arXiv subjects

F. Fillion-Gourdeau

Publications and source records attributed to F. Fillion-Gourdeau.

At least 19 recordsLinked to original sources

arXiv2025

Stringent requirements for detecting light-induced gravitational effects using interferometry

Intense laser fields have been proposed as a means to generate light-induced gravitational effects, providing a novel approach to investigate gravity and its coupling to electromagnetism in a controlled laboratory setting. In this article, a detection scheme based on interferometry is introduced to assess the feasibility of observing such effects. Initially, the space-time deformation and the resulting induced phase difference are evaluated in homogeneous electric fields. Using the theoretical minimum phase sensitivity bound -- a known result in quantum information -- and accounting for background signal coming from photon-photon scattering -- a fundamental quantum electrodynamics effect related to vacuum properties -- a set of stringent requirements for detectability is obtained. Then, a more realistic scenario is considered where gravitational effects are generated by an e-dipole pulse. In all cases considered, it is demonstrated that observing these effects presents significant challenges, even with the capabilities of current and foreseen laser infrastructures.

gr-qc↗

arXiv2023

Scattered field formalism in the particle-in-cell method for plasma acceleration in tightly focused ultrashort laser beams

The scattered field formalism is combined to the particle-in-cell method to model relativistic laser-plasma dynamics in complex field configurations. Despite the strong nonlinearity of the interactions, we demonstrate the validity of this technique theoretically, by using the semi-linear property of Maxwell-Vlasov equations, and empirically, by performing a systematic convergence analysis with simple 1D and 2D examples. Then, we apply this method to the description of electron acceleration in undercritical plasmas from tightly focused linear and radially polarized beams. For this purpose, an analytical solution for a linearly-polarized tightly focused beam is derived. According to our simulations and their analysis, this approach looks very promising for the optimization of laser-induced relativistic electron beams at ultrahigh intensities because it allows for tightly-focused geometries in reduced calculation volumes.

physics.optics↗

arXiv2022

High Dose-Rate Ionizing Radiation Source from Tight Focusing in Air of a mJ-class Femtosecond Laser

Ultrashort electron beams with femtosecond to picosecond bunch durations offer unique opportunities to explore active research areas ranging from ultrafast structural dynamics to ultra-high dose-rate radiobiological studies. We present a straightforward method to generate MeV-ranged electron beams in ambient air through the tight focusing of a few-cycle, mJ-class femtosecond IR laser. At one meter from the source, the highest measured dose rate of 0.15 Gy/s exceeds the yearly dose limit in less than one second and warrants the implementation of radiation protection. Two-dimensional Particle-In-Cell simulations confirm that the acceleration mechanism is based on the relativistic ponderomotive force and show theoretical agreement with the measured electron energy. Furthermore, we discuss the scalability of this method with the continuing development of mJ-class high average power lasers, moreover providing a promising approach for FLASH radiation therapy.

physics.optics↗

arXiv2021

Inverse design of strained graphene surfaces for electron control

This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime. Assuming that charge carriers are described by the Dirac equation in curved-space and exploiting the fact that wave propagation can be described by ray-optics in this regime, a general computational strategy is proposed in order to find strain fields associated with a desired effective refractive index profile. The latter is first determined by solving semi-classical trajectories and by optimizing a chosen objective functional using a genetic algorithm. Then, the graded refractive index corresponding to the strain field is obtained by using its connection to the metric component in isothermal coordinates. These coordinates are evaluated via numerical quasiconformal transformations by solving the Beltrami equation with a finite volume method. The graphene surface deformation is finally optimized, also using a genetic algorithm, to reproduce the desired index of refraction. Some analytical results and numerical experiments are performed to illustrate the methodology.

cond-mat.mes-hall↗

arXiv2021

Two-dimensional Dirac matter in the semiclassical regime

The semiclassical regime of 2D static Dirac matter is obtained from the Dirac equation in curved space-time. To simplify the formulation, the Cartesian space-time geometry parametrization is transformed to isothermal coordinates using quasi-conformal transformations. Using this framework, it is demonstrated that to first order, the semiclassical approximation yields the relativistic Lorentz force equation with additional fictitious forces related to the space curvature and to the mass gradient. An effective graded index of refraction is defined and is directly linked to the metric component in isothermal coordinates. Semiclassical trajectories are evaluated in a simple example by solving the equation of motion and the Beltrami equation numerically.

