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Article Dans Une Revue The European Physical Journal. Special Topics Année : 2017

Quantum revival for elastic waves in thin plate

Résumé

Quantum revival is described as the time-periodic reconstruction of a wave packet initially localized in space and time. This effect is expected in finite-size systems which exhibit commensurable discrete spectrum such as the infinite quantum well. Here, we report on the experimental observation of full and fractional quantum revival for classical waves in a two dimensional cavity. We consider flexural waves propagating in thin plates, as their quadratic dispersion at low frequencies mimics the dispersion relation of quantum systems governed by Schrödinger equation. Time-dependent excitation and measurement are performed at ultrasonic frequencies and reveal a periodic reconstruction of the initial elastic wave packet. In an infinite quantum well or a closed wave cavity, an eigenstate is a stationary oscillating field pattern, which self-reproduces at its eigenfrequency. A set of eigen-states can be adjusted in amplitude and phase to interfere constructively in a small region of space and synthesize a wave packet. Because it is composed of several eigen-states, the wave packet is not a stationary wavefunction that remains confined in space but will spread over the entire system. The time needed by this wave packet to get to the "maximum spreading" is often called the Ehrenfest time. Once this time is reached, a question is raised: can the spreading reverse and the wavefunction fold back to reconstruct the initial wave packet, in the manner of a time reversal operation [1]. The answer is positive for dispersive systems, namely for systems with not uniformly distributed discrete energy levels. This fundamental condition for observation of the quantum revival effect is naturally fulfilled in quantum systems following Schrödinger equation. For this reason, the ability of quantum systems to fold back to their initial state triggered a lot of interest in the quantum physics community. The quantum revival effect was first predicted in the Jaynes-Cummings model [2-4], in Rydberg wave packets [5, 6] and in chaotic quantum systems [7]. Its first experimental observation was achieved in low dimensional systems, such as Rydberg atoms [8-10], electrons in graphene under magnetic field [11], molecular systems [12] Supplementary material in the form of two wmv files available from the Journal web page at: https://doi.
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Dates et versions

hal-02145713 , version 1 (03-06-2019)

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Marc Dubois, Gautier Lefebvre, Patrick Sebbah. Quantum revival for elastic waves in thin plate. The European Physical Journal. Special Topics, 2017, 226 (7), pp.1593-1601. ⟨10.1140/epjst/e2016-60364-7⟩. ⟨hal-02145713⟩
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