Nonadiabatic Dynamics of Two Strongly Coupled Nanomechanical Resonator Modes

Abstract

The Landau-Zener transition is a fundamental concept for dynamical quantum systems and has been studied in numerous fields of physics. Here we present a classical mechanical model system exhibiting analogous behaviour using two inversely tuneable, strongly coupled modes of the same nanomechanical beam resonator. In the adiabatic limit, the anticrossing between the two modes is observed and the coupling strength extracted. Sweeping an initialized mode across the coupling region allows mapping of the progression from diabatic to adiabatic transitions as a function of the sweep rate.PACS numbers: 85.85.+j,62.25.Fg,05.45.Xt The time dynamics of two strongly coupled harmonic oscillators follows the Landau-Zener model [1][2][3][4], which is used to describe the quantum mechanical mode tunneling in a non-adiabatic transition. This phenomenon is observed and utilized in many areas of physics, e. g. atomic resonances [5], quantum dots [6], superconducting qubits [7] and nitrogen-vacancy centers in diamond [8]. It is also possible to create classical model systems exhibiting the same time evolution, which until now have been restricted to optical configurations [9,10]. Such systems are well suited for the study of diabatic behaviour over a wide parameter space; for example nonlinearities could be readily introduced, potentially leading to chaotic behaviour [9,11].Nanomechanical resonators with frequencies in the MHz range can be realized with high mechanical quality factors [12,13] and easily tuned [14] in frequency. This makes them particularly well-suited for exploration of their coupling to other mechanical, optical or electrical microwave resonators. Strong cavity coupling in the optical or microwave regime has been widely studied as it enables both cooling and self-oscillation of the mechanical modes [15][16][17][18]. In addition, the time-resolved Rabi oscillations between a strongly coupled two-level system and a micromechanical resonator have been observed [19].Purely mechanical, static coupling between different resonators [20][21][22][23] and between different harmonic modes of the same resonator [24] has also been demonstrated. Here, we explore the coupling between the two fundamental flexural modes [25] of a single nanomechanical beam vibrating in plane and out of plane, respectively. We study the adiabatic to non-adiabatic transitions between the two strongly coupled classical mechanical modes in time-dependent experiments, in correspondence to the Landau-Zener transition.The nanomechanical high stress silicon nitride string used in this work is shown in Fig. 1. Two parallel gold electrodes vertically offset to the beam are used to dielectrically couple the beam oscillation to an external microwave cavity with a quality factor of ≈ 70 at a resonance frequency of 3.44 GHz [26]. Displacement of the out of plane • also depicts the two adjacent gold electrodes (yellow) used to dielectrically drive, tune and read out the resonator motion. The arrows denote the two mechanical modes, one oscillating parallel and ...

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