Analog Simulation of Weyl Particles with Cold Atoms

  • Daniel Suchet, Mihail Rabinovic, +8 authors Norman Kretschmar
  • Published 2017


In this Letter we report on a novel approach to study the dynamics of harmonically confined Weyl particles using magnetically trapped fermionic atoms. We find that after a kick of its center of mass, the system relaxes towards a steady state even in the absence of interactions, in stark contrast with massive particles which would oscillate without damping. Remarkably, the equilibrium distribution is non-Boltzmann, exhibiting a strong anisotropy which we study both numerically and experimentally. Introduction. – Weyl fermions were introduced for the first time in 1929 as massless solutions of the Dirac equation [1]. Despite constituting one of the paradigms of contemporary high energy physics, their existence in nature has remained unconfirmed until very recently. While at first suggested to describe neutrinos, the observation of flavor oscillations implying a non-zero rest mass ruled out this hypothesis [2]. It had been pointed out that they could be observed in the form of low energy excitations of crystalline structures with a linear dispersion relation around a so-called Weyl point. The non-trivial topology of such Weyl semimetals is responsible for the Adler-Bell-Jackiw chiral anomaly [3, 4] which leads to remarkable properties such as negative magnetoresistance, anomalous Hall effect and non-local transport [5]. Moreover, the confinement of quasiparticles obeying a linear dispersion relation was suggested as a way to engineer individual quantum dots [6], notably for the improvement of multiple exciton generation in solar cells [7]. The mere existence of Weyl points in reciprocal space requires a broken time-reversal or inversion symmetry, which are challenging to implement experimentally. As a consequence, observations of Weyl particles were reported only recently in 3D-compounds such as HgCdTe, HgMnTe [8], TaAs [9, 10] as well as in photonic crystals [11]. Owing to their high degree of control and versatility, cold atoms offer a promising and complementary route for the experimental study of Weyl fermions. Early proposals in this context were based on the band structure of cold atoms in 3D optical lattices extending the 2D Harper Hamiltonian [12]. Yet another approach is analog simulation where one takes advantage of the mathematical equivalence between two seemingly different physical systems. Such mapping were successfully used in the past to relate, for instance, Anderson localization to the δ-kicked rotor [13–15], quantum magnetism to the filling factor of an optical lattice [16, 17], the solutions of Dirac equation to the dynamics of ion chains [18, 19], or quantum Hall edge states to the eigenmodes of classical coupled pendula [20]. In this letter, we report on the analog simulation of Weyl particles in a harmonic potential using a dilute gas of cold magnetically trapped atoms. Using a canonical mapping exchanging position and momentum in the system’s Hamiltonian, we address the dynamics of an ensemble of non-interacting Weyl particles after excitation of their center of mass. The system’s ensuing relaxation towards a steady-state exhibits intriguing dynamics, resulting in a strongly anisotropic and non-thermal momentum distribution of the cold gas. Our observations are interpreted using a kinetic model based on virial theorem and energy conservation. Mapping. – The magnetic quadrupole trap is a common technique for confining neutral atoms [21]. It is made up of a pair of coils carrying anti-parallel currents, cre-

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@inproceedings{Suchet2017AnalogSO, title={Analog Simulation of Weyl Particles with Cold Atoms}, author={Daniel Suchet and Mihail Rabinovic and Thomas Reimann and Norman Kretzschmar and Franz Sievers and Christophe Salomon and Johnathan Lau and Olga Goulko and Carlos Eduardo Lobo and Fr{\'e}d{\'e}ric Chevy and Norman Kretschmar}, year={2017} }