cond-mat.mes-hall↗

arXiv2020

Explicit volume-preserving numerical schemes for relativistic trajectories and spin dynamics

A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-BMT equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties: they are energy-conserving, volume-conserving and second order convergent. These properties are analysed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. It is demonstrated that the numerical error in a constant magnetic field remains bounded for long time simulations in contrast to the Boris pusher, whose angular error increases linearly with time. Finally, the intricate spin dynamics of a particle is investigated in a plane wave field configuration.

physics.comp-ph↗

arXiv2020

Numerical quasi-conformal transformations for electron dynamics on strained graphene surfaces

The dynamics of low energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a parametrization of the surface can be straightforwardly obtained, but the resulting Dirac equation is intricate for general surface deformations. Two different strategies are introduced to simplify this problem: the diagonal metric approximation and the change of variables to isothermal coordinates. These coordinates are obtained from quasi-conformal transformations characterized by the Beltrami equation, whose solution gives the mapping between both coordinate systems. To implement this second strategy, a least square finite-element numerical scheme is introduced to solve the Beltrami equation. The Dirac equation is then solved via an accurate pseudo-spectral numerical method in the pseudo-Hermitian representation that is endowed with explicit unitary evolution and conservation of the norm. The two approaches are compared and applied to the scattering of electrons on Gaussian shaped graphene surface deformations. It is demonstrated that electron wave packets can be focused by these local strained regions.

physics.comp-ph↗

arXiv2020

Plunging in the Dirac sea using graphene quantum dots

The dynamics of low energy charge carriers in a graphene quantum dot subjected to a time-dependent local field is investigated numerically. In particular, we study a configuration where a Coulomb electric field is provided by an ion traversing the graphene sample. A Galerkin-like numerical scheme is introduced to solve the massless Dirac equation describing charge carriers subjected to space- and time-dependent electromagnetic potentials and is used to evaluate the field induced interband transitions. It is demonstrated that as the ion goes through graphene, electron-hole pairs are generated dynamically via the adiabatic pair creation mechanism around avoided crossings, similar to electron-positron pair generation in low energy heavy ion collisions.

cond-mat.mes-hall↗

arXiv2018

Simple digital quantum algorithm for symmetric first order linear hyperbolic systems

This paper is devoted to the derivation of a digital quantum algorithm for the Cauchy problem for symmetric first order linear hyperbolic systems, thanks to the reservoir technique. The reservoir technique is a method designed to avoid artificial diffusion generated by first order finite volume methods approximating hyperbolic systems of conservation laws. For some class of hyperbolic systems, namely those with constant matrices in several dimensions, we show that the combination of i) the reservoir method and ii) the alternate direction iteration operator splitting approximation, allows for the derivation of algorithms only based on simple unitary transformations, thus perfectly suitable for an implementation on a quantum computer. The same approach can also be adapted to scalar one-dimensional systems with non-constant velocity by combining with a non-uniform mesh. The asymptotic computational complexity for the time evolution is determined and it is demonstrated that the quantum algorithm is more efficient than the classical version. However, in the quantum case, the solution is encoded in probability amplitudes of the quantum register. As a consequence, as with other similar quantum algorithms, a post-processing mechanism has to be used to obtain general properties of the solution because a direct reading cannot be performed as efficiently as the time evolution.

quant-ph↗

arXiv2018

Carrier-envelope phase effects in graphene

We numerically study the interaction of a terahertz pulse with monolayer graphene. We observe that the electron momentum density is affected by the carrier-envelope phase (CEP) of the single- to few-cycle terahertz laser pulse that induces the electron dynamics. In particular, we see strong asymmetric electron momentum distributions for non-zero values of the CEP. We explain the origin of the asymmetry within the adiabatic-impulse model by finding conditions to reach minimal adiabatic gap between the valence band and the conduction band. We discuss how these conditions and the interference pattern, emanating from successive non-adiabatic transitions at this minimal gap, affect the electron momentum density and how they are modified by the CEP. This opens the door to control fundamental time-dependent electron dynamics in the tunneling regime in Dirac materials. Also, this control suggests a way to measure the CEP of a terahertz laser pulse when it interacts with condensed matter systems.

cond-mat.mes-hall↗

arXiv2017

Algorithm for the solution of the Dirac equation on digital quantum computers

A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the Dirac operator to a quantum walk supplemented by unitary rotation steps in spinor space. Every step of the splitting method is decomposed into sets of quantum gates. It is demonstrated that the algorithm has an exponential speedup over the implementation of the same numerical scheme on a classical computer, as long as certain conditions are satisfied. Finally, an explicit decomposition of this algorithm into elementary gates from a universal set is carried out to determine the resource requirements. It is shown that a proof-of-principle calculation may be possible with actual quantum technologies.

