of structure. Measured structure conditioning, breakdown behavior, and achieved surface fields are reported as well as a postmortem analysis of the breakdown position and a scanning electron microscope analysis of the high-field surfaces. The results of these measurements are then compared to high-gradient results from monopole-mode cavities. Scaled to a breakdown rate of 10(-6), the cavities were found to operate at a peak electric field of 154 MV/m and a peak modified Poynting vector S-c of 5.48 MW/mm(2). The study provides important input for the further development of dipole-mode cavities for use in the Compact Linear Collider as a crab cavity and dipole-mode cavities for use in x-ray free-electron lasers as well as for studies of the fundamental processes in vacuum arcs. Of particular relevance are the unique field patterns in dipole cavities compared to monopole cavities, where the electric and magnetic fields peak in orthogonal planes, which allow the separation of the role of electric and magnetic fields in breakdown via postmortem damage observation. The azimuthal variation of breakdown crater density is measured and is fitted to sinusoidal functions. The best fit is a power law fit of exponent 6. This is significant, as it shows how breakdown probability varies over a surface area with a varying electric field after conditioning to a given peak field.
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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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Di Molfetta, G., Soares-Pinto, D. O., & Duarte Queiros, S. M. (2018). Elephant quantum walk. Phys. Rev. A, 97(6), 062112–6pp.
Abstract: We introduce an analytically treatable discrete time quantum walk in a one-dimensional lattice which combines non-Markovianity and hyperballistic diffusion associated with a Gaussian whose variance sigma(2)(t) grows cubicly with time sigma alpha t(3). These properties have have been numerically found in several systems, namely, tight-binding lattice models. For its rules, our model can be understood as the quantum version of the classical non-Markovian “elephant random walk” process for which the quantum coin operator only changes the value of the diffusion constant although, contrarily, to the classical coin.
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