Nonlinear dynamics of two coupled nano-electromechanical resonators

Chotorlishvili, L.; Ugulava, A.; Mchedlishvili, G. I.; Komnik, A.; Wimberger, Sandro; Berakdar, J.

doi:10.1088/0953-4075/44/21/215402

Cited by 18 publications

(11 citation statements)

References 32 publications

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“…Having the purpose of presenting and describing specific results for the multiphoton transitions, our consideration is limited to the Josephson-junction qubits. We note however that similar phenomena can be studied in different quantum objects, which can be described as two-or multi-level systems, such as quantum wires and dots [56][57][58][59][60], nitrogen vacancy centers in diamond [61,62], ultracold atoms [63][64][65], nanomechanical and optomechanical setups [66][67][68], electronic spin systems, two-dimensional electron gas, and graphene [69][70][71].…”

mentioning

confidence: 99%

Multiphoton transitions in Josephson-junction qubits (Review Article)

Shevchenko¹,

Omelyanchouk²,

Il’ichev³

2012

Low Temperature Physics

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Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator's state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices.We present recent results for the driven superconducting qubit -resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau-Zener-Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing. Contents

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confidence: 99%

Multiphoton transitions in Josephson-junction qubits (Review Article)

Shevchenko¹,

Omelyanchouk²,

Il’ichev³

2012

Low Temperature Physics

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“…ω , ϕ → 2ϕ, respectively. A detailed analysis of the Mathieu-Schrödinger equation (19) was done in numerous works, for example the references [43][44][45][46] . The energy spectrum of the Mathieu-Schrödinger equation depends parametrically on the potential barrier E n l and contains two degenerate G − , G + and one non-degenerate domain G 0 (See Fig.…”

Section: Quantum Cantilever Dynamicsmentioning

confidence: 99%

Generation of coherence in an exactly solvable nonlinear nanomechanical system

et al. 2020

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This study is focused on the quantum dynamics of a nitrogen-vacancy (NV) center coupled to a nonlinear, periodically driven mechanical oscillator. For a continuous periodic driving that depends on the position of the oscillator, the mechanical motion is described by Mathieu elliptic functions. This solution is employed to study the dynamics of the quantum spin system including environmental effects and to evaluate the purity and the von Neumann entropy of the NV-spin. The unitary generation of coherence is addressed. We observe that the production of coherence through a unitary transformation depends on whether the system is prepared initially in mixed state. Production of coherence is efficient when the system initially is prepared in the region of the separatrix (i.e., the region where classical systems exhibit dynamical chaos). From the theory of dynamical chaos, we know that phase trajectories of the system passing through the homoclinic tangle have limited memory, and therefore the information about the initial conditions is lost. We proved that quantum chaos and diminishing of information about the mixed initial state favors the generation of quantum coherence through the unitary evolution. We introduced quantum distance from the homoclinic tangle and proved that for the initial states permitting efficient generation of coherence, this distance is minimal.

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“…Our interest here concerns the case when cantilever coupled to the NV center performs nonlinear oscillations. For more details about the model in question, we refer to the earlier works [31,39,40]. In particular, we assume that kicks of the external driving field force the classical motion of the cantilever and the overlapping of nonlinear resonances may induce the chaotic motion of the cantilever.…”

Section: Introductionmentioning

confidence: 99%

Hybrid quantum-classical chaotic NEMS

Singh,

Chotorlishvili,

Toklikishvili

et al. 2020

Preprint

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We present an exactly solvable model of a hybrid quantum-classical system of a Nitrogen-Vacancy (NV) center spin (quantum spin) coupled with a nanocantilever (classical) and analyze the enforcement of the regular or chaotic classical dynamics onto to the quantum spin dynamics. The main problem we focus in this paper is whether the classical dynamical chaos may induce chaotic quantum effects in the spin dynamics. We explore several characteristic criteria of the quantum chaos, such as quantum Poincaré recurrences, generation of coherence and energy level distribution and observe interesting chaotic effects in the spin dynamics. Dynamical chaos imposed in the cantilever dynamics through the kicking pulses induces the stochastic dynamics of the quantum subsystem. However, we show that this type of stochasticity does not possess all the characteristic features of the quantum chaos and is distinct from it. The phenomenon of the hybrid quantum-classical chaos leads to dynamical freezing of the NV spin.

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Nonlinear dynamics of two coupled nano-electromechanical resonators

Cited by 18 publications

References 32 publications

Multiphoton transitions in Josephson-junction qubits (Review Article)

Multiphoton transitions in Josephson-junction qubits (Review Article)

Generation of coherence in an exactly solvable nonlinear nanomechanical system

Hybrid quantum-classical chaotic NEMS

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