quant-ph↗

arXiv2017

Efficient state initialization by a quantum spectral filtering algorithm

An algorithm that initializes a quantum register to a state with a specified energy range is given, corresponding to a quantum implementation of the celebrated Feit-Fleck method. This is performed by introducing a nondeterministic quantum implementation of a standard spectral filtering procedure combined with an apodization technique, allowing for accurate state initialization. It is shown that the implementation requires only two ancilla qubits. A lower bound for the total probability of success of this algorithm is derived, showing that this scheme can be realized using a finite, relatively low number of trials. Assuming the time evolution can be performed efficiently and using a trial state polynomially close to the desired states, it is demonstrated that the number of operations required scales polynomially with the number of qubits. Tradeoffs between accuracy and performance are demonstrated in a simple example: the harmonic oscillator. This algorithm would be useful for the initialization phase of the simulation of quantum systems on digital quantum computers.

quant-ph↗

arXiv2016

Numerical computation of dynamical Schwinger-like pair production in graphene

The density of electron-hole pairs produced in a graphene sample immersed in a homogeneous time-dependent electrical field is evaluated. Because low energy charge carriers in graphene are described by relativistic quantum mechanics, the calculation is performed within the strong field quantum electrodynamics formalism, requiring a solution of the Dirac equation in momentum space. The latter is solved using a split-operator numerical scheme on parallel computers, allowing for the investigation of several field configurations. The strength of the method is illustrated by computing the electron momentum density generated from a realistic laser pulse model. We observe quantum interference patterns reminiscent of Landau-Zener-Stückelberg interferometry.

cond-mat.mes-hall↗

arXiv2016

Time-domain quantum interference in graphene

The electron momentum density obtained from the Schwinger-like mechanism is evaluated for a graphene sample immersed in a homogeneous time-dependent electric field. Based on the analogy between graphene low-energy electrons and quantum electrodynamics (QED), numerical techniques borrowed from strong field QED are employed and compared to approximate analytical approaches. It is demonstrated that for some range of experimentally accessible parameters, the pair production proceeds by sequences of adiabatic evolutions followed by non-adiabatic Landau-Zener transitions, reminiscent of the Kibble-Zurek mechanism describing topological defect density in second order phase transitions. For some field configurations, this yields interference patterns in momentum space which are explained in terms of the adiabatic-impulse model and the Landau-Zener-Stückelberg interferometry.

cond-mat.mes-hall↗

arXiv2015

Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.

physics.comp-ph↗

arXiv2015

Scheme for the detection of mixing processes in vacuum

A scheme for the detection of photons generated by vacuum mixing processes is proposed. The strategy consists in the utilization of a high numerical aperture parabolic mirror which tightly focuses two co-propagating laser beams with different frequencies. This produces a very high intensity region in the vicinity of the focus, where the photon-photon nonlinear interaction can then induce new electromagnetic radiation by wave mixing processes. These processes are investigated theoretically. The field at the focus is obtained from the Stratton-Chu vector diffraction theory, which can accomodate any configuration of an incoming laser beam. The number of photons generated is evaluated for an incident radially polarized beam. It is demonstrated that using this field configuration, vacuum mixing processes could be detected with envisaged laser technologies.

hep-ph↗

arXiv2013

Formal analogy between the Dirac equation in its Majorana form and the discrete-velocity version of the Boltzmann kinetic equation

We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and non-relativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wavefunction) propagates in space-time as a classical statistical process (Boltzmann distribution).

quant-ph↗

arXiv2012

Numerical solution of the time-independent Dirac equation for diatomic molecules: B-splines without spurious states

Two numerical methods are used to evaluate the relativistic spectrum of the two-centre Coulomb problem (for the $H_{2}^{+}$ and $Th_{2}^{179+}$ diatomic molecules) in the fixed nuclei approximation by solving the single particle time-independent Dirac equation. The first one is based on a min-max principle and uses a two-spinor formulation as a starting point. The second one is the Rayleigh-Ritz variational method combined with kinematically balanced basis functions. Both methods use a B-spline basis function expansion. We show that accurate results can be obtained with both methods and that no spurious states appear in the discretization process.

physics.chem-ph↗