Classical realization of a strongly driven two-level system

Spreeuw, R. J. C.; Druten, N. J. van; Beijersbergen, Marco W.; Eliel, E. R.; Woerdman, J. P.

doi:10.1103/physrevlett.65.2642

Cited by 94 publications

(72 citation statements)

References 14 publications

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“…Interesting dynamic features including classical Rabi oscillation, magnetically induced transparency, and Purcell effect are demonstrated in this highly versatile platform, highlighting its great potential for coherent information processing. Introduction.-Systems with strong light-matter interaction have played crucial roles in quantum [1,2] and classical information processing [3,4] as they enable coherent information transfer between distinct physical platforms. It is well known that systems with large electric dipole moment can couple strongly with the optical fields.…”

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confidence: 99%

Strongly Coupled Magnons and Cavity Microwave Photons

et al. 2014

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We realize a cavity magnon-microwave photon system in which magnetic dipole interaction mediates strong coupling between collective motion of large number of spins in a ferrimagnet and the microwave field in a three-dimensional cavity. By scaling down the cavity size and increasing number of spins, an ultrastrong coupling regime is achieved with a cooperativity reaching 12600. Interesting dynamic features including classical Rabi oscillation, magnetically induced transparency, and Purcell effect are demonstrated in this highly versatile platform, highlighting its great potential for coherent information processing. Introduction.-Systems with strong light-matter interaction have played crucial roles in quantum [1,2] and classical information processing [3,4] as they enable coherent information transfer between distinct physical platforms. It is well known that systems with large electric dipole moment can couple strongly with the optical fields. However, the possibility of strong light-matter interaction via magnetic dipoles is mostly ignored. It is only recently that Imamoglu [5] has pointed out the direction to achieve strong light-matter interaction using collective excitations of spin ensembles, and visioned the promise of quantum information processing in these systems. Since then, various implementations have been proposed and experimentally investigated. Ensembles including ultracold atomic clouds [6], molecules [7], nitrogen vacancy centers in diamond [8][9][10][11][12][13], and ion doped crystals [14][15][16] have been used to couple to microwave resonators or even superconducting qubits.

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confidence: 99%

Strongly Coupled Magnons and Cavity Microwave Photons

et al. 2014

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“…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].…”

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confidence: 99%

“…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.…”

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Nonadiabatic Dynamics of Two Strongly Coupled Nanomechanical Resonator Modes

et al. 2012

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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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“…Within t cav we must perform our experiments, i.e., drive the EOMs with the proper time-dependent voltages (up to 400 V) and analyse the small fraction of the light intensity that leaks through one of the cavity mirrors. In order to make such experiments electronically feasible t cav must be at least a few m s; for our cavity length this corresponds to a cavity ® nesse & of the order of 10 3 . To obtain such a high cavity ® nesse the optical losses inside the cavity must be compensated for.…”

Section: Optical Realizationmentioning

confidence: 99%

Observation of the geometric amplitude factor in an optical system

Bouwmeester¹,

Karman²,

Dekker³

et al. 1996

Journal of Modern Optics

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A bstract.By manipulating the discrete optical levels inside an optical resonator, we obtain a classical realization of a twisted Landau ± Zener model.We experimentally demonstrate the geometric amplitude factor in the transition amplitude that arises for this model. We consider in particular the region of parameter space addressed in the original study of the geometric amplitude factor by M. V. Berry [7].

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Classical realization of a strongly driven two-level system

Cited by 94 publications

References 14 publications

Strongly Coupled Magnons and Cavity Microwave Photons

Strongly Coupled Magnons and Cavity Microwave Photons

Nonadiabatic Dynamics of Two Strongly Coupled Nanomechanical Resonator Modes

Observation of the geometric amplitude factor in an optical system

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