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Revista Mexicana de Física

Frequency response of the nonclassicality and its correspondence to the classical dynamics

Shihui Zhang., Yingmin Cui.

Published Jan 1, 2016• 0 citations
Publisher

Abstract

The time evolution of the nonclassicality is found to have strong dependence on the driving frequency in a Duffing-type driven nonlinear system with the Gaussian state as the initial Wigner function. Its frequency response curve has a remarkable peak, near which the nonclassicality of the state is enhanced. Furthermore, good correspondences are found between the frequency response curves of the time-average of the nonclassicality indicator and those of the classical mean square amplitude. Such correspondences can also be observed, when using a superposition of two coherent states as the initial Wigner function.

DOI
10.31349/revmexfis.62.6.549

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The time evolution of the nonclassicality is found to have strong dependence on the driving frequency in a Duffing-type driven nonlinear system with the Gaussian state as the initial Wigner function. Its frequency response curve has a remarkable peak, near which the nonclassicality of the state is enhanced. Furthermore, good correspondences are found between the frequency response curves of the time-average of the nonclassicality indicator and those of the classical mean square amplitude. Such correspondences can also be observed, when using a superposition of two coherent states as the initial Wigner function.
The decay of the Loschmidt echo and its relation to the frequency response of the underlying classical dynamics are investigated in an open Duffing system by means of the Wigner function. The initial Wigner function of the system is Gaussian and centered at a phase point ( x 0 , p 0 ). For different ( x 0 , p 0 ), significant peaks are observed in the frequency response curves of the Loschmidt echo decay during the evolution of the Wigner function. Furthermore, there is good correspondence between the frequency response curves of the Loschmidt echo decay and the underlying classical dynamics. This can be attributed to the increase of the fringes of the Wigner function by the external driving force, which can be revealed by the frequency response of the underlying classical dynamics.
The influence of the frequency modulation on the nonclassicality is explored in a system of nanomechanical resonator, which is a promising device in the fields of quantum information engineering. It is shown that the nonclassicality of the quantum state is dependent on the value of the modulation rate during the quantum evolution. A pronounced peak is observed in the curve of the nonclassicality versus the modulation rate. It indicates that the system's nonclassicality can be enhanced by the modulation rate. The enhancement of the nonclassicality by the modulation rate is induced by the effects of the external driving source on the quantum interference between different energy levels. This is supported by the correspondences between the dependence curves of the nonclassicality indicator and the uncertainty of the Wigner distribution function on the modulation rate.
We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems.
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We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems.